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<span class="vector-toc-numb">3</span> <span>Properties</span> </div> </a> <button aria-controls="toc-Properties-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Properties subsection</span> </button> <ul id="toc-Properties-sublist" class="vector-toc-list"> <li id="toc-Strength" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Strength"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Strength</span> </div> </a> <ul id="toc-Strength-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Security" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Security"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Security</span> </div> </a> <ul id="toc-Security-sublist" class="vector-toc-list"> <li id="toc-Slipping" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Slipping"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>Slipping</span> </div> </a> <ul id="toc-Slipping-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Capsizing" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Capsizing"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.2</span> <span>Capsizing</span> </div> </a> <ul id="toc-Capsizing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sliding" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Sliding"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.3</span> <span>Sliding</span> </div> </a> <ul id="toc-Sliding-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Releasability" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Releasability"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Releasability</span> </div> </a> <ul id="toc-Releasability-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Components" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Components"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Components</span> </div> </a> <button aria-controls="toc-Components-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Components subsection</span> </button> <ul id="toc-Components-sublist" class="vector-toc-list"> <li id="toc-Bight" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bight"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Bight</span> </div> </a> <ul id="toc-Bight-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bitter_end" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bitter_end"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Bitter end</span> </div> </a> <ul id="toc-Bitter_end-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Loop" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Loop"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Loop</span> </div> </a> <ul id="toc-Loop-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Elbow" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elbow"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Elbow</span> </div> </a> <ul id="toc-Elbow-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Standing_end" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Standing_end"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Standing end</span> </div> </a> <ul id="toc-Standing_end-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Standing_part" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Standing_part"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Standing part</span> </div> </a> <ul id="toc-Standing_part-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Turn" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Turn"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Turn</span> </div> </a> <ul id="toc-Turn-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Working_end" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Working_end"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Working end</span> </div> </a> <ul id="toc-Working_end-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Working_part" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Working_part"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.9</span> <span>Working part</span> </div> </a> <ul id="toc-Working_part-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Knot_categories" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Knot_categories"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Knot categories</span> </div> </a> <button aria-controls="toc-Knot_categories-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Knot categories subsection</span> </button> <ul id="toc-Knot_categories-sublist" class="vector-toc-list"> <li id="toc-Basic_useful_knots" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Basic_useful_knots"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Basic useful knots</span> </div> </a> <ul id="toc-Basic_useful_knots-sublist" class="vector-toc-list"> <li id="toc-Hitches" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Hitches"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.1</span> <span>Hitches</span> </div> </a> <ul id="toc-Hitches-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Trick_knots" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Trick_knots"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Trick knots</span> </div> </a> <ul id="toc-Trick_knots-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Coxcombing" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Coxcombing"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Coxcombing</span> </div> </a> <ul id="toc-Coxcombing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Knot_theory" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Knot_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Knot theory</span> </div> </a> <ul id="toc-Knot_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physical_theory_of_friction_knots" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Physical_theory_of_friction_knots"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Physical theory of friction knots</span> </div> </a> <ul id="toc-Physical_theory_of_friction_knots-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Knot_tying" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Knot_tying"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Knot tying</span> </div> </a> <button aria-controls="toc-Knot_tying-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Knot tying subsection</span> </button> <ul id="toc-Knot_tying-sublist" class="vector-toc-list"> <li id="toc-Difficulty" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Difficulty"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.1</span> <span>Difficulty</span> </div> </a> <ul id="toc-Difficulty-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Material" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Material"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.2</span> <span>Material</span> </div> </a> <ul id="toc-Material-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tools" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tools"> <div class="vector-toc-text"> <span class="vector-toc-numb">9.3</span> <span>Tools</span> </div> </a> <ul id="toc-Tools-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Use_by_animals" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Use_by_animals"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Use by animals</span> </div> </a> <ul id="toc-Use_by_animals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">12.1</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-General_sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#General_sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">12.2</span> <span>General sources</span> </div> </a> <ul id="toc-General_sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Knot</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 63 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-63" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">63 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Knoop_(tou)" title="Knoop (tou) – Afrikaans" lang="af" hreflang="af" data-title="Knoop (tou)" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D9%82%D8%AF%D8%A9" title="عقدة – Arabic" lang="ar" hreflang="ar" data-title="عقدة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Nyudo_(lazo)" title="Nyudo (lazo) – Aragonese" lang="an" hreflang="an" data-title="Nyudo (lazo)" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Apokyt%C3%A3" title="Apokytã – Guarani" lang="gn" hreflang="gn" data-title="Apokytã" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Chinu" title="Chinu – Aymara" lang="ay" hreflang="ay" data-title="Chinu" data-language-autonym="Aymar aru" data-language-local-name="Aymara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/D%C3%BCy%C3%BCn" title="Düyün – Azerbaijani" lang="az" hreflang="az" data-title="Düyün" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A6%BF%E0%A6%81%E0%A6%9F" title="গিঁট – Bangla" lang="bn" hreflang="bn" data-title="গিঁট" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%92%D1%8A%D0%B7%D0%B5%D0%BB" title="Възел – Bulgarian" lang="bg" hreflang="bg" data-title="Възел" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/%C4%8Cvor" title="Čvor – Bosnian" lang="bs" hreflang="bs" data-title="Čvor" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nus_(lla%C3%A7)" title="Nus (llaç) – Catalan" lang="ca" hreflang="ca" data-title="Nus (llaç)" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%C4%95%D0%B2%C4%95" title="Тĕвĕ – Chuvash" lang="cv" hreflang="cv" data-title="Тĕвĕ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Uzel" title="Uzel – Czech" lang="cs" hreflang="cs" data-title="Uzel" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Knob" title="Knob – Danish" lang="da" hreflang="da" data-title="Knob" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Knoten_(Kn%C3%BCpfen)" title="Knoten (Knüpfen) – German" lang="de" hreflang="de" data-title="Knoten (Knüpfen)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/S%C3%B5lm" title="Sõlm – Estonian" lang="et" hreflang="et" data-title="Sõlm" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CF%8C%CE%BC%CF%80%CE%BF%CF%82" title="Κόμπος – Greek" lang="el" hreflang="el" data-title="Κόμπος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Nudo_(lazo)" title="Nudo (lazo) – Spanish" lang="es" hreflang="es" data-title="Nudo (lazo)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Nodo_(kunigo)" title="Nodo (kunigo) – Esperanto" lang="eo" hreflang="eo" data-title="Nodo (kunigo)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Korapilo" title="Korapilo – Basque" lang="eu" hreflang="eu" data-title="Korapilo" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%AF%D8%B1%D9%87" title="گره – Persian" lang="fa" hreflang="fa" data-title="گره" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/N%C5%93ud_(lien)" title="Nœud (lien) – French" lang="fr" hreflang="fr" data-title="Nœud (lien)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/N%C3%B3" title="Nó – Galician" lang="gl" hreflang="gl" data-title="Nó" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A7%A4%EB%93%AD" title="매듭 – Korean" lang="ko" hreflang="ko" data-title="매듭" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A4%BE%E0%A4%82%E0%A4%A0" title="गांठ – Hindi" lang="hi" hreflang="hi" data-title="गांठ" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Nodo" title="Nodo – Ido" lang="io" hreflang="io" data-title="Nodo" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Simpul" title="Simpul – Indonesian" lang="id" hreflang="id" data-title="Simpul" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hn%C3%BAtur" title="Hnútur – Icelandic" lang="is" hreflang="is" data-title="Hnútur" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Nodo" title="Nodo – Italian" lang="it" hreflang="it" data-title="Nodo" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A9%D7%A8_(%D7%97%D7%91%D7%9C)" title="קשר (חבל) – Hebrew" lang="he" hreflang="he" data-title="קשר (חבל)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%97%E0%B2%82%E0%B2%9F%E0%B3%81" title="ಗಂಟು – Kannada" lang="kn" hreflang="kn" data-title="ಗಂಟು" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Fundo" title="Fundo – Swahili" lang="sw" hreflang="sw" data-title="Fundo" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Ne" title="Ne – Haitian Creole" lang="ht" hreflang="ht" data-title="Ne" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Nodus" title="Nodus – Latin" lang="la" hreflang="la" data-title="Nodus" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Mazgas" title="Mazgas – Lithuanian" lang="lt" hreflang="lt" data-title="Mazgas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Groppo" title="Groppo – Ligurian" lang="lij" hreflang="lij" data-title="Groppo" data-language-autonym="Ligure" data-language-local-name="Ligurian" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Gropp" title="Gropp – Lombard" lang="lmo" hreflang="lmo" data-title="Gropp" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Csom%C3%B3_(k%C3%B6t%C3%A9len)" title="Csomó (kötélen) – Hungarian" lang="hu" hreflang="hu" data-title="Csomó (kötélen)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Knoop_(touw)" title="Knoop (touw) – Dutch" lang="nl" hreflang="nl" data-title="Knoop (touw)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B5%90%E3%81%B3%E7%9B%AE" title="結び目 – Japanese" lang="ja" hreflang="ja" data-title="結び目" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Knop_(knute)" title="Knop (knute) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Knop (knute)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Knute" title="Knute – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Knute" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Nos_(ligam)" title="Nos (ligam) – Occitan" lang="oc" hreflang="oc" data-title="Nos (ligam)" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Knutt" title="Knutt – Low German" lang="nds" hreflang="nds" data-title="Knutt" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/W%C4%99ze%C5%82" title="Węzeł – Polish" lang="pl" hreflang="pl" data-title="Węzeł" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%B3" title="Nó – Portuguese" lang="pt" hreflang="pt" data-title="Nó" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Nod_(marin%C4%83rie)" title="Nod (marinărie) – Romanian" lang="ro" hreflang="ro" data-title="Nod (marinărie)" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Khipu" title="Khipu – Quechua" lang="qu" hreflang="qu" data-title="Khipu" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A3%D0%B7%D0%B5%D0%BB" title="Узел – Russian" lang="ru" hreflang="ru" data-title="Узел" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Gruppu_(nudu_ntricatu)" title="Gruppu (nudu ntricatu) – Sicilian" lang="scn" hreflang="scn" data-title="Gruppu (nudu ntricatu)" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Knot" title="Knot – Simple English" lang="en-simple" hreflang="en-simple" data-title="Knot" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Vozli_in_vezave" title="Vozli in vezave – Slovenian" lang="sl" hreflang="sl" data-title="Vozli in vezave" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A7%D0%B2%D0%BE%D1%80" title="Чвор – Serbian" lang="sr" hreflang="sr" data-title="Чвор" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Solmu" title="Solmu – Finnish" lang="fi" hreflang="fi" data-title="Solmu" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Knop" title="Knop – Swedish" lang="sv" hreflang="sv" data-title="Knop" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%81%E0%AE%9F%E0%AE%BF%E0%AE%9A%E0%AF%8D%E0%AE%9A%E0%AF%81" title="முடிச்சு – Tamil" lang="ta" hreflang="ta" data-title="முடிச்சு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%87%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%99" title="เงื่อน – Thai" lang="th" hreflang="th" data-title="เงื่อน" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/D%C3%BC%C4%9F%C3%BCm" title="Düğüm – Turkish" lang="tr" hreflang="tr" data-title="Düğüm" 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Method of fastening or securing linear material</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For speeds, see <a href="/wiki/Knot_(unit)" title="Knot (unit)">Knot (unit)</a>. For the mathematical object, see <a href="/wiki/Knot_(mathematics)" title="Knot (mathematics)">Knot (mathematics)</a>. For other uses, see <a href="/wiki/Knot_(disambiguation)" class="mw-disambig" title="Knot (disambiguation)">Knot (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Nf_knots.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/6e/Nf_knots.png" decoding="async" width="339" height="333" class="mw-file-element" data-file-width="339" data-file-height="333" /></a><figcaption><span title="Swedish-language text"><i lang="sv"><a href="/wiki/Nordisk_familjebok" title="Nordisk familjebok">Nordisk familjebok</a></i></span> knots: <div><ol><li>Yarn knot (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #2688)</li><li><a href="/wiki/Manrope_knot" class="mw-redirect" title="Manrope knot">Manrope knot</a> (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #847)</li><li><a href="/wiki/Granny_knot" title="Granny knot">Granny knot</a> (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #1206)</li><li><a href="/wiki/Wall_and_crown_knot" title="Wall and crown knot">Wall and crown knot</a> (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #670, #671)</li><li><a href="/wiki/Matthew_Walker_knot" title="Matthew Walker knot">Matthew Walker's knot</a> (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #681)</li><li><a href="/wiki/Shroud_knot" title="Shroud knot">Shroud knot</a> (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #1580)</li><li><a href="/wiki/Turk%27s_head_knot" title="Turk's head knot">Turk's head knot</a> (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #1278-#1397)</li><li><a href="/wiki/Overhand_knot" title="Overhand knot">Overhand knot</a>, <a href="/wiki/Figure-eight_knot" title="Figure-eight knot">Figure-of-eight knot</a> (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #514, #520)</li><li><a href="/wiki/Reef_knot" title="Reef knot">Reef knot</a>, <a href="/wiki/Reef_knot" title="Reef knot">Square knot</a> (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #1402)</li><li><a href="/wiki/Two_half-hitches" title="Two half-hitches">Two half-hitches</a> (<a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">ABoK</a> #54)</li></ol></div></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Knopar_-_2017.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Knopar_-_2017.jpg/220px-Knopar_-_2017.jpg" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Knopar_-_2017.jpg/330px-Knopar_-_2017.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/Knopar_-_2017.jpg/440px-Knopar_-_2017.jpg 2x" data-file-width="1500" data-file-height="939" /></a><figcaption><a href="/w/index.php?title=Knot_board&action=edit&redlink=1" class="new" title="Knot board (page does not exist)">Knot board</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://es.wikipedia.org/wiki/Cuadro_de_nudos" class="extiw" title="es:Cuadro de nudos">es</a>]</span> on <a href="https://de.wikipedia.org/wiki/Elbe_1_(Schiff,_1965)" class="extiw" title="de:Elbe 1 (Schiff, 1965)">Elbe 1 (ship, 1965)</a></figcaption></figure> <p>A <b>knot</b> is an intentional complication in <a href="/wiki/Rope" title="Rope">cordage</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> which may be practical or decorative, or both. Practical knots are classified by function, including <a href="/wiki/List_of_hitch_knots" class="mw-redirect" title="List of hitch knots">hitches</a>, <a href="/wiki/List_of_bend_knots" class="mw-redirect" title="List of bend knots">bends</a>, <a href="/wiki/List_of_loop_knots" class="mw-redirect" title="List of loop knots">loop knots</a>, and <a href="/wiki/Rope_splicing" title="Rope splicing">splices</a>: a <i>hitch</i> fastens a rope to another object; a <i>bend</i> fastens two ends of a rope to each another; a <i>loop knot</i> is any knot creating a loop; and <i>splice</i> denotes any multi-strand knot, including bends and loops.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> A knot may also refer, in the strictest sense, to a stopper or knob at the end of a rope to keep that end from slipping through a grommet or eye.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Knots have excited interest since ancient times for their practical uses, as well as their <a href="/wiki/Topology" title="Topology">topological</a> intricacy, studied in the area of mathematics known as <a href="/wiki/Knot_theory" title="Knot theory">knot theory</a>. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Inca_Quipu.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Inca_Quipu.jpg/220px-Inca_Quipu.jpg" decoding="async" width="220" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Inca_Quipu.jpg/330px-Inca_Quipu.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Inca_Quipu.jpg/440px-Inca_Quipu.jpg 2x" data-file-width="625" data-file-height="380" /></a><figcaption>An example of a <a href="/wiki/Quipu" title="Quipu">quipu</a> from the Inca Empire, currently in the <a href="/wiki/Larco_Museum" title="Larco Museum">Larco Museum Collection</a>.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Alexander_cuts_the_Gordian_Knot.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Alexander_cuts_the_Gordian_Knot.jpg/220px-Alexander_cuts_the_Gordian_Knot.jpg" decoding="async" width="220" height="172" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Alexander_cuts_the_Gordian_Knot.jpg/330px-Alexander_cuts_the_Gordian_Knot.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bb/Alexander_cuts_the_Gordian_Knot.jpg/440px-Alexander_cuts_the_Gordian_Knot.jpg 2x" data-file-width="2048" data-file-height="1601" /></a><figcaption><i><a href="/wiki/Alexander_the_Great" title="Alexander the Great">Alexander</a> cuts the <a href="/wiki/Gordian_Knot" title="Gordian Knot">Gordian Knot</a></i>, by <a href="/wiki/Jean-Simon_Berth%C3%A9lemy" title="Jean-Simon Berthélemy">Jean-Simon Berthélemy</a> (1743–1812)</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Gordischer_Knoten_Frechen_Kirilowitsch.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Gordischer_Knoten_Frechen_Kirilowitsch.jpg/110px-Gordischer_Knoten_Frechen_Kirilowitsch.jpg" decoding="async" width="110" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Gordischer_Knoten_Frechen_Kirilowitsch.jpg/165px-Gordischer_Knoten_Frechen_Kirilowitsch.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/Gordischer_Knoten_Frechen_Kirilowitsch.jpg/220px-Gordischer_Knoten_Frechen_Kirilowitsch.jpg 2x" data-file-width="3993" data-file-height="3376" /></a><figcaption>Gordian Knot statue (1990)</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Magimagi_-_Mainbeam.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Magimagi_-_Mainbeam.jpg/220px-Magimagi_-_Mainbeam.jpg" decoding="async" width="220" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Magimagi_-_Mainbeam.jpg/330px-Magimagi_-_Mainbeam.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Magimagi_-_Mainbeam.jpg/440px-Magimagi_-_Mainbeam.jpg 2x" data-file-width="842" data-file-height="626" /></a><figcaption><a href="/wiki/Magimagi" title="Magimagi">Magimagi</a> <a href="/wiki/Sennit" title="Sennit">sennit</a> of <a href="/wiki/Fiji" title="Fiji">Fiji</a> around wooden ceiling posts.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Teton_tipi_tie.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Teton_tipi_tie.jpg/110px-Teton_tipi_tie.jpg" decoding="async" width="110" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Teton_tipi_tie.jpg/165px-Teton_tipi_tie.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Teton_tipi_tie.jpg/220px-Teton_tipi_tie.jpg 2x" data-file-width="355" data-file-height="658" /></a><figcaption><a href="/wiki/Blackfoot_people" class="mw-redirect" title="Blackfoot people">Blackfoot</a> "Teton" tipi tie<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></figcaption></figure> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Knot" title="Special:EditPage/Knot">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Knot%22">"Knot"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Knot%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Knot%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Knot%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Knot%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Knot%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">December 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>Knots and <b>knotting</b> have been used and studied throughout history. For example, <a href="/wiki/Chinese_knotting" title="Chinese knotting">Chinese knotting</a> is a decorative handicraft art that began as a form of Chinese folk art in the Tang and Song Dynasty (960–1279 AD) in China, later popularized in the Ming. <a href="/wiki/Knot_theory" title="Knot theory">Knot theory</a> is the recent mathematical study of knots. </p><p>Knots of ancient origin include the <a href="/wiki/Bottle_sling" title="Bottle sling">bottle sling</a>, <a href="/wiki/Bowline" title="Bowline">bowline</a>, <a href="/wiki/Cat%27s_paw_(knot)" title="Cat's paw (knot)">cat's paw</a>, <a href="/wiki/Clove_hitch" title="Clove hitch">clove hitch</a>, <a href="/wiki/Cow_hitch" title="Cow hitch">cow hitch</a>, <a href="/wiki/Double_fisherman%27s_knot" title="Double fisherman's knot">double fisherman's knot</a>, <a href="/wiki/Eskimo_bowline" title="Eskimo bowline">eskimo bowline</a>, <a href="/wiki/Figure-eight_knot" title="Figure-eight knot">figure-eight knot</a>, <a href="/wiki/Fisherman%27s_knot" title="Fisherman's knot">fisherman's knot</a>, <a href="/wiki/Half_hitch" title="Half hitch">half hitch</a>, <a href="/wiki/Kalmyk_loop" title="Kalmyk loop">kalmyk loop</a>, <a href="/wiki/One-sided_overhand_bend" class="mw-redirect" title="One-sided overhand bend">one-sided overhand bend</a>, <a href="/wiki/Overhand_knot" title="Overhand knot">overhand knot</a>, <a href="/wiki/Overhand_loop" title="Overhand loop">overhand loop</a>, <a href="/wiki/Reef_knot" title="Reef knot">reef knot</a>, <a href="/wiki/Running_bowline" title="Running bowline">running bowline</a>, <a href="/wiki/Single_hitch" class="mw-redirect" title="Single hitch">single hitch</a>, <a href="/wiki/Thief_knot" title="Thief knot">thief knot</a>, <a href="/wiki/Turk%27s_head_knot" title="Turk's head knot">Turk's head knot</a>, and <a href="/wiki/Two_half-hitches" title="Two half-hitches">two half-hitches</a>. </p><p>The eleven main knots of Chinese knotting are the four-flower knot, six-flower knot, <a href="/wiki/Chinese_button_knot" title="Chinese button knot">Chinese button knot</a>, <a href="/wiki/Matthew_Walker_knot" title="Matthew Walker knot">double connection knot</a>, <a href="/wiki/Carrick_bend" title="Carrick bend">double coin knot</a>, agemaki, <a href="/wiki/Friendship_knot" title="Friendship knot">cross knot</a>, square knot, <a href="/wiki/Plafond_knot" title="Plafond knot">Plafond knot</a>, <a href="/wiki/Pan_Chang_knot" title="Pan Chang knot">Pan Chang knot</a>, and the <a href="/wiki/Good_luck_knot" title="Good luck knot">good luck knot</a>. </p><p>Knots of more recent origin include the <a href="/wiki/Friendship_knot" title="Friendship knot">friendship knot</a> of Chinese knotting.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2023)">citation needed</span></a></i>]</sup> The <a href="/wiki/Sheepshank" title="Sheepshank">sheepshank knot</a> originates from 1627<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (August 2023)">citation needed</span></a></i>]</sup> while the <a href="/wiki/Western_Union_splice" title="Western Union splice">Western Union splice</a> originates from the beginning of <a href="/wiki/Telegraphy" title="Telegraphy">telegraphy</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Use">Use</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=2" title="Edit section: Use"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Knot" title="Special:EditPage/Knot">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">July 2011</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>There is a large variety of knots, each with properties that make it suitable for a range of tasks. Some knots are used to attach the rope (or other knotting material) to other objects such as another rope, <a href="/wiki/Cleat_(nautical)" title="Cleat (nautical)">cleat</a>, ring, or stake. Some knots are used to bind or constrict objects. Decorative knots usually bind to themselves to produce attractive patterns. </p> <div class="mw-heading mw-heading3"><h3 id="Teaching">Teaching</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=3" title="Edit section: Teaching"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:School_for_Sailors_NGM-v31-p351.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/School_for_Sailors_NGM-v31-p351.jpg/220px-School_for_Sailors_NGM-v31-p351.jpg" decoding="async" width="220" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/School_for_Sailors_NGM-v31-p351.jpg/330px-School_for_Sailors_NGM-v31-p351.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/School_for_Sailors_NGM-v31-p351.jpg/440px-School_for_Sailors_NGM-v31-p351.jpg 2x" data-file-width="2398" data-file-height="1443" /></a><figcaption>Sailors learning knots and <a href="/wiki/Ropework" title="Ropework">ropework</a> in the early 20th century</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Sj%C3%B6manss%C3%A4ck_-_1991.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Sj%C3%B6manss%C3%A4ck_-_1991.jpg/220px-Sj%C3%B6manss%C3%A4ck_-_1991.jpg" decoding="async" width="220" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Sj%C3%B6manss%C3%A4ck_-_1991.jpg/330px-Sj%C3%B6manss%C3%A4ck_-_1991.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/Sj%C3%B6manss%C3%A4ck_-_1991.jpg/440px-Sj%C3%B6manss%C3%A4ck_-_1991.jpg 2x" data-file-width="1211" data-file-height="999" /></a><figcaption>Sailor bag with different knots</figcaption></figure> <p>While some people can look at diagrams or photos and tie the illustrated knots, others learn best by watching how a knot is tied. Knot tying skills are often transmitted by <a href="/wiki/Sailors" class="mw-redirect" title="Sailors">sailors</a>, <a href="/wiki/Scouting" title="Scouting">scouts</a>, <a href="/wiki/Climbing" title="Climbing">climbers</a>, <a href="/wiki/Canyoning" title="Canyoning">canyoners</a>, <a href="/wiki/Caving" title="Caving">cavers</a>, <a href="/wiki/Arborist" title="Arborist">arborists</a>, <a href="/wiki/Firefighter#Rescue" title="Firefighter">rescue professionals</a>, <a href="/wiki/Stagehand" title="Stagehand">stagehands</a>, <a href="/wiki/Fishermen" class="mw-redirect" title="Fishermen">fishermen</a>, <a href="/wiki/Lineman_(technician)" class="mw-redirect" title="Lineman (technician)">linemen</a> and <a href="/wiki/Surgeons" class="mw-redirect" title="Surgeons">surgeons</a>. <a href="/wiki/International_Guild_of_Knot_Tyers" title="International Guild of Knot Tyers">The International Guild of Knot Tyers</a> is an organization dedicated to the promotion of knot tying. </p> <div class="mw-heading mw-heading3"><h3 id="Applications">Applications</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=4" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Truckers in need of securing a load may use a <a href="/wiki/Trucker%27s_hitch" title="Trucker's hitch">trucker's hitch</a>, gaining <a href="/wiki/Mechanical_advantage" title="Mechanical advantage">mechanical advantage</a>. Knots can save <a href="/wiki/Spelunking" class="mw-redirect" title="Spelunking">spelunkers</a> from being buried under rock. Many knots can also be used as makeshift tools, for example, the <a href="/wiki/Bowline" title="Bowline">bowline</a> can be used as a rescue loop, and the <a href="/wiki/Munter_hitch" title="Munter hitch">munter hitch</a> can be used for <a href="/wiki/Belaying" title="Belaying">belaying</a>. The <a href="/wiki/Diamond_hitch" title="Diamond hitch">diamond hitch</a> was widely used to tie packages on to <a href="/wiki/Donkey" title="Donkey">donkeys</a> and <a href="/wiki/Mule" title="Mule">mules</a>. </p><p>In hazardous environments such as mountains, knots are very important. In the event of someone falling into a ravine or a similar terrain feature, with the correct equipment and knowledge of knots a rappel system can be set up to lower a rescuer down to a casualty and set up a hauling system to allow a third individual to pull both the rescuer and the casualty out of the ravine. Further application of knots includes developing a high line, which is similar to a zip line, and which can be used to move supplies, injured people, or the untrained across rivers, crevices, or ravines. Note the systems mentioned typically require carabiners and the use of multiple appropriate knots. These knots include the bowline, double figure eight, munter hitch, munter mule, prusik, autoblock, and clove hitch. Thus any individual who goes into a mountainous environment should have basic knowledge of knots and knot systems to increase safety and the ability to undertake activities such as rappelling. </p><p>Knots can be applied in combination to produce complex objects such as <a href="/wiki/Lanyard" title="Lanyard">lanyards</a> and <a href="/wiki/Net_(textile)" title="Net (textile)">netting</a>. In <a href="/wiki/Ropework" title="Ropework">ropework</a>, the frayed end of a rope is held together by a type of knot called a <a href="/wiki/Whipping_knot" title="Whipping knot">whipping knot</a>. Many types of <a href="/wiki/Textile" title="Textile">textiles</a> use knots to repair damage. <a href="/wiki/Macram%C3%A9" title="Macramé">Macramé</a>, one kind of textile, is generated exclusively through the use of knotting, instead of <a href="/wiki/Knitting" title="Knitting">knits</a>, crochets, weaves or felting. Macramé can produce self-supporting three-dimensional textile structures, as well as flat work, and is often used ornamentally or decoratively. </p> <div class="mw-heading mw-heading2"><h2 id="Properties">Properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=5" title="Edit section: Properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Strength">Strength</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=6" title="Edit section: Strength"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Knots weaken the rope in which they are made.<sup id="cite_ref-Richards2005_6-0" class="reference"><a href="#cite_note-Richards2005-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> When knotted rope is strained to its breaking point, it almost always fails at the knot or close to it, unless it is defective or damaged elsewhere. The bending, crushing, and chafing forces that hold a knot in place also unevenly stress rope fibers and ultimately lead to a reduction in strength. The exact mechanisms that cause the weakening and failure are complex and are the subject of continued study. Special fibers that show differences in color in response to strain are being developed and used to study stress as it relates to types of knots.<sup id="cite_ref-Greenfieldboyce_7-0" class="reference"><a href="#cite_note-Greenfieldboyce-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Patil_8-0" class="reference"><a href="#cite_note-Patil-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Relative <b>knot strength</b>, also called <b>knot efficiency</b>, is the breaking strength of a knotted rope in proportion to the breaking strength of the rope without the knot. Determining a precise value for a particular knot is difficult because many factors can affect a knot efficiency test: the type of <a href="/wiki/Fiber" title="Fiber">fiber</a>, the <a href="/wiki/Rope#Styles_of_rope_construction" title="Rope">style of rope</a>, the size of rope, whether it is wet or dry, how the knot is dressed before loading, how rapidly it is loaded, whether the knot is repeatedly loaded, and so on. The efficiency of common knots ranges between 40 and 80% of the rope's original strength.<sup id="cite_ref-hsok-ch10_9-0" class="reference"><a href="#cite_note-hsok-ch10-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>In most situations forming loops and bends with conventional knots is far more practical than using <a href="/wiki/Rope_splicing" title="Rope splicing">rope splices</a>, even though the latter can maintain nearly the rope's full strength. Prudent users allow for a large <a href="/wiki/Factor_of_safety" title="Factor of safety">safety margin</a> in the strength of rope chosen for a task due to the weakening effects of knots, aging, damage, shock loading, etc. The <a href="/wiki/Safe_working_load" class="mw-redirect" title="Safe working load">working load limit</a> of a rope is generally specified with a significant safety factor, up to 15:1 for critical applications.<sup id="cite_ref-grog-reliability_11-0" class="reference"><a href="#cite_note-grog-reliability-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> For life-threatening applications, other factors come into play.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2012)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Security">Security</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=7" title="Edit section: Security"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Even if the rope does not break, a knot may still fail to hold. Knots that hold firm under a variety of adverse conditions are said to be more secure than those that do not. </p><p>The following sections describe the main ways that knots fail to hold. </p> <div class="mw-heading mw-heading4"><h4 id="Slipping">Slipping</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=8" title="Edit section: Slipping"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The load creates tension that pulls the rope back through the knot in the direction of the load. If this continues far enough, the working end passes into the knot and the knot unravels and fails. This behavior can worsen when the knot is repeatedly strained and let slack, dragged over rough terrain, or repeatedly struck against hard objects such as <a href="/wiki/Mast_(sailing)" title="Mast (sailing)">masts</a> and <a href="/wiki/Flagpole" title="Flagpole">flagpoles</a>. </p><p>Even with secure knots, slippage may occur when the knot is first put under real tension. This can be mitigated by leaving plenty of rope at the working end outside of the knot, and by dressing the knot cleanly and tightening it as much as possible before loading. Sometimes, the use of a <a href="/wiki/Stopper_knot" title="Stopper knot">stopper knot</a> or, even better, a <a href="/wiki/Backup_knot" class="mw-redirect" title="Backup knot">backup knot</a> can prevent the working end from passing through the knot; but if a knot is observed to slip, it is generally preferable to use a more secure knot. Life-critical applications often require backup knots to maximize safety. </p> <div class="mw-heading mw-heading4"><h4 id="Capsizing">Capsizing</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=9" title="Edit section: Capsizing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Bowline_(PSF).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Bowline_%28PSF%29.jpg/220px-Bowline_%28PSF%29.jpg" decoding="async" width="220" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Bowline_%28PSF%29.jpg/330px-Bowline_%28PSF%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Bowline_%28PSF%29.jpg/440px-Bowline_%28PSF%29.jpg 2x" data-file-width="454" data-file-height="164" /></a><figcaption><a href="/wiki/Bowline" title="Bowline">Bowline</a></figcaption></figure> <p>To capsize (or spill) a knot is to change its form and rearrange its parts, usually by pulling on specific ends in certain ways.<sup id="cite_ref-hsok-ch10_9-1" class="reference"><a href="#cite_note-hsok-ch10-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> When used inappropriately, some knots tend to capsize easily or even spontaneously. Often the capsized form of the knot offers little resistance to slipping or unraveling. A <a href="/wiki/Reef_knot" title="Reef knot">reef knot</a>, when misused as a bend, can capsize dangerously. </p><p>Sometimes a knot is intentionally capsized as a method of tying another knot, as with the <a href="/wiki/Bowline#Tying" title="Bowline">"lightning method"</a> of tying a <a href="/wiki/Bowline" title="Bowline">bowline</a>. Some knots, such as the <a href="/wiki/Carrick_bend" title="Carrick bend">carrick bend</a>, are generally tied in one form then capsized to obtain a stronger or more stable form. </p> <div class="mw-heading mw-heading4"><h4 id="Sliding">Sliding</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=10" title="Edit section: Sliding"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In knots that are meant to grip other objects, failure can be defined as the knot moving relative to the gripped object. While the knot itself is not untied, it ceases to perform the desired function. For instance, a simple <a href="/wiki/Rolling_hitch" title="Rolling hitch">rolling hitch</a> tied around a railing and pulled parallel to the railing might hold up to a certain tension, then start sliding. Sometimes this problem can be corrected by working-up the knot tighter before subjecting it to load, but usually the problem requires either a knot with more wraps or a rope of different diameter or material. </p> <div class="mw-heading mw-heading3"><h3 id="Releasability">Releasability</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=11" title="Edit section: Releasability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Knots differ in the effort required to untie them after loading. Knots that are very difficult to untie, such as the <a href="/wiki/Water_knot" title="Water knot">water knot</a>, are said to "jam" or be <b>jamming knots</b>. Knots that come untied with less difficulty, such as the <a href="/wiki/Zeppelin_bend" title="Zeppelin bend">Zeppelin bend</a>, are referred to as "<b>non-jamming</b>". </p> <div class="mw-heading mw-heading2"><h2 id="Components">Components</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=12" title="Edit section: Components"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Eyes_and_turns.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Eyes_and_turns.jpg/220px-Eyes_and_turns.jpg" decoding="async" width="220" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Eyes_and_turns.jpg/330px-Eyes_and_turns.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d1/Eyes_and_turns.jpg/440px-Eyes_and_turns.jpg 2x" data-file-width="448" data-file-height="198" /></a><figcaption>A: open loop, B: closed loop, C: turn, D: round turn, E: two round turns.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Cross_knots_ABOK_34.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Cross_knots_ABOK_34.jpg/220px-Cross_knots_ABOK_34.jpg" decoding="async" width="220" height="56" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Cross_knots_ABOK_34.jpg/330px-Cross_knots_ABOK_34.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Cross_knots_ABOK_34.jpg/440px-Cross_knots_ABOK_34.jpg 2x" data-file-width="1451" data-file-height="368" /></a><figcaption>#34 Cross #35 Elbow #36 Round turn</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ansted_Sea_Terms_1898_-_Names_of_the_parts_of_a_rope.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Ansted_Sea_Terms_1898_-_Names_of_the_parts_of_a_rope.jpg/220px-Ansted_Sea_Terms_1898_-_Names_of_the_parts_of_a_rope.jpg" decoding="async" width="220" height="112" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Ansted_Sea_Terms_1898_-_Names_of_the_parts_of_a_rope.jpg/330px-Ansted_Sea_Terms_1898_-_Names_of_the_parts_of_a_rope.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Ansted_Sea_Terms_1898_-_Names_of_the_parts_of_a_rope.jpg/440px-Ansted_Sea_Terms_1898_-_Names_of_the_parts_of_a_rope.jpg 2x" data-file-width="495" data-file-height="251" /></a><figcaption>#27 End #29 Bight #28 Standing</figcaption></figure> <dl><dd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/List_of_knot_terminology" title="List of knot terminology">List of knot terminology</a></div></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Bight">Bight</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=13" title="Edit section: Bight"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>A <a href="/wiki/Bight_(knot)" title="Bight (knot)">bight</a> is any curved section, slack part, or loop between the ends of a rope, string, or yarn.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Bitter_end">Bitter end</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=14" title="Edit section: Bitter end"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>As a ropeworker's term, "bitter end" refers to the end of a rope that is tied off. In British nautical usage, the bitter end is the ship end of the anchor cable, secured by the anchor bitts and the bitter pin in the cable locker under the <a href="/wiki/Forecastle" title="Forecastle">forecastle</a>. At anchor, the more anchor line that is payed out, the better the anchor's hold. In a storm, if the anchor drags, ships will pay out more and more anchor line until they reach the "bitter end." At this point, they can only hope the anchor holds, hence the expression "hanging on to the bitter end". (A <i><a href="/wiki/Bitts" title="Bitts">bitt</a></i> is a metal block with a crosspin for tying lines to, also found on piers.) Also, the working end.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Loop">Loop</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=15" title="Edit section: Loop"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>A curve narrower than a bight but with separate ends.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Elbow">Elbow</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=16" title="Edit section: Elbow"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>Two crossing points created by an extra twist in a loop or a circle.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Standing_end">Standing end</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=17" title="Edit section: Standing end"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>The standing end is the longer end of the rope not involved in the knot, often shown as unfinished. It is often (but not always) the end of the rope under load after the knot is complete. For example, when a clove hitch ties a boat to a pier, the end going to the boat is the <i>standing end</i>.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Standing_part">Standing part</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=18" title="Edit section: Standing part"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>Section of line between knot and the standing end (seen above).</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Turn">Turn</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=19" title="Edit section: Turn"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>A <b><a href="/wiki/Turn_(knot)" title="Turn (knot)">turn</a></b> or <b>single turn</b> is a curve with crossed legs.</dd> <dd>A <b>round turn</b> is the complete encirclement of an object; requires two passes.</dd> <dd><b>Two round turns</b> circles the object twice; requires three passes.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Working_end">Working end</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=20" title="Edit section: Working end"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>The active end of a line used in making the knot. May also be called the "running end", "live end", or "tag end".</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Working_part">Working part</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=21" title="Edit section: Working part"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd>Section of line between knot and the working end.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Knot_categories">Knot categories</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=22" title="Edit section: Knot categories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/List_of_knots" title="List of knots">List of knots</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Knot" title="Special:EditPage/Knot">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">July 2011</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>The <a href="/wiki/List_of_knots" title="List of knots">list of knots</a> is extensive, but common properties allow for a useful system of categorization. For example, <i><a href="/wiki/Loop_(knot)" class="mw-redirect" title="Loop (knot)">loop</a></i> knots share the attribute of having some kind of an anchor point constructed on the <a href="/wiki/Standing_end" class="mw-redirect" title="Standing end">standing end</a> (such as a loop or overhand knot) into which the working end is easily hitched, using a <a href="/wiki/Round_turn" class="mw-redirect" title="Round turn">round turn</a>. An example of this is the <a href="/wiki/Bowline" title="Bowline">bowline</a>. <i>Constricting</i> knots often rely on friction to cinch down tight on loose bundles; an example is the <a href="/wiki/Miller%27s_knot" title="Miller's knot">Miller's knot</a>. Knots may belong to more than one category. </p> <dl><dt><a href="/wiki/Bend_knot" class="mw-redirect" title="Bend knot">Bend</a></dt> <dd>A knot uniting two lines<sup id="cite_ref-EB1911_12-0" class="reference"><a href="#cite_note-EB1911-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> (for knots joining two ends of the same line, see <a href="/wiki/Binding_(knot)" class="mw-redirect" title="Binding (knot)">binding knots</a> or <a href="/wiki/Loop_(knot)" class="mw-redirect" title="Loop (knot)">loops</a>).</dd> <dt><a href="/wiki/Binding_(knot)" class="mw-redirect" title="Binding (knot)">Binding</a></dt> <dd>A knot that restricts object(s) by making multiple winds.</dd> <dt><a href="/wiki/Coiling" title="Coiling">Coil knot</a></dt> <dd>Knots used to tie up lines for storage.</dd> <dt><a href="/wiki/Decorative_knot" title="Decorative knot">Decorative knot</a></dt> <dd>A complex knot exhibiting repeating patterns often constructed around and enhancing an object.</dd> <dt><a href="/wiki/Hitch_knot" class="mw-redirect" title="Hitch knot">Hitch</a></dt> <dd>A knot tied to a post, cable, ring, or spar.</dd> <dt><a href="/wiki/Lashing_knot" class="mw-redirect" title="Lashing knot">Lashing</a></dt> <dd>A knot used to hold (usually) poles together.</dd> <dt><a href="/wiki/Loop_(knot)" class="mw-redirect" title="Loop (knot)">Loop</a></dt> <dd>A knot used to create a closed circle in a line.</dd> <dt><a href="/wiki/Braid" title="Braid">Plait</a> (or braid)</dt> <dd>A number of lines interwoven in a simple regular pattern.</dd> <dt><a href="/wiki/Slip_knot" title="Slip knot">Slip</a> (or running)</dt> <dd>A knot tied with a hitch around one of its parts. In contrast, a loop is closed with a bend. While a slip knot can be closed, a loop remains the same size.</dd> <dt><a href="/wiki/Bight_(knot)#Slipped_knot" title="Bight (knot)">Slipped</a></dt> <dd>Some knots may be finished by passing a <a href="/wiki/Bight_(knot)" title="Bight (knot)">bight</a> rather than the end, for ease of untying. The common shoelace knot is an example, being a <a href="/wiki/Reef_knot" title="Reef knot">reef knot</a> with both ends slipped.</dd> <dt><a href="/wiki/Seizing" title="Seizing">Seizing</a></dt> <dd>A knot used to hold two lines or two parts of the same line together.<sup id="cite_ref-EB1911_12-1" class="reference"><a href="#cite_note-EB1911-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></dd> <dt><a href="/wiki/Sennit" title="Sennit">Sennit</a></dt> <dd>A number of lines interwoven in a complex pattern. See also <a href="/wiki/Chain_sinnet" title="Chain sinnet">Chain sinnet</a>.</dd> <dt><a href="/wiki/Rope_splicing" title="Rope splicing">Splice</a></dt> <dd>A knot formed by interweaving strands of rope rather than whole lines. More time-consuming but usually stronger than simple knots.</dd> <dt><a href="/wiki/Stopper_knot" title="Stopper knot">Stopper</a></dt> <dd>A knot tied to hold a line through a hole.</dd> <dt><a href="/wiki/Whipping_knot" title="Whipping knot">Whipping</a></dt> <dd>A binding knot used to prevent another line from fraying.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Basic_useful_knots">Basic useful knots</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=23" title="Edit section: Basic useful knots"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Alpine_butterfly_knot" class="mw-redirect" title="Alpine butterfly knot">Alpine butterfly knot</a> for a secure loop in the middle of a rope when the ends are not free</li> <li><a href="/wiki/Bowline" title="Bowline">Bowline</a> for tying a loop in the end of a rope, as around one's waist or to secure a ring or grommet. The knot is also used as an anchor knot and is used in many knot systems that are used in mountainous terrain such as a highline or hauling system.</li> <li><a href="/wiki/Constrictor_knot" title="Constrictor knot">Constrictor knot</a> for making bundles or cinching the neck of a sack, though this knot jams and may need to be cut</li> <li><a href="/wiki/Figure-eight_knot" title="Figure-eight knot">Figure-eight knot</a> as a stopper</li> <li><a href="/wiki/Grass_bend" class="mw-redirect" title="Grass bend">Grass bend</a> for tying belts together, though insecure with ropes</li> <li><a href="/wiki/Monkey%27s_fist" title="Monkey's fist">Monkey's fist</a> used to weight the end of a rope</li> <li><a href="/wiki/Prusik" title="Prusik">Prusik</a> for ascending a rope</li> <li><a href="/wiki/Reef_knot" title="Reef knot">Reef knot</a> (square knot), a common but insecure <a href="/wiki/Binding_knot" class="mw-redirect" title="Binding knot">binding knot</a> for joining the ends of a piece of cordage wrapped around an object or objects</li> <li><a href="/wiki/Sheet_bend" title="Sheet bend">Sheet bend</a> for joining the ends of two ropes, which need not be the same diameter <ul><li><a href="/wiki/Sheet_bend#Double_sheet_bend" title="Sheet bend">Double sheet bend</a> for tying the ends of two dissimilarly sized ropes together</li></ul></li> <li><a href="/wiki/Spanish_bowline" title="Spanish bowline">Spanish bowline</a> used to hoist crewmen aloft or suspend them over the side</li> <li><a href="/wiki/Versatackle_knot" title="Versatackle knot">Versatackle</a> for hoisting heavy loads and tightening rigging</li> <li><a href="/wiki/Water_knot" title="Water knot">Water knot</a> for tying a knot in flat material such as nylon webbing</li></ul> <div class="mw-heading mw-heading4"><h4 id="Hitches">Hitches</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=24" title="Edit section: Hitches"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Anchor_bend" title="Anchor bend">Anchor bend</a> (or anchor hitch) for tying a rope to a boat anchor</li> <li><a href="/wiki/Clove_hitch" title="Clove hitch">Clove hitch</a> for tying a rope to a pole – simple and will not jam, but not particularly secure and will not work on rectangular shapes</li> <li><a href="/wiki/Buntline_hitch" title="Buntline hitch">Buntline hitch</a> for tying a rope to a pole or other shape, but can jam</li> <li><a href="/wiki/Diamond_hitch" title="Diamond hitch">Diamond hitch</a> for packing trail animals</li> <li><a href="/wiki/Rolling_hitch" title="Rolling hitch">Rolling hitch</a> for securing a rope to a pole when the pull is lengthwise rather than outward, or to tie one rope to the middle of another</li> <li><a href="/wiki/Taut-line_hitch" title="Taut-line hitch">Taut-line hitch</a> (or Midshipman's hitch) for forming an adjustable (ratcheting) loop that does not slip smaller under tension</li> <li><a href="/wiki/Timber_hitch" title="Timber hitch">Timber hitch</a> for securing or hauling long narrow loads, with the pull in one direction</li> <li><a href="/wiki/Trucker%27s_hitch" title="Trucker's hitch">Trucker's hitch</a> for clinching down a load</li></ul> <div class="mw-heading mw-heading3"><h3 id="Trick_knots">Trick knots</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=25" title="Edit section: Trick knots"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Magic_(illusion)" title="Magic (illusion)">Trick</a> knots are knots that are used as part of a <a href="/wiki/Magic_trick" class="mw-redirect" title="Magic trick">magic trick</a>, a <a href="/wiki/Joke" title="Joke">joke</a>, or a <a href="/wiki/Puzzle" title="Puzzle">puzzle</a>. They are useful for these purposes because they have a deceptive appearance, being easier or more difficult to tie or untie than their appearance would suggest. The easiest trick knot is the <a href="/wiki/Slip_knot" title="Slip knot">slip knot</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Other noted trick knots include: </p> <ul><li><a href="/wiki/Grief_knot" title="Grief knot">Grief knot</a>. The starkly differing behavior of the knot, depending on how it is arranged, has been exploited as the basis of a <a href="/wiki/Parlor_trick" class="mw-redirect" title="Parlor trick">parlor trick</a>.<sup id="cite_ref-ashley415_14-0" class="reference"><a href="#cite_note-ashley415-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> When pulling on the standing ends the knot starts slipping and the working ends become crossed. By twisting the working ends so that they uncross and then recross in reverse, the knot's structure capsizes so that it will no longer slip. The twisting motion resembles the turning of a key, "locking" and "unlocking" the knot.</li> <li><a href="/wiki/Tom_fool%27s_knot" title="Tom fool's knot">Tom fool's knot</a>, used as a trick knot due to the speed with which it can be made.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Coxcombing">Coxcombing</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=26" title="Edit section: Coxcombing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Coxcombing</b> is a decorative knotwork performed by <a href="/wiki/Sailors" class="mw-redirect" title="Sailors">sailors</a> during the <a href="/wiki/Age_of_Sail" title="Age of Sail">Age of Sail</a>. </p><p>The general purpose was to dress-up, protect, or help identify specific items and parts of ships and boats. </p><p>It is still found today in some whippings and wrappings of small diameter line on boat tillers and ships' wheels to enhance the grip, or to identify rudder amidships. </p><p>Knots used in coxcombing include <a href="/wiki/Turk%27s_head_knot" title="Turk's head knot">Turk's head knot</a>, <a href="/wiki/Figure-eight_knot" title="Figure-eight knot">Flemish</a>, <a href="/wiki/French_whipping" class="mw-redirect" title="French whipping">French whipping</a>, and others. </p> <div class="mw-heading mw-heading2"><h2 id="Knot_theory">Knot theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=27" title="Edit section: Knot theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Knot_theory" title="Knot theory">Knot theory</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:TrefoilKnot_01.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/TrefoilKnot_01.svg/150px-TrefoilKnot_01.svg.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/TrefoilKnot_01.svg/225px-TrefoilKnot_01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/TrefoilKnot_01.svg/300px-TrefoilKnot_01.svg.png 2x" data-file-width="250" data-file-height="250" /></a><figcaption>A <a href="/wiki/Trefoil_knot" title="Trefoil knot">trefoil knot</a> is a mathematical version of an <a href="/wiki/Overhand_knot" title="Overhand knot">overhand knot</a>.</figcaption></figure> <p>Knot theory is a branch of <a href="/wiki/Topology" title="Topology">topology</a>. It deals with the <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> analysis of knots, their structure and properties, and with the relationships between different knots. In topology, a <a href="/wiki/Knot_(mathematics)" title="Knot (mathematics)">knot</a> is a figure consisting of a single loop with any number of crossing or knotted elements: a closed curve in space which may be moved around so long as its strands never pass through each other. As a closed loop, a mathematical knot has no proper ends, and cannot be undone or untied; however, any physical knot in a piece of string can be thought of as a mathematical knot by fusing the two ends. A configuration of several knots winding around each other is called a <i>link</i>. Various mathematical techniques are used to classify and distinguish knots and links. For instance, the <a href="/wiki/Alexander_polynomial" title="Alexander polynomial">Alexander polynomial</a> associates certain numbers with any given knot; these numbers are different for the <a href="/wiki/Trefoil_knot" title="Trefoil knot">trefoil knot</a>, the <a href="/wiki/Figure-eight_knot_(mathematics)" title="Figure-eight knot (mathematics)">figure-eight knot</a>, and the <a href="/wiki/Unknot" title="Unknot">unknot</a> (a simple loop), showing that one cannot be moved into the other (without strands passing through each other).<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Physical_theory_of_friction_knots">Physical theory of friction knots</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=28" title="Edit section: Physical theory of friction knots"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Capstan_equation" title="Capstan equation">Capstan equation</a></div> <p>A simple mathematical theory of hitches has been proposed by Bayman<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> and extended by Maddocks and Keller.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> It makes predictions that are approximately correct when tested empirically.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> No similarly successful theory has been developed for knots in general. </p> <div class="mw-heading mw-heading2"><h2 id="Knot_tying">Knot tying</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=29" title="Edit section: Knot tying"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Knot" title="Special:EditPage/Knot">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">January 2011</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:AshleyBook.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/AshleyBook.jpg/220px-AshleyBook.jpg" decoding="async" width="220" height="93" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/AshleyBook.jpg/330px-AshleyBook.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/AshleyBook.jpg/440px-AshleyBook.jpg 2x" data-file-width="1946" data-file-height="826" /></a><figcaption><a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">The Ashley Book of Knots</a> is considered the definitive work on the topic</figcaption></figure> <p>Knot tying consists of the techniques and skills employed in tying a knot in <a href="/wiki/Rope" title="Rope">rope</a>, <a href="/wiki/Nylon_webbing" class="mw-redirect" title="Nylon webbing">nylon webbing</a>, or other articles. The proper tying of a knot can be the difference between an attractive knot and a messy one, and occasionally life and death. It is important to understand the often subtle differences between what works, and what does not. For example, many knots "spill" or pull through, particularly if they are not "backed up," usually with a single or double overhand knot to make sure the end of the rope does not make its way through the main knot, causing all strength to be lost. </p> <div class="mw-heading mw-heading3"><h3 id="Difficulty">Difficulty</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=30" title="Edit section: Difficulty"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The tying of a knot may be very straightforward (such as with an <a href="/wiki/Overhand_knot" title="Overhand knot">overhand knot</a>), or it may be more complicated, such as a <a href="/wiki/Monkey%27s_fist" title="Monkey's fist">monkey's fist</a> knot. Tying knots correctly requires an understanding of the type of material being tied (string, <a href="/wiki/Rope" title="Rope">cord</a>, <a href="/wiki/Monofilament_line" class="mw-redirect" title="Monofilament line">monofilament line</a>, <a href="/wiki/Kernmantle_rope" title="Kernmantle rope">kernmantle rope</a>, or nylon webbing). For example, cotton string may be very small and easy to tie with much internal friction to keep it from falling apart once tied, while stiff 5/8" thick kernmantle rope will be very difficult to tie, and may be so slick as to tend to come apart once tied. </p> <div class="mw-heading mw-heading3"><h3 id="Material">Material</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=31" title="Edit section: Material"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The form of the material will influence the tying of a knot as well. Rope is round in cross-section, and has little dependence upon the manner in which the material is tied. Nylon webbing, on the other hand, is flat, and usually "tubular" in construction, meaning that it is spiral-woven, and has a hollow core. In order to retain as much of the strength as possible with webbing, the material must be tied "flat" such that parallel sections do not cross, and that the sections of webbing are not twisted when they cross each other within a knot. </p><p>The crossing of strands is important when dealing with round rope in other knots; for example, the <a href="/wiki/Figure-eight_loop" title="Figure-eight loop">figure-eight loop</a> loses strength when strands are crossed while the knot is being "finished" and tightened. Moreover, the <a href="/wiki/Standing_end" class="mw-redirect" title="Standing end">standing end</a> or the end from which the hauling will be done must have the greater radius of curvature in the finished knot to maximize the strength of the knot. </p> <div class="mw-heading mw-heading3"><h3 id="Tools">Tools</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=32" title="Edit section: Tools"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tools are sometimes employed in the finishing or untying of a knot, such as a <a href="/wiki/Fid" title="Fid">fid</a>, a tapered piece of wood that is often used in splicing. With the advent of <a href="/wiki/Wire_rope" title="Wire rope">wire rope</a>, many other tools are used in the tying of "knots." However, for cordage and other non-metallic appliances, the tools used are generally limited to sharp edges or blades such as a <a href="/w/index.php?title=Sheepsfoot_blade&action=edit&redlink=1" class="new" title="Sheepsfoot blade (page does not exist)">sheepsfoot blade</a>, occasionally a fine needle for proper whipping of <a href="/w/index.php?title=Laid_rope&action=edit&redlink=1" class="new" title="Laid rope (page does not exist)">laid rope</a>, a hot cutter for nylon and other synthetic fibers, and (for larger ropes) a shoe for smoothing out large knots by rolling them on the ground. </p> <div class="mw-heading mw-heading2"><h2 id="Use_by_animals">Use by animals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=33" title="Edit section: Use by animals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Hagfish" title="Hagfish">hagfish</a> is known to strip slime from its skin by tying itself into a simple overhand knot, and moving its body to make the knot travel toward the tail. It also uses this action in reverse (tail to head) to pry out flesh after biting into a carcass.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=34" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Circuit_topology" title="Circuit topology">Circuit topology</a></li> <li><a href="/wiki/Chinese_knot" class="mw-redirect" title="Chinese knot">Chinese knotting</a></li> <li><a href="/wiki/Gordian_Knot" title="Gordian Knot">Gordian Knot</a></li> <li><a href="/wiki/International_Guild_of_Knot_Tyers" title="International Guild of Knot Tyers">International Guild of Knot Tyers</a></li> <li><a href="/wiki/List_of_knots" title="List of knots">List of knots</a></li> <li><a href="/wiki/Quipu" title="Quipu">Quipu</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=35" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=36" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFAshley1944" class="citation cs2">Ashley, Clifford W. (1944), <i>The Ashley Book of Knots</i>, New York: Doubleday, p. 12, <q>The word knot has three distinct meanings in common use. In the broadest sense it applies to all complications in cordage, except accidental ones, such as snarls and kinks, and complications adapted for storage, such as coils, hanks, skeins, balls, etc.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Ashley+Book+of+Knots&rft.place=New+York&rft.pages=12&rft.pub=Doubleday&rft.date=1944&rft.aulast=Ashley&rft.aufirst=Clifford+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAshley1944" class="citation cs2">Ashley, Clifford W. (1944), <i>The Ashley Book of Knots</i>, New York: Doubleday, p. 12</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Ashley+Book+of+Knots&rft.place=New+York&rft.pages=12&rft.pub=Doubleday&rft.date=1944&rft.aulast=Ashley&rft.aufirst=Clifford+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAshley1944" class="citation cs2">Ashley, Clifford W. (1944), <i>The Ashley Book of Knots</i>, New York: Doubleday, p. 12, <q>In its second sense it does not include bends, hitches, splices, and sinnets, and in its third and narrowest sense the term applies only to a knob tied in a rope to prevent unreeving, to provide a handhold, or (in small material only) to prevent fraying.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Ashley+Book+of+Knots&rft.place=New+York&rft.pages=12&rft.pub=Doubleday&rft.date=1944&rft.aulast=Ashley&rft.aufirst=Clifford+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Anthropological Papers of the American Museum of Natural History. 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(eds.), <i>History and Science of Knots</i>, K&E Series on Knots and Everything, vol. 11, Singapore: World Scientific Publishing, pp. <span class="nowrap">181–</span>203, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-02-2469-1" title="Special:BookSources/978-981-02-2469-1"><bdi>978-981-02-2469-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Studies+on+the+Behaviour+of+Knots&rft.btitle=History+and+Science+of+Knots&rft.place=Singapore&rft.series=K%26E+Series+on+Knots+and+Everything&rft.pages=%3Cspan+class%3D%22nowrap%22%3E181-%3C%2Fspan%3E203&rft.pub=World+Scientific+Publishing&rft.date=1996&rft.isbn=978-981-02-2469-1&rft.aulast=Warner&rft.aufirst=Charles&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFŠimonDekýšPalček2020" class="citation journal cs1">Šimon, J.; Dekýš, V.; Palček, P. (2020). <a rel="nofollow" class="external text" href="https://doi.org/10.12693%2FAPhysPolA.138.404">"Revision of Commonly Used Loop Knots Efficiencies"</a>. <i>Acta Physica Polonica A</i>. <b>138</b> (3): <span class="nowrap">404–</span>420. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020AcPPA.138..404S">2020AcPPA.138..404S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.12693%2FAPhysPolA.138.404">10.12693/APhysPolA.138.404</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Physica+Polonica+A&rft.atitle=Revision+of+Commonly+Used+Loop+Knots+Efficiencies&rft.volume=138&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E404-%3C%2Fspan%3E420&rft.date=2020&rft_id=info%3Adoi%2F10.12693%2FAPhysPolA.138.404&rft_id=info%3Abibcode%2F2020AcPPA.138..404S&rft.aulast=%C5%A0imon&rft.aufirst=J.&rft.au=Dek%C3%BD%C5%A1%2C+V.&rft.au=Pal%C4%8Dek%2C+P.&rft_id=https%3A%2F%2Fdoi.org%2F10.12693%252FAPhysPolA.138.404&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> <li id="cite_note-grog-reliability-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-grog-reliability_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150407023208/http://www.animatedknots.com/reliability.php">"Knot & Rope Safety"</a>. Animated Knots by Grog. 2010. Archived from <a rel="nofollow" class="external text" href="http://www.animatedknots.com/reliability.php?">the original</a> on April 7, 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-09-14</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Knot+%26+Rope+Safety&rft.pub=Animated+Knots+by+Grog&rft.date=2010&rft_id=http%3A%2F%2Fwww.animatedknots.com%2Freliability.php%3F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span>. "<a rel="nofollow" class="external text" href="http://www.animatedknots.com/safety.php?Categ=ropecare&LogoImage=LogoGrog.png&Website=www.animatedknots.com#ScrollPoint">Knot & Rope Safety</a>", <i>AnimatedKnots.com</i>. Accessed April 2016.</span> </li> <li id="cite_note-EB1911-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-EB1911_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-EB1911_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChisholm1911" class="citation encyclopaedia cs1"><a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm, Hugh</a>, ed. (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Knot"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Knot">"Knot" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 15 (11th ed.). Cambridge University Press. p. 871.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Knot&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=871&rft.edition=11th&rft.pub=Cambridge+University+Press&rft.date=1911&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">Karl Fulves, Joseph K. Schmidt, <i>Self-Working Rope Magic: 70 Foolproof Tricks</i> (1990), page 17.</span> </li> <li id="cite_note-ashley415-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-ashley415_14-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAshley1944" class="citation cs2">Ashley, Clifford W. (1944), <i>The Ashley Book of Knots</i>, New York: Doubleday, p. 415</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Ashley+Book+of+Knots&rft.place=New+York&rft.pages=415&rft.pub=Doubleday&rft.date=1944&rft.aulast=Ashley&rft.aufirst=Clifford+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNakanishiOkada2012" class="citation journal cs1">Nakanishi, Yasutaka; Okada, Yuki (2012). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.topol.2011.11.023">"Differences of Alexander polynomials for knots caused by a single crossing change"</a>. <i>Topology and Its Applications</i>. <b>159</b> (4): <span class="nowrap">1016–</span>1025. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.topol.2011.11.023">10.1016/j.topol.2011.11.023</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Topology+and+Its+Applications&rft.atitle=Differences+of+Alexander+polynomials+for+knots+caused+by+a+single+crossing+change&rft.volume=159&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1016-%3C%2Fspan%3E1025&rft.date=2012&rft_id=info%3Adoi%2F10.1016%2Fj.topol.2011.11.023&rft.aulast=Nakanishi&rft.aufirst=Yasutaka&rft.au=Okada%2C+Yuki&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252Fj.topol.2011.11.023&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Bayman, "Theory of hitches," Am J Phys, 45 (1977) 185</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Maddocks, J.H. and Keller, J. B., "Ropes in Equilibrium," SIAM J Appl. Math., 47 (1987), pp. 1185–1200.</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.lightandmatter.com/article/knots.html">"The physics of knots"</a>. <i>www.lightandmatter.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.lightandmatter.com&rft.atitle=The+physics+of+knots&rft_id=http%3A%2F%2Fwww.lightandmatter.com%2Farticle%2Fknots.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWaters2012" class="citation web cs1">Waters, Hannah (2012-10-17). <a rel="nofollow" class="external text" href="https://www.smithsonianmag.com/science-nature/14-fun-facts-about-hagfish-77165589/">"14 Fun Facts About Hagfish"</a>. <i>Smithsonian Magazine</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-03-18</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Smithsonian+Magazine&rft.atitle=14+Fun+Facts+About+Hagfish&rft.date=2012-10-17&rft.aulast=Waters&rft.aufirst=Hannah&rft_id=https%3A%2F%2Fwww.smithsonianmag.com%2Fscience-nature%2F14-fun-facts-about-hagfish-77165589%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="General_sources">General sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=37" title="Edit section: General sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Clifford_Ashley" class="mw-redirect" title="Clifford Ashley">Clifford W. Ashley</a>. <i><a href="/wiki/The_Ashley_Book_of_Knots" title="The Ashley Book of Knots">The Ashley Book of Knots</a></i>. Doubleday, New York. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-385-04025-3" title="Special:BookSources/0-385-04025-3">0-385-04025-3</a>.</li> <li>Geoffrey Budworth (1999). <i>The Ultimate Encyclopedia of Knots & Ropework</i>. Annes Publishing Limited. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-55267-986-1" title="Special:BookSources/1-55267-986-1">1-55267-986-1</a>.</li> <li>John Cassidy (1985). <i>The Klutz Book of Knots</i>. Klutz Press, <a href="/wiki/Palo_Alto,_California" title="Palo Alto, California">Palo Alto, California</a>. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-932592-10-4" title="Special:BookSources/0-932592-10-4">0-932592-10-4</a>.</li> <li>Paul Hasluck with foreword by Des Pawson (2018) <i>The Art of Tying Knots.</i> Endless Mountains Publishing Company. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-998852-73-2" title="Special:BookSources/0-998852-73-2">0-998852-73-2</a>.</li> <li>Cyrus L. Day. <i>Knots & Splices</i>. International Marine/McGraw-Hill Companies. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-87742-252-4" title="Special:BookSources/0-87742-252-4">0-87742-252-4</a>.</li> <li>Raoul Graumont. <i>Handbook of Knots</i>. Cornell Maritime Press/Tidewater Publishers. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-87033-030-6" title="Special:BookSources/0-87033-030-6">0-87033-030-6</a>.</li> <li>R.S. Lee. <i>All The Knots You Need</i>. Algrove Publishing. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-921335-47-4" title="Special:BookSources/0-921335-47-4">0-921335-47-4</a>.</li> <li>Allen Padgett and Bruce Smith. <i>On Rope</i>. National Speleological Society. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-9615093-2-5" title="Special:BookSources/0-9615093-2-5">0-9615093-2-5</a>.</li> <li>Des Pawson (2001). <i>Pocket Guide to Knots & Splices</i>. Produced for Propsero Books by RPC Publishing Ltd., London. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-55267-218-2" title="Special:BookSources/1-55267-218-2">1-55267-218-2</a>.</li> <li>Brion Toss. <i>The Complete Rigger's Apprentice</i>. International Marine/McGraw-Hill Companies. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-064840-9" title="Special:BookSources/0-07-064840-9">0-07-064840-9</a>.</li> <li>J. C. Turner and P. van de Griend (ed.) (1996). <i>History and Science of Knots</i>. World Scientific. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/981-02-2469-9" title="Special:BookSources/981-02-2469-9">981-02-2469-9</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFŠimonDekýšPalček2020" class="citation journal cs1">Šimon, J.; Dekýš, V.; Palček, P. (2020). <a rel="nofollow" class="external text" href="https://doi.org/10.12693%2FAPhysPolA.138.404">"Revision of Commonly Used Loop Knots Efficiencies"</a>. <i>Acta Physica Polonica A</i>. <b>138</b> (3): <span class="nowrap">404–</span>420. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020AcPPA.138..404S">2020AcPPA.138..404S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.12693%2FAPhysPolA.138.404">10.12693/APhysPolA.138.404</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acta+Physica+Polonica+A&rft.atitle=Revision+of+Commonly+Used+Loop+Knots+Efficiencies&rft.volume=138&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E404-%3C%2Fspan%3E420&rft.date=2020&rft_id=info%3Adoi%2F10.12693%2FAPhysPolA.138.404&rft_id=info%3Abibcode%2F2020AcPPA.138..404S&rft.aulast=%C5%A0imon&rft.aufirst=J.&rft.au=Dek%C3%BD%C5%A1%2C+V.&rft.au=Pal%C4%8Dek%2C+P.&rft_id=https%3A%2F%2Fdoi.org%2F10.12693%252FAPhysPolA.138.404&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAldridge1918" class="citation book cs1">Aldridge, Arthur F. (1918). <a rel="nofollow" class="external text" href="https://archive.org/details/knotsstudyofmarl00aldr"><i>Knots, a study of marlinespike seamanship which embraces bends, hitches, ties, fastenings and splices and their practical application</i></a>. New York City: Rudder. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1047502131">1047502131</a>. <a href="/wiki/OL_(identifier)" class="mw-redirect" title="OL (identifier)">OL</a> <a rel="nofollow" class="external text" href="https://openlibrary.org/books/OL18970340M">18970340M</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Knots%2C+a+study+of+marlinespike+seamanship+which+embraces+bends%2C+hitches%2C+ties%2C+fastenings+and+splices+and+their+practical+application&rft.place=New+York+City&rft.pub=Rudder&rft.date=1918&rft_id=info%3Aoclcnum%2F1047502131&rft_id=https%3A%2F%2Fopenlibrary.org%2Fbooks%2FOL18970340M%23id-name%3DOL&rft.aulast=Aldridge&rft.aufirst=Arthur+F.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fknotsstudyofmarl00aldr&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBurgess1884" class="citation book cs1"><a href="/wiki/Joseph_Tom_Burgess" title="Joseph Tom Burgess">Burgess, J. Tom</a> (1884). <a rel="nofollow" class="external text" href="https://archive.org/details/cu31924014519940"><i>Knots, ties and splices; a handbook for seafarers, travellers, and all who use cordage; with historical, heraldic, and practical notes</i></a>. London: George Routledge and sons. <a href="/wiki/OL_(identifier)" class="mw-redirect" title="OL (identifier)">OL</a> <a rel="nofollow" class="external text" href="https://openlibrary.org/books/OL24176273M">24176273M</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Knots%2C+ties+and+splices%3B+a+handbook+for+seafarers%2C+travellers%2C+and+all+who+use+cordage%3B+with+historical%2C+heraldic%2C+and+practical+notes&rft.place=London&rft.pub=George+Routledge+and+sons&rft.date=1884&rft_id=https%3A%2F%2Fopenlibrary.org%2Fbooks%2FOL24176273M%23id-name%3DOL&rft.aulast=Burgess&rft.aufirst=J.+Tom&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcu31924014519940&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDanaPearl1922" class="citation book cs1">Dana, Homer Jackson; Pearl, William Armour (1922). <a rel="nofollow" class="external text" href="https://archive.org/details/useofropestackle00danarich"><i>The use of ropes and tackle</i></a>. Pullman, WA: Washington State College. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1158196429">1158196429</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+use+of+ropes+and+tackle&rft.place=Pullman%2C+WA&rft.pub=Washington+State+College&rft.date=1922&rft_id=info%3Aoclcnum%2F1158196429&rft.aulast=Dana&rft.aufirst=Homer+Jackson&rft.au=Pearl%2C+William+Armour&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fuseofropestackle00danarich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHasluck1907" class="citation book cs1"><a href="/wiki/Paul_Nooncree_Hasluck" title="Paul Nooncree Hasluck">Hasluck, Paul Nooncree</a> (1907). <a rel="nofollow" class="external text" href="https://archive.org/details/gri_33125000664421"><i>Knotting and splicing ropes and cordage</i></a>. Philadelphia: David McKay. <a href="/wiki/OL_(identifier)" class="mw-redirect" title="OL (identifier)">OL</a> <a rel="nofollow" class="external text" href="https://openlibrary.org/books/OL6954703M">6954703M</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Knotting+and+splicing+ropes+and+cordage&rft.place=Philadelphia&rft.pub=David+McKay&rft.date=1907&rft_id=https%3A%2F%2Fopenlibrary.org%2Fbooks%2FOL6954703M%23id-name%3DOL&rft.aulast=Hasluck&rft.aufirst=Paul+Nooncree&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgri_33125000664421&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVerrill1917" class="citation book cs1"><a href="/wiki/Alpheus_Hyatt_Verrill" title="Alpheus Hyatt Verrill">Verrill, Alpheus Hyatt</a> (1917). <a rel="nofollow" class="external text" href="https://www.gutenberg.org/ebooks/13510"><i>Knots, Splices and Rope Work</i></a>. Norman W. Henley Publishing.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Knots%2C+Splices+and+Rope+Work&rft.pub=Norman+W.+Henley+Publishing&rft.date=1917&rft.aulast=Verrill&rft.aufirst=Alpheus+Hyatt&rft_id=https%3A%2F%2Fwww.gutenberg.org%2Febooks%2F13510&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKnot" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Knot&action=edit&section=38" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikibooks-logo-en-noslogan.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, 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src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Knots" class="extiw" title="commons:Category:Knots">Knots</a></span>.</div></div> </div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist 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.navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Knots" title="Template:Knots"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Knots" title="Template talk:Knots"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Knots" title="Special:EditPage/Template:Knots"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Knots535" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Knots</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Bight_(knot)" title="Bight (knot)">Bight</a></li> <li><a href="/wiki/Loop_(knot)" class="mw-redirect" title="Loop (knot)">Loop</a></li> <li><a href="/wiki/Turn_(knot)" title="Turn (knot)">Turn</a></li> <li><a href="/wiki/List_of_knots" title="List of knots">List of knots</a></li> <li><a href="/wiki/List_of_knot_terminology" title="List of knot terminology">List of knot terminology</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_type535" style="font-size:114%;margin:0 4em">By type</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_bend_knots" class="mw-redirect" title="List of bend knots">Bends</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adjustable_bend" title="Adjustable bend">Adjustable</a></li> <li><a href="/wiki/Albright_special" title="Albright special">Albright special</a></li> <li><a href="/wiki/Ashley%27s_bend" title="Ashley's bend">Ashley's</a></li> <li><a href="/wiki/Butterfly_bend" title="Butterfly bend">Alpine butterfly</a></li> <li><a href="/wiki/Basket_weave_knot" title="Basket weave knot">Basket weave</a></li> <li><a href="/wiki/Beer_knot" title="Beer knot">Beer</a></li> <li><a href="/wiki/Blood_knot" title="Blood knot">Blood</a></li> <li><a href="/wiki/Carrick_bend" title="Carrick bend">Carrick</a></li> <li><a href="/wiki/Double_fisherman%27s_knot" title="Double fisherman's knot">Double fisherman's</a></li> <li><a href="/wiki/Fisherman%27s_knot" title="Fisherman's knot">Fisherman's</a></li> <li><a href="/wiki/Flemish_bend" title="Flemish bend">Flemish</a></li> <li><a href="/wiki/Grief_knot" title="Grief knot">Grief</a></li> <li><a href="/wiki/Halyard_bend" title="Halyard bend">Halyard</a></li> <li><a href="/wiki/Harness_bend" title="Harness bend">Harness</a></li> <li><a href="/wiki/Heaving_line_bend" title="Heaving line bend">Heaving line</a></li> <li><a href="/wiki/Hunter%27s_bend" title="Hunter's bend">Hunter's</a></li> <li><a href="/wiki/Nail_knot" title="Nail knot">Nail</a></li> <li><a href="/wiki/One-sided_overhand_bend" class="mw-redirect" title="One-sided overhand bend">One-sided overhand</a></li> <li><a href="/wiki/Racking_bend" title="Racking bend">Racking</a></li> <li><a href="/wiki/Sheet_bend" title="Sheet bend">Sheet</a></li> <li><a href="/wiki/Shoelace_knot" title="Shoelace knot">Shoelace</a></li> <li><a href="/wiki/Shroud_knot" title="Shroud knot">Shroud</a></li> <li><a href="/wiki/Simple_Simon_under" title="Simple Simon under">Simple Simon under</a></li> <li><a href="/wiki/Single_carrick_bend" title="Single carrick bend">Single carrick</a></li> <li><a href="/wiki/Surgeon%27s_knot" title="Surgeon's knot">Surgeon's</a></li> <li><a href="/wiki/Surgeon%27s_loop" title="Surgeon's loop">Surgeon's loop</a></li> <li><a href="/wiki/Triple_fisherman%27s_knot" title="Triple fisherman's knot">Triple fisherman's</a></li> <li><a href="/wiki/True_lover%27s_knot" title="True lover's knot">True lover's</a></li> <li><a href="/wiki/Water_knot" title="Water knot">Water</a></li> <li><a href="/wiki/Zeppelin_bend" title="Zeppelin bend">Zeppelin</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_binding_knots" title="List of binding knots">Binding</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boa_knot" title="Boa knot">Boa</a></li> <li><a href="/wiki/Bottle_sling" title="Bottle sling">Bottle sling</a></li> <li><a href="/wiki/Constrictor_knot" title="Constrictor knot">Constrictor</a></li> <li><a href="/wiki/Corned_beef_knot" title="Corned beef knot">Corned beef</a></li> <li><a href="/wiki/Granny_knot" title="Granny knot">Granny</a></li> <li><a href="/wiki/Ground-line_hitch" title="Ground-line hitch">Ground-line hitch</a></li> <li><a href="/wiki/Jamming_knot" title="Jamming knot">Jamming</a></li> <li><a href="/wiki/Miller%27s_knot" title="Miller's knot">Miller's</a></li> <li><a href="/wiki/Packer%27s_knot" title="Packer's knot">Packer's</a></li> <li><a href="/wiki/Reef_knot" title="Reef knot">Reef</a></li> <li><a href="/wiki/Strangle_knot" title="Strangle knot">Strangle</a></li> <li><a href="/wiki/Thief_knot" title="Thief knot">Thief</a></li> <li><a href="/wiki/Transom_knot" title="Transom knot">Transom</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_climbing_knots" title="List of climbing knots">Climbing</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Autoblock" title="Autoblock">Autoblock</a></li> <li><a href="/wiki/Bachmann_knot" title="Bachmann knot">Bachmann</a></li> <li><a href="/wiki/Beer_knot" title="Beer knot">Beer</a></li> <li><a href="/wiki/Bowline_on_a_bight" title="Bowline on a bight">Bowline on a bight</a></li> <li><a href="/wiki/Butterfly_loop" title="Butterfly loop">Alpine butterfly</a></li> <li><a href="/wiki/Directional_figure_eight" title="Directional figure eight">Directional figure eight</a></li> <li><a href="/wiki/Double_bowline" title="Double bowline">Double bowline</a></li> <li><a href="/wiki/Farmer%27s_loop" title="Farmer's loop">Farmer's loop</a></li> <li><a href="/wiki/Figure-eight_knot" title="Figure-eight knot">Figure-eight</a></li> <li><a href="/wiki/Figure-eight_loop" title="Figure-eight loop">Figure-eight loop</a></li> <li><a href="/wiki/Figure-of-nine_loop" title="Figure-of-nine loop">Figure-of-nine loop</a></li> <li><a href="/wiki/List_of_friction_hitch_knots" title="List of friction hitch knots">Friction hitch</a></li> <li><a href="/wiki/Klemheist_knot" title="Klemheist knot">Klemheist</a></li> <li><a href="/wiki/Munter_hitch" title="Munter hitch">Munter hitch</a></li> <li><a href="/wiki/Noose" title="Noose">Noose</a></li> <li><a href="/wiki/Overhand_loop" title="Overhand loop">Overhand loop</a></li> <li><a href="/wiki/Prusik" title="Prusik">Prusik</a></li> <li><a href="/wiki/Trident_loop" title="Trident loop">Trident loop</a></li> <li><a href="/wiki/Yosemite_bowline" title="Yosemite bowline">Yosemite bowline</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Coiling" title="Coiling">Coils</a> &<br /> shanks</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chain_sinnet" title="Chain sinnet">Chain sinnet</a></li> <li><a href="/wiki/Sheepshank" title="Sheepshank">Sheepshank</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_decorative_knots" class="mw-redirect" title="List of decorative knots">Decorative</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Carrick_mat" title="Carrick mat">Carrick mat</a></li> <li><a href="/wiki/Chinese_button_knot" title="Chinese button knot">Chinese button</a></li> <li><a href="/wiki/Celtic_button_knot" title="Celtic button knot">Celtic button</a></li> <li><a href="/wiki/Diamond_knot" title="Diamond knot">Diamond</a></li> <li><a href="/wiki/Fiador_knot" title="Fiador knot">Fiador</a></li> <li><a href="/wiki/Friendship_knot" title="Friendship knot">Friendship</a></li> <li><a href="/wiki/Knotted-pile_carpet" title="Knotted-pile carpet">Ghiordes & Senneh</a></li> <li><a href="/wiki/Matthew_Walker_knot" title="Matthew Walker knot">Matthew Walker</a></li> <li><a href="/wiki/Turk%27s_head_knot" title="Turk's head knot">Turk's head</a></li> <li><a href="/wiki/Wall_and_crown_knot" title="Wall and crown knot">Wall and crown</a> (triple crown knot)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Angling" title="Angling">Fishing <br />(angling)</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Angler%27s_loop" title="Angler's loop">Angler's loop</a></li> <li><a href="/wiki/Arbor_knot" title="Arbor knot">Arbor</a></li> <li><a href="/wiki/Bimini_twist" title="Bimini twist">Bimini twist</a></li> <li><a href="/wiki/Blood_knot" title="Blood knot">Blood</a></li> <li><a href="/wiki/Fisherman%27s_knot" title="Fisherman's knot">Fisherman's</a></li> <li><a href="/wiki/Improved_clinch_knot" title="Improved clinch knot">Improved clinch</a></li> <li><a href="/wiki/Knotless_knot" title="Knotless knot">Knotless</a></li> <li><a href="/wiki/Nail_knot" title="Nail knot">Nail</a></li> <li><a href="/wiki/Palomar_knot" title="Palomar knot">Palomar</a></li> <li><a href="/wiki/Snell_knot" title="Snell knot">Snell</a></li> <li><a href="/wiki/Trilene_knot" title="Trilene knot">Trilene</a></li> <li><a href="/wiki/Triple_fisherman%27s_knot" title="Triple fisherman's knot">Triple fisherman's</a></li> <li><a href="/wiki/Turle_knot" title="Turle knot">Turle</a></li> <li><a href="/wiki/Uni_knot" title="Uni knot">Uni</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_hitch_knots" class="mw-redirect" title="List of hitch knots">Hitches</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adjustable_grip_hitch" title="Adjustable grip hitch">Adjustable grip</a></li> <li><a href="/wiki/Anchor_bend" title="Anchor bend">Anchor bend</a></li> <li><a href="/wiki/Axle_hitch" title="Axle hitch">Axle</a></li> <li><a href="/wiki/Bachmann_knot" title="Bachmann knot">Bachmann</a></li> <li><a href="/wiki/Bale_sling_hitch" title="Bale sling hitch">Bale sling</a></li> <li><a href="/wiki/Barrel_hitch" title="Barrel hitch">Barrel</a></li> <li><a href="/wiki/Becket_hitch" title="Becket hitch">Becket</a></li> <li><a href="/wiki/Blackwall_hitch" title="Blackwall hitch">Blackwall</a></li> <li><a href="/wiki/Blake%27s_hitch" title="Blake's hitch">Blake's</a></li> <li><a href="/wiki/Boom_hitch" title="Boom hitch">Boom</a></li> <li><a href="/wiki/Buntline_hitch" title="Buntline hitch">Buntline</a></li> <li><a href="/wiki/Cat%27s_paw_(knot)" title="Cat's paw (knot)">Cat's paw</a></li> <li><a href="/wiki/Clove_hitch" title="Clove hitch">Clove</a></li> <li><a href="/wiki/Cow_hitch" title="Cow hitch">Cow</a></li> <li><a href="/wiki/Distel_hitch" title="Distel hitch">Distel</a></li> <li><a href="/wiki/Double_overhand_noose" title="Double overhand noose">Double overhand noose</a></li> <li><a href="/wiki/Falconer%27s_knot" title="Falconer's knot">Falconer's</a></li> <li><a href="/wiki/Farrimond_friction_hitch" title="Farrimond friction hitch">Farrimond friction</a></li> <li><a href="/wiki/List_of_friction_hitch_knots" title="List of friction hitch knots">Friction hitch</a></li> <li><a href="/wiki/Garda_hitch" title="Garda hitch">Garda</a></li> <li><a href="/wiki/Ground-line_hitch" title="Ground-line hitch">Ground-line</a></li> <li><a href="/wiki/Half_hitch" title="Half hitch">Half</a></li> <li><a href="/wiki/Halter_hitch" title="Halter hitch">Halter</a></li> <li><a href="/wiki/Highpoint_hitch" title="Highpoint hitch">Highpoint</a></li> <li><a href="/wiki/Highwayman%27s_hitch" title="Highwayman's hitch">Highwayman's</a></li> <li><a href="/wiki/Hitching_tie" title="Hitching tie">Hitching tie</a></li> <li><a href="/wiki/Icicle_hitch" title="Icicle hitch">Icicle</a></li> <li><a href="/wiki/Improved_clinch_knot" title="Improved clinch knot">Improved clinch</a></li> <li><a href="/wiki/Killick_hitch" title="Killick hitch">Killick</a></li> <li><a href="/wiki/Knute_hitch" title="Knute hitch">Knute</a></li> <li><a href="/wiki/Lobster_buoy_hitch" title="Lobster buoy hitch">Lobster buoy</a></li> <li><a href="/wiki/Marlinespike_hitch" title="Marlinespike hitch">Marlinespike</a></li> <li><a href="/wiki/Munter_hitch" title="Munter hitch">Munter</a></li> <li><a href="/wiki/Ossel_hitch" title="Ossel hitch">Ossel</a></li> <li><a href="/wiki/Pile_hitch" title="Pile hitch">Pile</a></li> <li><a href="/wiki/Pipe_hitch" title="Pipe hitch">Pipe</a></li> <li><a href="/wiki/Sailor%27s_hitch" title="Sailor's hitch">Sailor's</a></li> <li><a href="/wiki/Snuggle_hitch" title="Snuggle hitch">Snuggle</a></li> <li><a href="/wiki/Swing_hitch" title="Swing hitch">Swing</a></li> <li><a href="/wiki/Taut-line_hitch" title="Taut-line hitch">Taut-line</a></li> <li><a href="/wiki/Timber_hitch" title="Timber hitch">Timber</a></li> <li><a href="/wiki/Trucker%27s_hitch" title="Trucker's hitch">Trucker's</a></li> <li><a href="/wiki/Tumble_hitch" title="Tumble hitch">Tumble</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Loop_(knot)" class="mw-redirect" title="Loop (knot)">Loop</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Angler%27s_loop" title="Angler's loop">Angler's</a></li> <li><a href="/wiki/Artillery_loop" title="Artillery loop">Artillery loop</a></li> <li><a href="/wiki/Bale_sling_hitch" title="Bale sling hitch">Bale sling hitch</a></li> <li><a href="/wiki/Bowline" title="Bowline">Bowline</a></li> <li><a href="/wiki/Bumper_knot" title="Bumper knot">Bumper</a></li> <li><a href="/wiki/Carrick_bend_loop" title="Carrick bend loop">Carrick bend loop</a></li> <li><a href="/wiki/Cossack_knot" class="mw-redirect" title="Cossack knot">Cossack</a></li> <li><a href="/wiki/Cowboy_bowline" title="Cowboy bowline">Cowboy bowline</a></li> <li><a href="/wiki/Diamond_knot" title="Diamond knot">Diamond</a></li> <li><a href="/wiki/Double_bowline" title="Double bowline">Double bowline</a></li> <li><a href="/wiki/Dropper_loop" title="Dropper loop">Dropper loop</a></li> <li><a href="/wiki/Eskimo_bowline" title="Eskimo bowline">Eskimo bowline</a></li> <li><a href="/wiki/Fiador_knot" title="Fiador knot">Fiador</a></li> <li><a href="/wiki/Fireman%27s_chair_knot" title="Fireman's chair knot">Fireman's chair</a></li> <li><a href="/wiki/Friendship_knot_loop" title="Friendship knot loop">Friendship knot</a></li> <li><a href="/wiki/Halter_hitch" title="Halter hitch">Halter hitch</a></li> <li><a href="/wiki/Handcuff_knot" title="Handcuff knot">Handcuff</a></li> <li><a href="/wiki/Honda_knot" title="Honda knot">Honda</a></li> <li><a href="/wiki/Jury_mast_knot" title="Jury mast knot">Jury mast</a></li> <li><a href="/wiki/Overhand_loop" title="Overhand loop">Overhand</a></li> <li><a href="/wiki/Portuguese_bowline" title="Portuguese bowline">Portuguese bowline</a></li> <li><a href="/wiki/Rigid_double_splayed_loop_in_the_bight" title="Rigid double splayed loop in the bight">Rigid double splayed loop in the bight</a></li> <li><a href="/wiki/Slippery_eight_loop" title="Slippery eight loop">Slippery eight</a></li> <li><a href="/wiki/Span_loop" title="Span loop">Span</a></li> <li><a href="/wiki/Spanish_bowline" title="Spanish bowline">Spanish bowline</a></li> <li><a href="/wiki/Tom_fool%27s_knot" title="Tom fool's knot">Tom fool's</a></li> <li><a href="/wiki/Trident_loop" title="Trident loop">Trident</a></li> <li><a href="/wiki/Triple_bowline" title="Triple bowline">Triple bowline</a></li> <li><a href="/wiki/Water_bowline" title="Water bowline">Water bowline</a></li> <li><a href="/wiki/Yosemite_bowline" title="Yosemite bowline">Yosemite bowline</a></li> <li><a href="/wiki/Zeppelin_loop" title="Zeppelin loop">Zeppelin</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Slip_knot" title="Slip knot">Running<br /> (slip)</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hangman%27s_knot" title="Hangman's knot">Hangman's</a></li> <li><a href="/wiki/Running_bowline" title="Running bowline">Running bowline</a></li> <li>Running highwayman's hitch</li> <li><a href="/wiki/Tarbuck_knot" title="Tarbuck knot">Tarbuck</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Rope_splicing" title="Rope splicing">Splices</a> &<br /> splicing</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Eye_splice" title="Eye splice">Eye</a></li> <li><a href="/wiki/Fid" title="Fid">Fid</a></li> <li><a href="/wiki/Marlinspike" title="Marlinspike">Marlinspike</a></li> <li><a href="/wiki/Rat-tail_splice" title="Rat-tail splice">Rat-tail</a></li> <li><a href="/wiki/T-splice" title="T-splice">T</a></li> <li><a href="/wiki/Western_Union_splice" title="Western Union splice">Western Union</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Stopper_knot" title="Stopper knot">Stopper</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ashley%27s_stopper_knot" title="Ashley's stopper knot">Ashley's stopper</a></li> <li><a href="/wiki/Button_knot" title="Button knot">Button</a></li> <li><a href="/wiki/Double_overhand_knot" title="Double overhand knot">Double overhand</a></li> <li><a href="/wiki/Figure-eight_knot" title="Figure-eight knot">Figure-eight knot</a></li> <li><a href="/wiki/Monkey%27s_fist" title="Monkey's fist">Monkey's fist</a></li> <li><a href="/wiki/Overhand_knot" title="Overhand knot">Overhand</a></li> <li><a href="/wiki/Stevedore_knot" title="Stevedore knot">Stevedore</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Whipping_knot" title="Whipping knot">Whipping</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Common_whipping" title="Common whipping">Common</a></li> <li><a href="/wiki/Overhand_knot_with_draw-loop" title="Overhand knot with draw-loop">Overhand knot with draw-loop</a></li> <li><a href="/wiki/Portuguese_whipping" class="mw-redirect" title="Portuguese whipping">Portuguese</a></li> <li><a href="/wiki/Sailmaker%27s_whipping" title="Sailmaker's whipping">Sailmaker's</a></li> <li><a href="/wiki/West_Country_whipping" title="West Country whipping">West Country</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Lists_of_knotsRelated_topics535" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li>Lists of knots</li><li>Related topics</li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Lists of knots</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_bend_knots" class="mw-redirect" title="List of bend knots">Bends</a></li> <li><a href="/wiki/List_of_binding_knots" title="List of binding knots">Bindings</a></li> <li><a href="/wiki/List_of_decorative_knots" class="mw-redirect" title="List of decorative knots">Decorative knots</a></li> <li><a href="/wiki/List_of_hitch_knots" class="mw-redirect" title="List of hitch knots">Hitches</a> (<a href="/wiki/List_of_friction_hitch_knots" title="List of friction hitch knots">friction</a>)</li> <li><a href="/wiki/List_of_mathematical_knots_and_links" title="List of mathematical knots and links">Mathematical</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chinese_knotting" title="Chinese knotting">Chinese knotting</a></li> <li><a href="/wiki/Knot_density" title="Knot density">Density</a></li> <li><a href="/wiki/History_of_knotting" class="mw-redirect" title="History of knotting">History</a></li> <li><a href="/wiki/International_Guild_of_Knot_Tyers" title="International Guild of Knot Tyers">International Guild of Knot Tyers</a></li> <li><a href="/wiki/Macram%C3%A9" title="Macramé">Macramé</a></li> <li><i><a href="/wiki/Mizuhiki" title="Mizuhiki">Mizuhiki</a></i></li> <li><i><a href="/wiki/Norigae" title="Norigae">Norigae</a></i></li> <li><a href="/wiki/Ropework" title="Ropework">Ropework</a> <ul><li><a href="/wiki/Lashing_(ropework)" title="Lashing (ropework)">Lashing</a></li> <li><a href="/wiki/Rope_splicing" title="Rope splicing">Splicing</a></li> <li><a href="/wiki/Seizing" title="Seizing">Seizing</a></li></ul></li> <li><a href="/wiki/Sennit" title="Sennit">Sennit</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="font-weight:bold;padding-bottom:0.3em;"><div> <ul><li> <span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Knots" title="Category:Knots">Category</a></li> <li> <span class="noviewer" typeof="mw:File"><span title="WikiProject"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /></span></span> <a href="/wiki/Wikipedia:WikiProject_Knots" title="Wikipedia:WikiProject Knots">WikiProject</a></li> <li> <span style="position:relative; bottom:1px;"><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></span> <a href="https://commons.wikimedia.org/wiki/Category:Knots" class="extiw" title="commons:Category:Knots">Commons</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Mathematics_and_art295" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Mathematics_and_art" title="Template:Mathematics and art"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Mathematics_and_art" title="Template talk:Mathematics and art"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Mathematics_and_art" title="Special:EditPage/Template:Mathematics and art"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Mathematics_and_art295" style="font-size:114%;margin:0 4em"><a href="/wiki/Mathematics_and_art" title="Mathematics and art">Mathematics and art</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algorithm" title="Algorithm">Algorithm</a></li> <li><a href="/wiki/Catenary" title="Catenary">Catenary</a></li> <li><a href="/wiki/Fractal" title="Fractal">Fractal</a></li> <li><a href="/wiki/Golden_ratio" title="Golden ratio">Golden ratio</a></li> <li><a href="/wiki/Hyperboloid_structure" title="Hyperboloid structure">Hyperboloid structure</a></li> <li><a href="/wiki/Minimal_surface" title="Minimal surface">Minimal surface</a></li> <li><a href="/wiki/Paraboloid" title="Paraboloid">Paraboloid</a></li> <li><a href="/wiki/Perspective_(graphical)" title="Perspective (graphical)">Perspective</a> <ul><li><a href="/wiki/Camera_lucida" title="Camera lucida">Camera lucida</a></li> <li><a href="/wiki/Camera_obscura" title="Camera obscura">Camera obscura</a></li></ul></li> <li><a href="/wiki/Plastic_ratio" title="Plastic ratio">Plastic ratio</a></li> <li><a href="/wiki/Projective_geometry" title="Projective geometry">Projective geometry</a></li> <li>Proportion <ul><li><a href="/wiki/Proportion_(architecture)" title="Proportion (architecture)">Architecture</a></li> <li><a href="/wiki/Body_proportions" title="Body proportions">Human</a></li></ul></li> <li><a href="/wiki/Symmetry" title="Symmetry">Symmetry</a></li> <li><a href="/wiki/Tessellation" title="Tessellation">Tessellation</a></li> <li><a href="/wiki/Wallpaper_group" title="Wallpaper group">Wallpaper group</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="9" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:FWF_Samuel_Monnier_(vertical_detail).jpg" class="mw-file-description" title="Fibonacci word: detail of artwork by Samuel Monnier, 2009"><img alt="Fibonacci word: detail of artwork by Samuel Monnier, 2009" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/FWF_Samuel_Monnier_%28vertical_detail%29.jpg/75px-FWF_Samuel_Monnier_%28vertical_detail%29.jpg" decoding="async" width="75" height="187" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/FWF_Samuel_Monnier_%28vertical_detail%29.jpg/113px-FWF_Samuel_Monnier_%28vertical_detail%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/FWF_Samuel_Monnier_%28vertical_detail%29.jpg/150px-FWF_Samuel_Monnier_%28vertical_detail%29.jpg 2x" data-file-width="281" data-file-height="700" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Forms</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algorithmic_art" title="Algorithmic art">Algorithmic art</a></li> <li><a href="/wiki/Anamorphosis" title="Anamorphosis">Anamorphic art</a></li> <li><a href="/wiki/Mathematics_and_architecture" title="Mathematics and architecture">Architecture</a> <ul><li><a href="/wiki/Geodesic_dome" title="Geodesic dome">Geodesic dome</a></li> <li><a href="/wiki/Pyramid" title="Pyramid">Pyramid</a></li> <li><a href="/wiki/Vastu_shastra" title="Vastu shastra">Vastu shastra</a></li></ul></li> <li><a href="/wiki/Computer_art" title="Computer art">Computer art</a></li> <li><a href="/wiki/Mathematics_and_fiber_arts" title="Mathematics and fiber arts">Fiber arts</a></li> <li><a href="/wiki/Fourth_dimension_in_art" title="Fourth dimension in art">4D art</a></li> <li><a href="/wiki/Fractal_art" title="Fractal art">Fractal art</a></li> <li><a href="/wiki/Islamic_geometric_patterns" title="Islamic geometric patterns">Islamic geometric patterns</a> <ul><li><a href="/wiki/Girih" title="Girih">Girih</a></li> <li><a href="/wiki/Jali" title="Jali">Jali</a></li> <li><a href="/wiki/Muqarnas" title="Muqarnas">Muqarnas</a></li> <li><a href="/wiki/Zellij" title="Zellij">Zellij</a></li></ul></li> <li><a class="mw-selflink selflink">Knotting</a> <ul><li><a href="/wiki/Celtic_knot" title="Celtic knot">Celtic knot</a></li> <li><a href="/wiki/Croatian_interlace" title="Croatian interlace">Croatian interlace</a></li> <li><a href="/wiki/Interlace_(art)" title="Interlace (art)">Interlace</a></li></ul></li> <li><a href="/wiki/Music_and_mathematics" title="Music and mathematics">Music</a></li> <li><a href="/wiki/Origami" title="Origami">Origami</a> <ul><li><a href="/wiki/Mathematics_of_paper_folding" title="Mathematics of paper folding">Mathematics</a></li></ul></li> <li><a href="/wiki/Mathematical_sculpture" title="Mathematical sculpture">Sculpture</a></li> <li><a href="/wiki/String_art" title="String art">String art</a></li> <li><a href="/wiki/String_figure" title="String figure">String figure</a></li> <li><a href="/wiki/Tessellation" title="Tessellation">Tiling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Artworks</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_works_designed_with_the_golden_ratio" title="List of works designed with the golden ratio">List of works designed with the golden ratio</a></li> <li><i><a href="/wiki/Continuum_(sculpture)" title="Continuum (sculpture)">Continuum</a></i></li> <li><i><a href="/wiki/Mathemalchemy" title="Mathemalchemy">Mathemalchemy</a></i></li> <li><i><a href="/wiki/Mathematica:_A_World_of_Numbers..._and_Beyond" title="Mathematica: A World of Numbers... and Beyond">Mathematica: A World of Numbers... and Beyond</a></i></li> <li><i><a href="/wiki/Octacube_(sculpture)" title="Octacube (sculpture)">Octacube</a></i></li> <li><i><a href="/wiki/Pi_(art_project)" title="Pi (art project)">Pi</a></i></li> <li><i><a href="/wiki/Pi_in_the_Sky" title="Pi in the Sky">Pi in the Sky</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mathematics_and_architecture" title="Mathematics and architecture">Buildings</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cathedral_of_Saint_Mary_of_the_Assumption_(San_Francisco)" title="Cathedral of Saint Mary of the Assumption (San Francisco)">Cathedral of Saint Mary of the Assumption</a></li> <li><a href="/wiki/Hagia_Sophia" title="Hagia Sophia">Hagia Sophia</a></li> <li><a href="/wiki/Kresge_Auditorium" title="Kresge Auditorium">Kresge Auditorium</a></li> <li><a href="/wiki/Pantheon,_Rome" title="Pantheon, Rome">Pantheon</a></li> <li><a href="/wiki/Parthenon" title="Parthenon">Parthenon</a></li> <li><a href="/wiki/Great_Pyramid_of_Giza" title="Great Pyramid of Giza">Pyramid of Khufu</a></li> <li><a href="/wiki/Sagrada_Fam%C3%ADlia" title="Sagrada Família">Sagrada Família</a></li> <li><a href="/wiki/Sydney_Opera_House" title="Sydney Opera House">Sydney Opera House</a></li> <li><a href="/wiki/Taj_Mahal" title="Taj Mahal">Taj Mahal</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_mathematical_artists" title="List of mathematical artists">Artists</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Renaissance</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Paolo_Uccello" title="Paolo Uccello">Paolo Uccello</a></li> <li><a href="/wiki/Piero_della_Francesca" title="Piero della Francesca">Piero della Francesca</a></li> <li><a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a> <ul><li><i><a href="/wiki/Vitruvian_Man" title="Vitruvian Man">Vitruvian Man</a></i></li></ul></li> <li><a href="/wiki/Albrecht_D%C3%BCrer" title="Albrecht Dürer">Albrecht Dürer</a></li> <li><a href="/wiki/Parmigianino" title="Parmigianino">Parmigianino</a> <ul><li><i><a href="/wiki/Self-portrait_in_a_Convex_Mirror" class="mw-redirect" title="Self-portrait in a Convex Mirror">Self-portrait in a Convex Mirror</a></i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">19th–20th<br />Century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/William_Blake" title="William Blake">William Blake</a> <ul><li><i><a href="/wiki/The_Ancient_of_Days" title="The Ancient of Days">The Ancient of Days</a></i></li> <li><i><a href="/wiki/Newton_(Blake)" title="Newton (Blake)">Newton</a></i></li></ul></li> <li><a href="/wiki/Jean_Metzinger" title="Jean Metzinger">Jean Metzinger</a> <ul><li><i><a href="/wiki/Dancer_in_a_Caf%C3%A9" title="Dancer in a Café">Danseuse au café</a></i></li> <li><i><a href="/wiki/L%27Oiseau_bleu_(Metzinger)" class="mw-redirect" title="L'Oiseau bleu (Metzinger)">L'Oiseau bleu</a></i></li></ul></li> <li><a href="/wiki/Giorgio_de_Chirico" title="Giorgio de Chirico">Giorgio de Chirico</a></li> <li><a href="/wiki/Man_Ray" title="Man Ray">Man Ray</a></li> <li><a href="/wiki/M._C._Escher" title="M. C. Escher">M. C. Escher</a> <ul><li><i><a href="/wiki/Circle_Limit_III" title="Circle Limit III">Circle Limit III</a></i></li> <li><i><a href="/wiki/Print_Gallery_(M._C._Escher)" title="Print Gallery (M. C. Escher)">Print Gallery</a></i></li> <li><i><a href="/wiki/Relativity_(M._C._Escher)" title="Relativity (M. C. Escher)">Relativity</a></i></li> <li><i><a href="/wiki/Reptiles_(M._C._Escher)" title="Reptiles (M. C. Escher)">Reptiles</a></i></li> <li><i><a href="/wiki/Waterfall_(M._C._Escher)" title="Waterfall (M. C. Escher)">Waterfall</a></i></li></ul></li> <li><a href="/wiki/Ren%C3%A9_Magritte" title="René Magritte">René Magritte</a> <ul><li><i><a href="/wiki/The_Human_Condition_(Magritte)" title="The Human Condition (Magritte)">La condition humaine</a></i></li></ul></li> <li><a href="/wiki/Salvador_Dal%C3%AD" title="Salvador Dalí">Salvador Dalí</a> <ul><li><i><a href="/wiki/Crucifixion_(Corpus_Hypercubus)" title="Crucifixion (Corpus Hypercubus)">Crucifixion</a></i></li> <li><i><a href="/wiki/The_Swallow%27s_Tail" title="The Swallow's Tail">The Swallow's Tail</a></i></li></ul></li> <li><a href="/wiki/Crockett_Johnson" title="Crockett Johnson">Crockett Johnson</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Contemporary</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Max_Bill" title="Max Bill">Max Bill</a></li> <li><a href="/wiki/Martin_Demaine" title="Martin Demaine">Martin</a> and <a href="/wiki/Erik_Demaine" title="Erik Demaine">Erik Demaine</a></li> <li><a href="/wiki/Scott_Draves" title="Scott Draves">Scott Draves</a></li> <li><a href="/wiki/Jan_Dibbets" title="Jan Dibbets">Jan Dibbets</a></li> <li><a href="/wiki/John_Ernest" title="John Ernest">John Ernest</a></li> <li><a href="/wiki/Helaman_Ferguson" title="Helaman Ferguson">Helaman Ferguson</a></li> <li><a href="/wiki/Peter_Forakis" title="Peter Forakis">Peter Forakis</a></li> <li><a href="/wiki/Susan_Goldstine" title="Susan Goldstine">Susan Goldstine</a></li> <li><a href="/wiki/Bathsheba_Grossman" title="Bathsheba Grossman">Bathsheba Grossman</a></li> <li><a href="/wiki/George_W._Hart" title="George W. Hart">George W. Hart</a></li> <li><a href="/wiki/Desmond_Paul_Henry" title="Desmond Paul Henry">Desmond Paul Henry</a></li> <li><a href="/wiki/Anthony_Hill_(artist)" title="Anthony Hill (artist)">Anthony Hill</a></li> <li><a href="/wiki/Charles_Jencks" title="Charles Jencks">Charles Jencks</a> <ul><li><i><a href="/wiki/Garden_of_Cosmic_Speculation" title="Garden of Cosmic Speculation">Garden of Cosmic Speculation</a></i></li></ul></li> <li><a href="/wiki/Andy_Lomas" title="Andy Lomas">Andy Lomas</a></li> <li><a href="/wiki/Robert_Longhurst" title="Robert Longhurst">Robert Longhurst</a></li> <li><a href="/wiki/Jeanette_McLeod" title="Jeanette McLeod">Jeanette McLeod</a></li> <li><a href="/wiki/Hamid_Naderi_Yeganeh" title="Hamid Naderi Yeganeh">Hamid Naderi Yeganeh</a></li> <li><a href="/wiki/Istv%C3%A1n_Orosz" title="István Orosz">István Orosz</a></li> <li><a href="/wiki/Hinke_Osinga" title="Hinke Osinga">Hinke Osinga</a></li> <li><a href="/wiki/Antoine_Pevsner" title="Antoine Pevsner">Antoine Pevsner</a></li> <li><a href="/wiki/Tony_Robbin" title="Tony Robbin">Tony Robbin</a></li> <li><a href="/wiki/Alba_Rojo_Cama" title="Alba Rojo Cama">Alba Rojo Cama</a></li> <li><a href="/wiki/Reza_Sarhangi" class="mw-redirect" title="Reza Sarhangi">Reza Sarhangi</a></li> <li><a href="/wiki/Oliver_Sin" title="Oliver Sin">Oliver Sin</a></li> <li><a href="/wiki/Hiroshi_Sugimoto" title="Hiroshi Sugimoto">Hiroshi Sugimoto</a></li> <li><a href="/wiki/Daina_Taimi%C5%86a" title="Daina Taimiņa">Daina Taimiņa</a></li> <li><a href="/wiki/Roman_Verostko" title="Roman Verostko">Roman Verostko</a></li> <li><a href="/wiki/Margaret_Wertheim" title="Margaret Wertheim">Margaret Wertheim</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theorists</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Ancient</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Polykleitos" title="Polykleitos">Polykleitos</a> <ul><li><i>Canon</i></li></ul></li> <li><a href="/wiki/Vitruvius" title="Vitruvius">Vitruvius</a> <ul><li><i><a href="/wiki/De_architectura" title="De architectura">De architectura</a></i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Renaissance</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Filippo_Brunelleschi" title="Filippo Brunelleschi">Filippo Brunelleschi</a></li> <li><a href="/wiki/Leon_Battista_Alberti" title="Leon Battista Alberti">Leon Battista Alberti</a> <ul><li><i><a href="/wiki/De_pictura" title="De pictura">De pictura</a></i></li> <li><i><a href="/wiki/De_re_aedificatoria" title="De re aedificatoria">De re aedificatoria</a></i></li></ul></li> <li><a href="/wiki/Piero_della_Francesca" title="Piero della Francesca">Piero della Francesca</a> <ul><li><i><a href="/wiki/De_prospectiva_pingendi" title="De prospectiva pingendi">De prospectiva pingendi</a></i></li></ul></li> <li><a href="/wiki/Luca_Pacioli" title="Luca Pacioli">Luca Pacioli</a> <ul><li><i><a href="/wiki/Divina_proportione" title="Divina proportione">De divina proportione</a></i></li></ul></li> <li><a href="/wiki/Leonardo_da_Vinci" title="Leonardo da Vinci">Leonardo da Vinci</a> <ul><li><i><a href="/wiki/A_Treatise_on_Painting" title="A Treatise on Painting">A Treatise on Painting</a></i></li></ul></li> <li><a href="/wiki/Albrecht_D%C3%BCrer" title="Albrecht Dürer">Albrecht Dürer</a> <ul><li><i>Vier Bücher von Menschlicher Proportion</i></li></ul></li> <li><a href="/wiki/Sebastiano_Serlio" title="Sebastiano Serlio">Sebastiano Serlio</a> <ul><li><i>Regole generali d'architettura</i></li></ul></li> <li><a href="/wiki/Andrea_Palladio" title="Andrea Palladio">Andrea Palladio</a> <ul><li><i><a href="/wiki/I_quattro_libri_dell%27architettura" title="I quattro libri dell'architettura">I quattro libri dell'architettura</a></i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Romantic</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Samuel_Colman" title="Samuel Colman">Samuel Colman</a> <ul><li><i>Nature's Harmonic Unity</i></li></ul></li> <li><a href="/wiki/Frederik_Macody_Lund" title="Frederik Macody Lund">Frederik Macody Lund</a> <ul><li><i>Ad Quadratum</i></li></ul></li> <li><a href="/wiki/Jay_Hambidge" title="Jay Hambidge">Jay Hambidge</a> <ul><li><i>The Greek Vase</i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modern</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Owen_Jones_(architect)" title="Owen Jones (architect)">Owen Jones</a> <ul><li><i><a href="/wiki/Owen_Jones_(architect)#The_Grammar_of_Ornament" title="Owen Jones (architect)">The Grammar of Ornament</a></i></li></ul></li> <li><a href="/wiki/Ernest_Hanbury_Hankin" title="Ernest Hanbury Hankin">Ernest Hanbury Hankin</a> <ul><li><i>The Drawing of Geometric Patterns in Saracenic Art</i></li></ul></li> <li><a href="/wiki/G._H._Hardy" title="G. H. Hardy">G. H. Hardy</a> <ul><li><i><a href="/wiki/A_Mathematician%27s_Apology" title="A Mathematician's Apology">A Mathematician's Apology</a></i></li></ul></li> <li><a href="/wiki/George_David_Birkhoff" title="George David Birkhoff">George David Birkhoff</a> <ul><li><i>Aesthetic Measure</i></li></ul></li> <li><a href="/wiki/Douglas_Hofstadter" title="Douglas Hofstadter">Douglas Hofstadter</a> <ul><li><i><a href="/wiki/G%C3%B6del,_Escher,_Bach" title="Gödel, Escher, Bach">Gödel, Escher, Bach</a></i></li></ul></li> <li><a href="/wiki/Nikos_Salingaros" title="Nikos Salingaros">Nikos Salingaros</a> <ul><li><i>The 'Life' of a Carpet</i></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Publications</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Journal_of_Mathematics_and_the_Arts" title="Journal of Mathematics and the Arts">Journal of Mathematics and the Arts</a></i></li> <li><i><a href="/wiki/Lumen_Naturae" title="Lumen Naturae">Lumen Naturae</a></i></li> <li><i><a href="/wiki/Making_Mathematics_with_Needlework" title="Making Mathematics with Needlework">Making Mathematics with Needlework</a></i></li> <li><i><a href="/wiki/Rhythm_of_Structure" title="Rhythm of Structure">Rhythm of Structure</a></i></li> <li><i><a href="/wiki/Viewpoints:_Mathematical_Perspective_and_Fractal_Geometry_in_Art" title="Viewpoints: Mathematical Perspective and Fractal Geometry in Art">Viewpoints: Mathematical Perspective and Fractal Geometry in Art</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Organizations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ars_Mathematica_(organization)" title="Ars Mathematica (organization)">Ars Mathematica</a></li> <li><a href="/wiki/The_Bridges_Organization" title="The Bridges Organization">The Bridges Organization</a></li> <li><a href="/wiki/European_Society_for_Mathematics_and_the_Arts" title="European Society for Mathematics and the Arts">European Society for Mathematics and the Arts</a></li> <li><a href="/wiki/Goudreau_Museum_of_Mathematics_in_Art_and_Science" title="Goudreau Museum of Mathematics in Art and Science">Goudreau Museum of Mathematics in Art and Science</a></li> <li><a href="/wiki/Institute_For_Figuring" title="Institute For Figuring">Institute For Figuring</a></li> <li><a href="/wiki/Mathemalchemy" title="Mathemalchemy">Mathemalchemy</a></li> <li><a href="/wiki/National_Museum_of_Mathematics" title="National Museum of Mathematics">National Museum of Mathematics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Droste_effect" title="Droste effect">Droste effect</a></li> <li><a href="/wiki/Mathematical_beauty" title="Mathematical beauty">Mathematical beauty</a></li> <li><a href="/wiki/Patterns_in_nature" title="Patterns in nature">Patterns in nature</a></li> <li><a href="/wiki/Sacred_geometry" title="Sacred geometry">Sacred geometry</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a 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