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id="toc-Environmental_heterogeneity" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Environmental_heterogeneity"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Environmental heterogeneity</span> </div> </a> <ul id="toc-Environmental_heterogeneity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Chemistry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Chemistry"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Chemistry</span> </div> </a> <ul id="toc-Chemistry-sublist" class="vector-toc-list"> <li id="toc-Homogeneous_and_heterogeneous_mixtures" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Homogeneous_and_heterogeneous_mixtures"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>Homogeneous and heterogeneous mixtures</span> </div> </a> <ul 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<span>Linguistics</span> </div> </a> <ul id="toc-Linguistics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Information_technology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Information_technology"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Information technology</span> </div> </a> <ul id="toc-Information_technology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mathematics_and_statistics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mathematics_and_statistics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Mathematics and statistics</span> </div> </a> <ul id="toc-Mathematics_and_statistics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Medicine" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Medicine"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Medicine</span> </div> </a> <ul id="toc-Medicine-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Physics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Physics</span> </div> </a> <ul id="toc-Physics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sociology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sociology"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.9</span> <span>Sociology</span> </div> </a> <ul id="toc-Sociology-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</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" > <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">Homogeneity and heterogeneity</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 17 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-17" 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">17 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AC%D8%A7%D9%86%D8%B3_%D9%88%D8%AA%D8%BA%D8%A7%D9%8A%D8%B1" title="تجانس وتغاير – Arabic" lang="ar" hreflang="ar" data-title="تجانس وتغاير" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%AE%E0%A6%B8%E0%A6%A4%E0%A7%8D%E0%A6%AC%E0%A6%A4%E0%A6%BE_%E0%A6%93_%E0%A6%85%E0%A6%B8%E0%A6%AE%E0%A6%B8%E0%A6%A4%E0%A7%8D%E0%A6%AC%E0%A6%A4%E0%A6%BE" title="সমসত্বতা ও অসমসত্বতা – Bangla" lang="bn" hreflang="bn" data-title="সমসত্বতা ও অসমসত্বতা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Heterogenit%C3%A4t" title="Heterogenität – German" lang="de" hreflang="de" data-title="Heterogenität" 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/Homogeensus_ja_heterogeensus" title="Homogeensus ja heterogeensus – Estonian" lang="et" hreflang="et" data-title="Homogeensus ja heterogeensus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Homogeneo_eta_heterogeneo" title="Homogeneo eta heterogeneo – Basque" lang="eu" hreflang="eu" data-title="Homogeneo eta heterogeneo" 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/%D9%87%D9%85%DA%AF%D9%86_%D9%88_%D9%86%D8%A7%D9%87%D9%85%DA%AF%D9%86" title="همگن و ناهمگن – Persian" lang="fa" hreflang="fa" data-title="همگن و ناهمگن" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Homogenitas_dan_heterogenitas" title="Homogenitas dan heterogenitas – Indonesian" lang="id" hreflang="id" data-title="Homogenitas dan heterogenitas" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Omogeneit%C3%A0_ed_eterogeneit%C3%A0" title="Omogeneità ed eterogeneità – Italian" lang="it" hreflang="it" data-title="Omogeneità ed eterogeneità" 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%94%D7%95%D7%9E%D7%95%D7%92%D7%A0%D7%99%D7%95%D7%AA_%D7%95%D7%94%D7%98%D7%A8%D7%95%D7%92%D7%A0%D7%99%D7%95%D7%AA" title="הומוגניות והטרוגניות – Hebrew" lang="he" hreflang="he" data-title="הומוגניות והטרוגניות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D1%96%D1%80%D1%82%D0%B5%D0%BA%D1%82%D1%96%D0%BB%D1%96%D0%BA_%D0%B6%D3%99%D0%BD%D0%B5_%D3%99%D1%80%D1%82%D0%B5%D0%BA%D1%82%D1%96%D0%BB%D1%96%D0%BA" title="Біртектілік және әртектілік – Kazakh" lang="kk" hreflang="kk" data-title="Біртектілік және әртектілік" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kehomogenan_dan_keheterogenan" title="Kehomogenan dan keheterogenan – Malay" lang="ms" hreflang="ms" data-title="Kehomogenan dan keheterogenan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Homogenitet_og_heterogenitet" title="Homogenitet og heterogenitet – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Homogenitet og heterogenitet" 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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Homogeneidade_e_heterogeneidade" title="Homogeneidade e heterogeneidade – Portuguese" lang="pt" hreflang="pt" data-title="Homogeneidade e heterogeneidade" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Homogenost_i_heterogenost" title="Homogenost i heterogenost – Serbian" lang="sr" hreflang="sr" data-title="Homogenost i heterogenost" 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-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Homogenost_i_heterogenost" title="Homogenost i heterogenost – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Homogenost i heterogenost" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Talu%E1%BA%93ert_d_tru%E1%BA%93ert" title="Taluẓert d truẓert – Kabyle" lang="kab" hreflang="kab" data-title="Taluẓert d truẓert" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" 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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 other uses, see <a href="/wiki/Homogeneity_(disambiguation)" class="mw-disambig" title="Homogeneity (disambiguation)">Homogeneity (disambiguation)</a> and <a href="/wiki/Heterogeneity_(disambiguation)" class="mw-disambig" title="Heterogeneity (disambiguation)">Heterogeneity (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Homog%C3%A8ne_h%C3%A9t%C3%A9rog%C3%A8ne.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Homog%C3%A8ne_h%C3%A9t%C3%A9rog%C3%A8ne.png/220px-Homog%C3%A8ne_h%C3%A9t%C3%A9rog%C3%A8ne.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/47/Homog%C3%A8ne_h%C3%A9t%C3%A9rog%C3%A8ne.png 1.5x" data-file-width="300" data-file-height="300" /></a><figcaption>Homogeneity and heterogeneity;<br />only '<b><span style="font-size:85%;">b</span>'</b> is homogeneous</figcaption></figure> <p><b>Homogeneity and heterogeneity</b> are concepts relating to the <a href="/wiki/Uniformity_(chemistry)" class="mw-redirect" title="Uniformity (chemistry)">uniformity</a> of a <a href="/wiki/Chemical_substance" title="Chemical substance">substance</a>, process or image. A <b>homogeneous</b> feature is uniform in composition or character (i.e. color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is <b>heterogeneous</b> is distinctly nonuniform in at least one of these qualities.<sup id="cite_ref-websters-hetrogeneity_1-0" class="reference"><a href="#cite_note-websters-hetrogeneity-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Heterogeneous_2-0" class="reference"><a href="#cite_note-Heterogeneous-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymology_and_spelling">Etymology and spelling</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=1" title="Edit section: Etymology and spelling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The words <i>homogeneous</i> and <i>heterogeneous</i> come from <a href="/wiki/Medieval_Latin" title="Medieval Latin">Medieval Latin</a> <i>homogeneus</i> and <i>heterogeneus</i>, from <a href="/wiki/Ancient_Greek" title="Ancient Greek">Ancient Greek</a> ὁμογενής (<i>homogenēs</i>) and ἑτερογενής (<i>heterogenēs</i>), from ὁμός (<i>homos</i>, "same") and ἕτερος (<i>heteros</i>, "other, another, different") respectively, followed by γένος (<i>genos</i>, "kind"); -ous is an adjectival suffix.<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> </p><p>Alternate spellings omitting the last <i>-e-</i> (and the associated pronunciations) are common, but mistaken:<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> <i><b>homogenous</b></i> is strictly a biological/pathological term which has largely been replaced by <i><a href="/wiki/Homology_(biology)" title="Homology (biology)">homologous</a></i>. But use of <i>homogenous</i> to mean <i>homogeneous</i> has seen a rise since 2000, enough for it to now be considered an "established variant".<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> Similarly, <i><b>heterogenous</b></i> is a spelling traditionally reserved to biology and <a href="/wiki/Pathology" title="Pathology">pathology</a>, referring to the property of an object in the body having its origin outside the body.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Scaling">Scaling</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=2" title="Edit section: Scaling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The concepts are the same to every level of complexity. From <a href="/wiki/Atom" title="Atom">atoms</a> to <a href="/wiki/Galaxy" title="Galaxy">galaxies</a>, <a href="/wiki/Plant" title="Plant">plants</a>, <a href="/wiki/Animal" title="Animal">animals</a>, <a href="/wiki/Human" title="Human">humans</a>, and other <a href="/wiki/Living_organism" class="mw-redirect" title="Living organism">living organisms</a> all share both a common or unique set of complexities. Hence, an element may be homogeneous on a larger scale, compared to being heterogeneous on a smaller scale. This is known as an <a href="/wiki/Effective_medium_approximation" class="mw-redirect" title="Effective medium approximation">effective medium approximation</a>.<sup id="cite_ref-Gueguen_7-0" class="reference"><a href="#cite_note-Gueguen-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Effective-medium_8-0" class="reference"><a href="#cite_note-Effective-medium-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=3" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Various disciplines understand <i>heterogeneity</i>, or being <i>heterogeneous</i>, in different ways.<sup id="cite_ref-Heterogeneous_2-1" class="reference"><a href="#cite_note-Heterogeneous-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Biology">Biology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=4" title="Edit section: Biology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Environmental_heterogeneity">Environmental heterogeneity</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=5" title="Edit section: Environmental heterogeneity"><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-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs expansion</b>. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=">adding to it</a>. <span class="date-container"><i>(<span class="date">January 2024</span>)</i></span></div></td></tr></tbody></table> <p><b>Environmental heterogeneity</b> (EH) is a <a href="/wiki/Hypernym" class="mw-redirect" title="Hypernym">hypernym</a> for different environmental factors that contribute to the diversity of species, like climate, topography, and land cover.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Biodiversity" title="Biodiversity">Biodiversity</a> is correlated with <a href="/wiki/Geodiversity" title="Geodiversity">geodiversity</a> on a global scale. Heterogeneity in geodiversity features and environmental variables are indicators of environmental heterogeneity. They drive biodiversity at local and regional scales. </p><p>Scientific literature in ecology contains a big number of different terms for environmental heterogeneity, often undefined or conflicting in their meaning.<sup id="cite_ref-ehreview_10-0" class="reference"><a href="#cite_note-ehreview-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style><span class="vanchor"><span id="'''Habitat_diversity'''"></span><span class="vanchor-text"><b>Habitat diversity</b></span></span> and <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238216509"><span class="vanchor"><span id="'''habitat_heterogeneity'''"></span><span class="vanchor-text"><b>habitat heterogeneity</b></span></span> are a synonyms of environmental heterogeneity.<sup id="cite_ref-ehreview_10-1" class="reference"><a href="#cite_note-ehreview-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Chemistry">Chemistry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=6" title="Edit section: Chemistry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Homogeneous_and_heterogeneous_mixtures">Homogeneous and heterogeneous mixtures</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=7" title="Edit section: Homogeneous and heterogeneous mixtures"><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/Homogeneous_and_heterogeneous_mixtures" class="mw-redirect" title="Homogeneous and heterogeneous mixtures">Homogeneous and heterogeneous mixtures</a></div> <p>In <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, a <a href="/wiki/Heterogeneous_mixture" class="mw-redirect" title="Heterogeneous mixture">heterogeneous mixture</a> consists of either or both of 1) multiple states of matter or 2) <a href="/wiki/Hydrophilic" class="mw-redirect" title="Hydrophilic">hydrophilic</a> and <a href="/wiki/Hydrophobic" class="mw-redirect" title="Hydrophobic">hydrophobic</a> substances in one mixture; an example of the latter would be a mixture of water, <a href="/wiki/Octane" title="Octane">octane</a>, and <a href="/wiki/Silicone_grease" title="Silicone grease">silicone grease</a>. Heterogeneous solids, liquids, and gases may be made homogeneous by melting, stirring, or by allowing time to pass for <a href="/wiki/Diffusion" title="Diffusion">diffusion</a> to distribute the molecules evenly. For example, adding dye to water will create a heterogeneous solution at first, but will become homogeneous over time. <a href="/wiki/Entropy" title="Entropy">Entropy</a> allows for heterogeneous substances to become homogeneous over time.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>A heterogeneous mixture is a <a href="/wiki/Mixture" title="Mixture">mixture</a> of two or more <a href="/wiki/Chemical_compound" title="Chemical compound">compounds</a>. Examples are: mixtures of sand and water or sand and iron filings, a conglomerate rock, water and oil, a salad, <a href="/wiki/Trail_mix" title="Trail mix">trail mix</a>, and concrete (not cement).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> A mixture can be determined to be homogeneous when everything is settled and equal, and the liquid, gas, the object is one color or the same form. Various models have been proposed to model the concentrations in different phases. The phenomena to be considered are mass rates and reaction.<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. (July 2022)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading4"><h4 id="Homogeneous_and_heterogeneous_reactions">Homogeneous and heterogeneous reactions</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=8" title="Edit section: Homogeneous and heterogeneous reactions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Homogeneous reactions are <a href="/wiki/Chemical_reaction" title="Chemical reaction">chemical reactions</a> in which the reactants and products are in the same <a href="/wiki/Phase_(matter)" title="Phase (matter)">phase</a>, while heterogeneous reactions have <a href="/wiki/Reactant" class="mw-redirect" title="Reactant">reactants</a> in two or more phases. Reactions that take place on the surface of a catalyst of a different phase are also heterogeneous. A reaction between two gases or two miscible liquids is homogeneous. A reaction between a gas and a liquid, a gas and a solid or a liquid and a solid is heterogeneous. <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. (September 2010)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Geology">Geology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=9" title="Edit section: Geology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Earth is a heterogeneous substance in many aspects; for instance, <a href="/wiki/Rock_(geology)" title="Rock (geology)">rocks</a> (geology) are inherently heterogeneous, usually occurring at the micro-scale and mini-scale.<sup id="cite_ref-Gueguen_7-1" class="reference"><a href="#cite_note-Gueguen-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Linguistics">Linguistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=10" title="Edit section: Linguistics"><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/Homogeneity_(linguistics)" class="mw-redirect" title="Homogeneity (linguistics)">Homogeneity (linguistics)</a></div> <p>In <a href="/wiki/Formal_semantics_(natural_language)" title="Formal semantics (natural language)">formal semantics</a>, homogeneity is the phenomenon in which <a href="/wiki/Plural" title="Plural">plural</a> expressions imply "all" when <a href="/wiki/Speech_act" title="Speech act">asserted</a> but "none" when <a href="/wiki/Negation" title="Negation">negated</a>. For example, the <a href="/wiki/English_language" title="English language">English</a> sentence "Robin read the books" means that Robin read all the books, while "Robin didn't read the books" means that she read none of them. Neither sentence can be asserted if Robin read exactly half of the books. This is a puzzle because the negative sentence does not appear to be the <a href="/wiki/Classical_logic" title="Classical logic">classical</a> <a href="/wiki/Negation" title="Negation">negation</a> of the sentence. A variety of explanations have been proposed including that natural language operates on a <a href="/wiki/Trivalent_logic" class="mw-redirect" title="Trivalent logic">trivalent logic</a>.<sup id="cite_ref-KrizLLC_13-0" class="reference"><a href="#cite_note-KrizLLC-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Information_technology">Information technology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=11" title="Edit section: Information technology"><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/Heterogeneous_network" title="Heterogeneous network">Heterogeneous network</a></div><p>With <a href="/wiki/Information_technology" title="Information technology">information technology</a>, <a href="/wiki/Heterogeneous_computing" title="Heterogeneous computing">heterogeneous computing</a> occurs in a <a href="/wiki/Network_science" title="Network science">network</a> comprising different types of computers, potentially with vastly differing <a href="/wiki/Computer_memory" title="Computer memory">memory</a> sizes, processing power and even basic underlying architecture. <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. (September 2010)">citation needed</span></a></i>]</sup> </p><div class="mw-heading mw-heading3"><h3 id="Mathematics_and_statistics">Mathematics and statistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=12" title="Edit section: Mathematics and statistics"><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/Homogeneity_(disambiguation)#In_mathematics" class="mw-disambig" title="Homogeneity (disambiguation)">Homogeneity (disambiguation) § In mathematics</a></div> <p>In algebra, <a href="/wiki/Homogeneous_polynomial" title="Homogeneous polynomial">homogeneous polynomials</a> have the same number of factors of a given kind. </p><p>In the study of <a href="/wiki/Binary_relation" title="Binary relation">binary relations</a>, a <a href="/wiki/Homogeneous_relation" title="Homogeneous relation">homogeneous relation</a> <i>R</i> is on a single set (<i>R</i> ⊆ <i>X</i> × <i>X</i>) while a <b>heterogeneous relation</b> concerns possibly distinct sets (<i>R</i> ⊆ <i>X</i> × <i>Y</i>,  <i>X</i> = <i>Y</i> or <i>X</i> ≠ <i>Y</i>).<sup id="cite_ref-Schmidt_14-0" class="reference"><a href="#cite_note-Schmidt-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>In statistical <a href="/wiki/Meta-analysis" title="Meta-analysis">meta-analysis</a>, <a href="/wiki/Study_heterogeneity" title="Study heterogeneity">study heterogeneity</a> is when multiple studies on an effect are measuring somewhat different effects due to differences in subject population, intervention, choice of analysis, experimental design, etc.; this can cause problems in attempts to summarize the meaning of the studies. </p> <div class="mw-heading mw-heading3"><h3 id="Medicine">Medicine</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=13" title="Edit section: Medicine"><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/Heterogeneous_condition" title="Heterogeneous condition">Heterogeneous condition</a></div> <p>In <a href="/wiki/Medicine" title="Medicine">medicine</a> and <a href="/wiki/Genetics" title="Genetics">genetics</a>, a <a href="/wiki/Genetic_heterogeneity" title="Genetic heterogeneity">genetic</a> or <a href="/wiki/Allelic_heterogeneity" title="Allelic heterogeneity">allelic</a> heterogeneous condition is one where the same disease or condition can be caused, or contributed to, by several factors, or in genetic terms, by varying or different <a href="/wiki/Gene" title="Gene">genes</a> or <a href="/wiki/Allele" title="Allele">alleles</a>. </p><p>In <a href="/wiki/Cancer_research" title="Cancer research">cancer research</a>, cancer cell heterogeneity is thought to be one of the underlying reasons that make treatment of <a href="/wiki/Cancer" title="Cancer">cancer</a> difficult.<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-heading3"><h3 id="Physics">Physics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=14" title="Edit section: Physics"><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/Homogeneity_(physics)" title="Homogeneity (physics)">Homogeneity (physics)</a></div> <p>In <a href="/wiki/Physics" title="Physics">physics</a>, "heterogeneous" is understood to mean "having physical properties that vary within the medium". </p> <div class="mw-heading mw-heading3"><h3 id="Sociology">Sociology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Homogeneity_and_heterogeneity&action=edit&section=15" title="Edit section: Sociology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Sociology" title="Sociology">sociology</a>, "heterogeneous" may refer to a society or group that includes individuals of differing ethnicities, cultural backgrounds, sexes, or ages. Diverse is the more common synonym in the context.<sup id="cite_ref-LawsonGarrod2012_16-0" class="reference"><a href="#cite_note-LawsonGarrod2012-16"><span class="cite-bracket">[</span>16<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=Homogeneity_and_heterogeneity&action=edit&section=16" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Complete_spatial_randomness" title="Complete spatial randomness">Complete spatial randomness</a></li> <li><a href="/wiki/Heterologous" title="Heterologous">Heterologous</a></li> <li><a href="/wiki/Epidemiology" title="Epidemiology">Epidemiology</a></li> <li><a href="/wiki/Spatial_analysis" title="Spatial analysis">Spatial analysis</a></li> <li><a href="/wiki/Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">Statistical hypothesis testing</a></li> <li><a href="/wiki/Homogeneity_blockmodeling" title="Homogeneity blockmodeling">Homogeneity blockmodeling</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=Homogeneity_and_heterogeneity&action=edit&section=17" title="Edit section: References"><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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-websters-hetrogeneity-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-websters-hetrogeneity_1-0">^</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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110728124025/http://machaut.uchicago.edu/?resource=Webster%27s&word=Heterogeneity&use1913=on&use1828=on">"Webster's Revised Unabridged Dictionary (1913 + 1828)"</a>. <i>Heterogeneity</i>. The ARTFL Project, University of Chicago. September 2010. Archived from <a rel="nofollow" class="external text" href="http://machaut.uchicago.edu/?resource=Webster%27s&word=Heterogeneity&use1913=on&use1828=on">the original</a> <span class="cs1-format">(Part of this paragraph is public domain material copyright 1828 and 1913)</span> on 2011-07-28<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-09-10</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Heterogeneity&rft.atitle=Webster%27s+Revised+Unabridged+Dictionary+%281913+%2B+1828%29&rft.date=2010-09&rft_id=http%3A%2F%2Fmachaut.uchicago.edu%2F%3Fresource%3DWebster%2527s%26word%3DHeterogeneity%26use1913%3Don%26use1828%3Don&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span></span> </li> <li id="cite_note-Heterogeneous-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Heterogeneous_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Heterogeneous_2-1"><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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110728124031/http://machaut.uchicago.edu/?action=search&word=heterogeneous&resource=Webster%27s&quicksearch=on">"Webster's Revised Unabridged Dictionary (1913 + 1828)"</a>. <i>Heterogeneous</i>. The ARTFL Project, University of Chicago. September 2010. Archived from <a rel="nofollow" class="external text" href="http://machaut.uchicago.edu/?action=search&word=heterogeneous&resource=Webster%27s&quicksearch=on">the original</a> <span class="cs1-format">(Part of this paragraph is public domain material copyright 1828 and 1913)</span> on 2011-07-28<span class="reference-accessdate">. Retrieved <span class="nowrap">2010-09-10</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Heterogeneous&rft.atitle=Webster%27s+Revised+Unabridged+Dictionary+%281913+%2B+1828%29&rft.date=2010-09&rft_id=http%3A%2F%2Fmachaut.uchicago.edu%2F%3Faction%3Dsearch%26word%3Dheterogeneous%26resource%3DWebster%2527s%26quicksearch%3Don&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" 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"> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120717050711/http://oxforddictionaries.com/definition/english/heterogeneous"><i>Heterogeneous:</i> Definition in the Oxford English Dictionary</a></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"> <a rel="nofollow" class="external text" href="https://dictionary.cambridge.org/dictionary/english/homogeneous">Cambridge Dictionary: <i>homogeneous</i></a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20121003000741/http://oxforddictionaries.com/definition/english/homogeneous"><i>Homogeneous:</i> Definition in the Oxford England Dictionary</a></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"> <a rel="nofollow" class="external text" href="http://grammarist.com/usage/heterogeneous-heterogenous/">Heterogeneous vs. heterogenous</a> - Grammarist)</span> </li> <li id="cite_note-Gueguen-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gueguen_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gueguen_7-1"><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="CITEREFGuéguenPalciauskas,_Victor1994" class="citation book cs1">Guéguen, Yves; Palciauskas, Victor (May 1994). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=fCP5qyRyX-oC&q=heterogeneous+physics&pg=PA53"><i>Introduction to the physics of rocks</i></a>. Princeton University Press. pp. 53–72 (Chapter 3). <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-03452-2" title="Special:BookSources/978-0-691-03452-2"><bdi>978-0-691-03452-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+the+physics+of+rocks&rft.pages=53-72+%28Chapter+3%29&rft.pub=Princeton+University+Press&rft.date=1994-05&rft.isbn=978-0-691-03452-2&rft.aulast=Gu%C3%A9guen&rft.aufirst=Yves&rft.au=Palciauskas%2C+Victor&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DfCP5qyRyX-oC%26q%3Dheterogeneous%2Bphysics%26pg%3DPA53&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span>Google Books preview download available</span> </li> <li id="cite_note-Effective-medium-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Effective-medium_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShadrivovKozyrevVan_Der_WeideKivshar2008" class="citation journal cs1">Shadrivov, Ilya V.; Kozyrev, AB; Van Der Weide, DW; Kivshar, YS (2008-11-24). <a rel="nofollow" class="external text" href="http://assets0.pubget.com/pdf/19065165.pdf">"Nonlinear magnetic metamaterials"</a> <span class="cs1-format">(Introduction section. Free PDF download)</span>. <i>Optics Express</i>. <b>16</b> (25): 20266–71. <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/2008OExpr..1620266S">2008OExpr..1620266S</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/10.1364%2FOE.16.020266">10.1364/OE.16.020266</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/10440%2F410">10440/410</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19065165">19065165</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2009-11-26</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optics+Express&rft.atitle=Nonlinear+magnetic+metamaterials&rft.volume=16&rft.issue=25&rft.pages=20266-71&rft.date=2008-11-24&rft_id=info%3Ahdl%2F10440%2F410&rft_id=info%3Apmid%2F19065165&rft_id=info%3Adoi%2F10.1364%2FOE.16.020266&rft_id=info%3Abibcode%2F2008OExpr..1620266S&rft.aulast=Shadrivov&rft.aufirst=Ilya+V.&rft.au=Kozyrev%2C+AB&rft.au=Van+Der+Weide%2C+DW&rft.au=Kivshar%2C+YS&rft_id=http%3A%2F%2Fassets0.pubget.com%2Fpdf%2F19065165.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged July 2016">dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWanWangMarquet2023" class="citation journal cs1">Wan, Ji-Zhong; Wang, Chun-Jing; Marquet, Pablo A (December 2023). <a rel="nofollow" class="external text" href="https://journals.sagepub.com/doi/abs/10.1177/03091333231189045">"Environmental heterogeneity as a driver of terrestrial biodiversity on a global scale"</a>. <i>Progress in Physical Geography: Earth and Environment</i>. <b>47</b> (6): 912–930. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F03091333231189045">10.1177/03091333231189045</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0309-1333">0309-1333</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:260849226">260849226</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Progress+in+Physical+Geography%3A+Earth+and+Environment&rft.atitle=Environmental+heterogeneity+as+a+driver+of+terrestrial+biodiversity+on+a+global+scale&rft.volume=47&rft.issue=6&rft.pages=912-930&rft.date=2023-12&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A260849226%23id-name%3DS2CID&rft.issn=0309-1333&rft_id=info%3Adoi%2F10.1177%2F03091333231189045&rft.aulast=Wan&rft.aufirst=Ji-Zhong&rft.au=Wang%2C+Chun-Jing&rft.au=Marquet%2C+Pablo+A&rft_id=https%3A%2F%2Fjournals.sagepub.com%2Fdoi%2Fabs%2F10.1177%2F03091333231189045&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span></span> </li> <li id="cite_note-ehreview-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-ehreview_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ehreview_10-1"><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="CITEREFSteinKreft2015" class="citation journal cs1">Stein, Anke; Kreft, Holger (August 2015). <a rel="nofollow" class="external text" href="https://onlinelibrary.wiley.com/doi/abs/10.1111/brv.12135">"Terminology and quantification of environmental heterogeneity in species-richness research"</a>. <i>Biological Reviews</i>. <b>90</b> (3): 815–836. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fbrv.12135">10.1111/brv.12135</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1464-7931">1464-7931</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/25099766">25099766</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:593580">593580</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Biological+Reviews&rft.atitle=Terminology+and+quantification+of+environmental+heterogeneity+in+species-richness+research&rft.volume=90&rft.issue=3&rft.pages=815-836&rft.date=2015-08&rft.issn=1464-7931&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A593580%23id-name%3DS2CID&rft_id=info%3Apmid%2F25099766&rft_id=info%3Adoi%2F10.1111%2Fbrv.12135&rft.aulast=Stein&rft.aufirst=Anke&rft.au=Kreft%2C+Holger&rft_id=https%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2Fabs%2F10.1111%2Fbrv.12135&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</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://cecs.wright.edu/~gdong/mining03/tuto1/lesson_6.html#:~:text=Entropy%20measures%20the%20homogeneity%20(purity,of%20examples%20has%20more%20information.">"Lessons"</a>. <i>cecs.wright.edu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-03-09</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=cecs.wright.edu&rft.atitle=Lessons&rft_id=https%3A%2F%2Fcecs.wright.edu%2F~gdong%2Fmining03%2Ftuto1%2Flesson_6.html%23%3A~%3Atext%3DEntropy%2520measures%2520the%2520homogeneity%2520%28purity%2Cof%2520examples%2520has%2520more%2520information.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGamow1967" class="citation book cs1"><a href="/wiki/George_Gamow" title="George Gamow">Gamow, George</a> (April 1967). "Chapter VI, "Descending Staircase"<span class="cs1-kern-right"></span>". <i>One Two Three... Infinity</i> (Mass market paperback) (Bantam Science and Mathematics, 5th printing ed.). Bantam. p. 117. <q>[Clam chowder] represents a nice example of what is known as a heterogeneous material.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+VI%2C+%22Descending+Staircase%22&rft.btitle=One+Two+Three...+Infinity&rft.pages=117&rft.edition=Bantam+Science+and+Mathematics%2C+5th+printing&rft.pub=Bantam&rft.date=1967-04&rft.aulast=Gamow&rft.aufirst=George&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span></span> </li> <li id="cite_note-KrizLLC-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-KrizLLC_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKriž2019" class="citation journal cs1">Križ, Manuel (2019). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7363159">"Homogeneity effects in natural language semantics"</a>. <i>Language and Linguistics Compass</i>. <b>13</b> (11): e12350. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Flnc3.12350">10.1111/lnc3.12350</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7363159">7363159</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/32699550">32699550</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Language+and+Linguistics+Compass&rft.atitle=Homogeneity+effects+in+natural+language+semantics&rft.volume=13&rft.issue=11&rft.pages=e12350&rft.date=2019&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7363159%23id-name%3DPMC&rft_id=info%3Apmid%2F32699550&rft_id=info%3Adoi%2F10.1111%2Flnc3.12350&rft.aulast=Kri%C5%BE&rft.aufirst=Manuel&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7363159&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span></span> </li> <li id="cite_note-Schmidt-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Schmidt_14-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchmidtStröhlein2012" class="citation book cs1"><a href="/wiki/Gunther_Schmidt" title="Gunther Schmidt">Schmidt, Gunther</a>; Ströhlein, Thomas (2012). <i>Relations and Graphs: Discrete Mathematics for Computer Scientists</i>. Springer Science & Business Media. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-77968-8" title="Special:BookSources/978-3-642-77968-8"><bdi>978-3-642-77968-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relations+and+Graphs%3A+Discrete+Mathematics+for+Computer+Scientists&rft.pub=Springer+Science+%26+Business+Media&rft.date=2012&rft.isbn=978-3-642-77968-8&rft.aulast=Schmidt&rft.aufirst=Gunther&rft.au=Str%C3%B6hlein%2C+Thomas&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" 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="CITEREFBhatiaJohn_V_FrangioniRobert_M_HoffmanA_John_Iafrate2012" class="citation journal cs1">Bhatia, Sangeeta; John V Frangioni; Robert M Hoffman; A John Iafrate; Kornelia Polyak (10 July 2012). "The challenges posed by cancer heterogeneity". <i>Nature Biotechnology</i>. <b>30</b> (7): 604–610. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnbt.2294">10.1038/nbt.2294</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22781679">22781679</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15083285">15083285</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Biotechnology&rft.atitle=The+challenges+posed+by+cancer+heterogeneity&rft.volume=30&rft.issue=7&rft.pages=604-610&rft.date=2012-07-10&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A15083285%23id-name%3DS2CID&rft_id=info%3Apmid%2F22781679&rft_id=info%3Adoi%2F10.1038%2Fnbt.2294&rft.aulast=Bhatia&rft.aufirst=Sangeeta&rft.au=John+V+Frangioni&rft.au=Robert+M+Hoffman&rft.au=A+John+Iafrate&rft.au=Kornelia+Polyak&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span></span> </li> <li id="cite_note-LawsonGarrod2012-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-LawsonGarrod2012_16-0">^</a></b></span> <span class="reference-text"><i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=ibzZZxWC_vEC">Dictionary of Sociology</a></i>. Routledge; 12 November 2012. <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/978-1-136-59845-6" title="Special:BookSources/978-1-136-59845-6">978-1-136-59845-6</a>.</span> </li> </ol></div> <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=Homogeneity_and_heterogeneity&action=edit&section=18" 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"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/homogeneity" class="extiw" title="wiktionary:homogeneity">homogeneity</a></b></i>, <i><b><a href="https://en.wiktionary.org/wiki/heterogeneity" class="extiw" title="wiktionary:heterogeneity">heterogeneity</a></b></i>, <i><b><a href="https://en.wiktionary.org/wiki/homogeneous" class="extiw" title="wiktionary:homogeneous">homogeneous</a></b></i>, or <i><b><a href="https://en.wiktionary.org/wiki/heterogeneous" class="extiw" title="wiktionary:heterogeneous">heterogeneous</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Homogeneity" class="extiw" title="q:Homogeneity">Homogeneity</a></b></i>.</div></div> </div> <ul><li>The following cited pages in this book cover the meaning of "homogeneity" across disciplines: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorris1992" class="citation book cs1">Morris, Christopher G. (1992). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/academicpressdic00morr"><i>Academic Press Dictionary of Science and Technology</i></a></span>. Gulf Professional Publishing. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/academicpressdic00morr/page/n1082">1039</a>, 1040. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-12-200400-0" title="Special:BookSources/0-12-200400-0"><bdi>0-12-200400-0</bdi></a>. <q>Homogeneity in physics.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Academic+Press+Dictionary+of+Science+and+Technology&rft.pages=1039%2C+1040&rft.pub=Gulf+Professional+Publishing&rft.date=1992&rft.isbn=0-12-200400-0&rft.aulast=Morris&rft.aufirst=Christopher+G.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Facademicpressdic00morr&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHomogeneity+and+heterogeneity" class="Z3988"></span></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Homogeneity_and_heterogeneity&oldid=1248490661">https://en.wikipedia.org/w/index.php?title=Homogeneity_and_heterogeneity&oldid=1248490661</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Chemical_reactions" title="Category:Chemical reactions">Chemical reactions</a></li><li><a href="/wiki/Category:Scientific_terminology" title="Category:Scientific terminology">Scientific terminology</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:All_articles_with_dead_external_links" title="Category:All articles with dead external links">All articles with dead external links</a></li><li><a href="/wiki/Category:Articles_with_dead_external_links_from_July_2016" title="Category:Articles with dead external links from July 2016">Articles with dead external links from July 2016</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Articles_to_be_expanded_from_January_2024" title="Category:Articles to be expanded from January 2024">Articles to be expanded from January 2024</a></li><li><a href="/wiki/Category:All_articles_to_be_expanded" title="Category:All articles to be expanded">All articles to be expanded</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_July_2022" title="Category:Articles with unsourced statements from July 2022">Articles with unsourced statements from July 2022</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_September_2010" title="Category:Articles with unsourced statements from September 2010">Articles with unsourced statements from September 2010</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 29 September 2024, at 20:17<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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