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<link rel="canonical" href="https://eo.wikipedia.org/wiki/Nepero"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.eo"> <link rel="alternate" type="application/atom+xml" title="Vikipedio Atom-fonto" href="/w/index.php?title=Speciala%C4%B5o:Lastaj_%C5%9Dan%C4%9Doj&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Nepero rootpage-Nepero skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Saltu al enhavo</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Retejo"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" 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vi povas fari, kie vi povas trovi ion"><span>Komunuma portalo</span></a></li><li id="n-villagepump" class="mw-list-item"><a href="/wiki/Vikipedio:Diskutejo"><span>Diskutejo</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Vikipedio:Aktuala%C4%B5oj" title="Trovi fonajn informojn pri nunaj eventoj"><span>Aktualaĵoj</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Lastaj_%C5%9Dan%C4%9Doj" title="Listo de la lastaj ŝanĝoj en la vikio. [r]" accesskey="r"><span>Lastaj ŝanĝoj</span></a></li><li id="n-newpages" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Novaj_pa%C4%9Doj"><span>Novaj paĝoj</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Hazarda_pa%C4%9Do" title="Iri al hazarda paĝo [x]" accesskey="x"><span>Hazarda paĝo</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Helpo:Enhavo" title="La loko por eltrovi"><span>Helpo</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Specialaj_pa%C4%9Doj"><span>Specialaj paĝoj</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Vikipedio:%C4%88efpa%C4%9Do" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Vikipedio" src="/static/images/mobile/copyright/wikipedia-wordmark-eo.svg" style="width: 6.875em; height: 1.125em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-eo.svg" width="109" height="13" style="width: 6.8125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Speciala%C4%B5o:Ser%C4%89i" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Serĉi tra Vikipedio [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Serĉi</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Serĉi tra Vikipedio" aria-label="Serĉi tra Vikipedio" autocapitalize="sentences" title="Serĉi tra Vikipedio [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Specialaĵo:Serĉi"> </div> <button class="cdx-button cdx-search-input__end-button">Serĉi</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personaj iloj"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Aspekto"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Aspekto" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Aspekto</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=eo.wikipedia.org&uselang=eo" class=""><span>Donaci</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciala%C4%B5o:Krei_konton&returnto=Nepero" title="Ni rekomendas ke vi kreu uzantokonton kaj ensalutu, kvankam tio ne estas deviga" class=""><span>Krei konton</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciala%C4%B5o:Ensaluti&returnto=Nepero" title="Ni rekomendas ke vi ensalutu, kvankam tio ne estas devige. [o]" accesskey="o" class=""><span>Ensaluti</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Pliaj agordoj" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personaj iloj" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personaj iloj</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Menuo de uzanto" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=eo.wikipedia.org&uselang=eo"><span>Donaci</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:Krei_konton&returnto=Nepero" title="Ni rekomendas ke vi kreu uzantokonton kaj ensalutu, kvankam tio ne estas deviga"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Krei konton</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:Ensaluti&returnto=Nepero" title="Ni rekomendas ke vi ensalutu, kvankam tio ne estas devige. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Ensaluti</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Paĝoj por elsalutitaj redaktistoj <a href="/wiki/Helpo:Enkonduko" aria-label="Lernu pli pri redaktado"><span>Lernu pli</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Miaj_kontribuoj" title="Listo de redaktoj faritaj el ĉi tiu IPa adreso [y]" accesskey="y"><span>Kontribuoj</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Mia_diskutpa%C4%9Do" title="Diskuto pri redaktoj sub tiu ĉi IP adreso [n]" accesskey="n"><span>Diskuto</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Retejo"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Enhavo" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Enhavo</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">movigi al flanka panelo</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">kaŝi</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Komenco</div> </a> </li> <li id="toc-Difino" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Difino"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Difino</span> </div> </a> <ul id="toc-Difino-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Konverto_al_aliaj_unuoj" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Konverto_al_aliaj_unuoj"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Konverto al aliaj unuoj</span> </div> </a> <ul id="toc-Konverto_al_aliaj_unuoj-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historio" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historio"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Historio</span> </div> </a> <ul id="toc-Historio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referencoj" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referencoj"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referencoj</span> </div> </a> <ul id="toc-Referencoj-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="Enhavo" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Enhavtabelo" > <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="Ŝaltu la enhavtabelon" > <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">Ŝaltu la enhavtabelon</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">Nepero</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="Iru al artikolo en alia lingvo. Havebla en 35 lingvo" > <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-35" 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">35 lingvoj</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/%D9%86%D9%8A%D8%A8%D8%B1" title="نيبر — araba" lang="ar" hreflang="ar" data-title="نيبر" data-language-autonym="العربية" data-language-local-name="araba" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер — belorusa" lang="be" hreflang="be" data-title="Непер" data-language-autonym="Беларуская" data-language-local-name="belorusa" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Neper" title="Neper — kataluna" lang="ca" hreflang="ca" data-title="Neper" data-language-autonym="Català" data-language-local-name="kataluna" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Neper" title="Neper — ĉeĥa" lang="cs" hreflang="cs" data-title="Neper" data-language-autonym="Čeština" data-language-local-name="ĉeĥa" 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/Neper" title="Neper — dana" lang="da" hreflang="da" data-title="Neper" data-language-autonym="Dansk" data-language-local-name="dana" 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/Neper_(Hilfsma%C3%9Feinheit)" title="Neper (Hilfsmaßeinheit) — germana" lang="de" hreflang="de" data-title="Neper (Hilfsmaßeinheit)" data-language-autonym="Deutsch" data-language-local-name="germana" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Neper" title="Neper — angla" lang="en" hreflang="en" data-title="Neper" data-language-autonym="English" data-language-local-name="angla" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Neper" title="Neper — hispana" lang="es" hreflang="es" data-title="Neper" data-language-autonym="Español" data-language-local-name="hispana" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D9%BE%D8%B1" title="نپر — persa" lang="fa" hreflang="fa" data-title="نپر" data-language-autonym="فارسی" data-language-local-name="persa" 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%C3%A9per" title="Néper — franca" lang="fr" hreflang="fr" data-title="Néper" data-language-autonym="Français" data-language-local-name="franca" 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/Neper" title="Neper — galega" lang="gl" hreflang="gl" data-title="Neper" data-language-autonym="Galego" data-language-local-name="galega" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Neper" title="Neper — kroata" lang="hr" hreflang="hr" data-title="Neper" data-language-autonym="Hrvatski" data-language-local-name="kroata" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Neper" title="Neper — hungara" lang="hu" hreflang="hu" data-title="Neper" data-language-autonym="Magyar" data-language-local-name="hungara" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%86%D5%A5%D5%BA%D5%A5%D6%80_(%D5%B9%D5%A1%D6%83%D5%B4%D5%A1%D5%B6_%D5%B4%D5%AB%D5%A1%D5%BE%D5%B8%D6%80)" title="Նեպեր (չափման միավոր) — armena" lang="hy" hreflang="hy" data-title="Նեպեր (չափման միավոր)" data-language-autonym="Հայերեն" data-language-local-name="armena" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Neper" title="Neper — itala" lang="it" hreflang="it" data-title="Neper" data-language-autonym="Italiano" data-language-local-name="itala" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%8D%E3%83%BC%E3%83%91" title="ネーパ — japana" lang="ja" hreflang="ja" data-title="ネーパ" data-language-autonym="日本語" data-language-local-name="japana" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9C%E1%83%94%E1%83%9E%E1%83%94%E1%83%A0%E1%83%98" title="ნეპერი — kartvela" lang="ka" hreflang="ka" data-title="ნეპერი" data-language-autonym="ქართული" data-language-local-name="kartvela" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер — kazaĥa" lang="kk" hreflang="kk" data-title="Непер" data-language-autonym="Қазақша" data-language-local-name="kazaĥa" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%84%A4%ED%8D%BC" title="네퍼 — korea" lang="ko" hreflang="ko" data-title="네퍼" data-language-autonym="한국어" data-language-local-name="korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Neperis" title="Neperis — litova" lang="lt" hreflang="lt" data-title="Neperis" data-language-autonym="Lietuvių" data-language-local-name="litova" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер — makedona" lang="mk" hreflang="mk" data-title="Непер" data-language-autonym="Македонски" data-language-local-name="makedona" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Neper" title="Neper — nederlanda" lang="nl" hreflang="nl" data-title="Neper" data-language-autonym="Nederlands" data-language-local-name="nederlanda" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Neper" title="Neper — novnorvega" lang="nn" hreflang="nn" data-title="Neper" data-language-autonym="Norsk nynorsk" data-language-local-name="novnorvega" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Neper" title="Neper — pola" lang="pl" hreflang="pl" data-title="Neper" data-language-autonym="Polski" data-language-local-name="pola" 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/Neper" title="Neper — portugala" lang="pt" hreflang="pt" data-title="Neper" data-language-autonym="Português" data-language-local-name="portugala" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер — rusa" lang="ru" hreflang="ru" data-title="Непер" data-language-autonym="Русский" data-language-local-name="rusa" 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/Neper" title="Neper — sicilia" lang="scn" hreflang="scn" data-title="Neper" data-language-autonym="Sicilianu" data-language-local-name="sicilia" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Neper" title="Neper — slovena" lang="sl" hreflang="sl" data-title="Neper" data-language-autonym="Slovenščina" data-language-local-name="slovena" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Neper" title="Neper — sveda" lang="sv" hreflang="sv" data-title="Neper" data-language-autonym="Svenska" data-language-local-name="sveda" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80" title="Непер — taĝika" lang="tg" hreflang="tg" data-title="Непер" data-language-autonym="Тоҷикӣ" data-language-local-name="taĝika" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%99%E0%B9%80%E0%B8%9B%E0%B8%AD%E0%B8%A3%E0%B9%8C" title="เนเปอร์ — taja" lang="th" hreflang="th" data-title="เนเปอร์" data-language-autonym="ไทย" data-language-local-name="taja" 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/Neper" title="Neper — turka" lang="tr" hreflang="tr" data-title="Neper" data-language-autonym="Türkçe" data-language-local-name="turka" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9D%D0%B5%D0%BF%D0%B5%D1%80_(%D0%BE%D0%B4%D0%B8%D0%BD%D0%B8%D1%86%D1%8F_%D0%B2%D0%B8%D0%BC%D1%96%D1%80%D1%8E%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F)" title="Непер (одиниця вимірювання) — ukraina" lang="uk" hreflang="uk" data-title="Непер (одиниця вимірювання)" data-language-autonym="Українська" data-language-local-name="ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Neper" title="Neper — uzbeka" lang="uz" hreflang="uz" data-title="Neper" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeka" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A5%88%E5%9F%B9" title="奈培 — ĉina" lang="zh" hreflang="zh" data-title="奈培" data-language-autonym="中文" data-language-local-name="ĉina" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q50094#sitelinks-wikipedia" title="Redakti interlingvajn ligilojn" class="wbc-editpage">Redakti ligilojn</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Nomspacoj"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Nepero" title="Vidi la artikolon [c]" accesskey="c"><span>Artikolo</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskuto:Nepero&action=edit&redlink=1" rel="discussion" class="new" title="Diskuto pri la artikolo (paĝo ne ekzistas) [t]" accesskey="t"><span>Diskuto</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Ŝanĝi lingvan varianton" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Esperanto</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Vidoj"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Nepero"><span>Legi</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Nepero&veaction=edit" title="Redakti ĉi tiun paĝon [v]" accesskey="v"><span>Redakti</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Nepero&action=edit" title="Redakti fontan kodon de tiu ĉi paĝo [e]" accesskey="e"><span>Redakti fonton</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Nepero&action=history" title="Antaŭaj versioj de ĉi tiu paĝo. [h]" accesskey="h"><span>Vidi historion</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Paĝaj iloj"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Iloj" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Iloj</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Iloj</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">movigi al flanka panelo</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">kaŝi</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Pliaj opcioj" > <div class="vector-menu-heading"> Agoj </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Nepero"><span>Legi</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Nepero&veaction=edit" title="Redakti ĉi tiun paĝon [v]" accesskey="v"><span>Redakti</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Nepero&action=edit" title="Redakti fontan kodon de tiu ĉi paĝo [e]" accesskey="e"><span>Redakti fonton</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Nepero&action=history"><span>Vidi historion</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Ĝenerale </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Kio_ligas_%C4%89i_tien%3F/Nepero" title="Listo de ĉiuj vikiaj paĝoj kiuj ligas ĉi tien [j]" accesskey="j"><span>Ligiloj ĉi tien</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciala%C4%B5o:Rilataj_%C5%9Dan%C4%9Doj/Nepero" rel="nofollow" title="Lastaj ŝanĝoj en paĝoj kiuj ligas al ĉi tiu paĝo [k]" accesskey="k"><span>Rilataj ŝanĝoj</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=eo" title="Alŝuti dosierojn [u]" accesskey="u"><span>Alŝuti dosieron</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Nepero&oldid=9028650" title="Porĉiama ligilo al ĉi versio de la paĝo"><span>Konstanta ligilo</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Nepero&action=info" title="Pli da informo pri ĉi tiu paĝo"><span>Informoj pri la paĝo</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:Citi&page=Nepero&id=9028650&wpFormIdentifier=titleform" title="Informoj pri kiel citi ĉi tiun paĝon"><span>Citi ĉi tiun artikolon</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:UrlShortener&url=https%3A%2F%2Feo.wikipedia.org%2Fwiki%2FNepero"><span>Akiri mallongigitan URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:QrCode&url=https%3A%2F%2Feo.wikipedia.org%2Fwiki%2FNepero"><span>Elŝutu QR-kodon</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Presi/elporti </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:Libro&bookcmd=book_creator&referer=Nepero"><span>Krei libron</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciala%C4%B5o:DownloadAsPdf&page=Nepero&action=show-download-screen"><span>Elŝuti kiel PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Nepero&printable=yes" title="Presebla versio de tiu ĉi paĝo [p]" accesskey="p"><span>Presebla versio</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> En aliaj projektoj </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q50094" title="Ligilo al konektita datuma ero [g]" accesskey="g"><span>Ero en Vikidatumoj</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Paĝaj iloj"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspekto"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspekto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">movigi al flanka panelo</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">kaŝi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">El Vikipedio, la libera enciklopedio</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="eo" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r8859571">.mw-parser-output .apartigilo{background-color:#F9F9F9;color:black;border-bottom:1px solid #AAAAAA;padding:0.5em}@media screen{html.skin-theme-clientpref-night .mw-parser-output .apartigilo{background-color:#202122;color:white;border-bottom:1px solid #333333}html.skin-theme-clientpref-light .mw-parser-output .apartigilo{background-color:#F9F9F9;color:black;border-bottom:1px solid #AAAAAA}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .apartigilo{background-color:#202122;color:white;border-bottom:1px solid #333333}}</style><div> <table class="apartigilo" style="width: 100%; font-size: 95%; margin-bottom: 1em; position:relative; font-style:italic;"> <tbody><tr> <td style="width: 26px; vertical-align: middle;"><span typeof="mw:File"><a href="/wiki/Helpo:Apartigiloj" title="Helpo:Apartigiloj"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Disambig.svg/18px-Disambig.svg.png" decoding="async" width="18" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Disambig.svg/27px-Disambig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Disambig.svg/36px-Disambig.svg.png 2x" data-file-width="230" data-file-height="183" /></a></span> </td> <td>Ĉi tiu artikolo temas pri la mezurunuo. Por la skota matematikisto, laŭ kies nomo la mezurunuo estas nomita, vidu la artikolon <a href="/wiki/John_Napier" title="John Napier">John Napier</a>. </td></tr></tbody></table> </div> <p>La <b>nepero</b><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> (simbole <b>Np</b>) estas <a href="/wiki/Mezurunuo" title="Mezurunuo">mezurunuo</a> por la karakterizo de niveloj kaj mezuroj. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Difino">Difino</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nepero&veaction=edit&section=1" title="Redakti sekcion: Difino" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Nepero&action=edit&section=1" title="Redakti la fontkodo de la sekcio: Difino"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Supozu ke ekzistas du <a href="/wiki/Amplitudo" title="Amplitudo">amplitudoj</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bc2435b217c1a0f46f8a517ffa225c6f9440e81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle A_{1}}" /></span> kaj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c98dbd929292d464de6942e95db306b8b8a6fca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.797ex; height:2.509ex;" alt="{\displaystyle A_{0}}" /></span>, kaj konsideru la <a href="/wiki/Rilatumo" title="Rilatumo">rilatumon</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{1}/A_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}/A_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a588cb16436306c6f94f45661efd31eec2441734" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.757ex; height:2.843ex;" alt="{\displaystyle A_{1}/A_{0}}" /></span>. La nombro de <b>neperoj</b> respondanta al tiu rilatumo estas la <a href="/wiki/Natura_logaritmo" class="mw-redirect" title="Natura logaritmo">natura logaritmo</a> de tiu rilatumo inter amplitudoj: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{nombro de neperoj}}=\ln {\frac {A_{1}}{A_{0}}}=\log _{\mathrm {e} }{\frac {A_{1}}{A_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>nombro de neperoj</mtext> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{nombro de neperoj}}=\ln {\frac {A_{1}}{A_{0}}}=\log _{\mathrm {e} }{\frac {A_{1}}{A_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5555006ef0274d0b5ba208438e4d22bb8b780fa9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:38.791ex; height:5.843ex;" alt="{\displaystyle {\text{nombro de neperoj}}=\ln {\frac {A_{1}}{A_{0}}}=\log _{\mathrm {e} }{\frac {A_{1}}{A_{0}}}}" /></span></dd></dl> <p>Alivorte, unu <b>nepero</b> respondas al la <a href="/wiki/Rilatumo" title="Rilatumo">rilatumo</a> inter du amplitudoj, kiu egalas 10. </p><p>Alternative, oni povas mezuri rilatumojn inter <a href="/wiki/Povumo" title="Povumo">povumoj</a>, kiuj estas proporciaj al la kvadratoj de la amplitudoj. Se la povumoj estas <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/398f438d75434e6fbf48dc232c1ad7228a738568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.547ex; height:2.509ex;" alt="{\displaystyle P_{1}}" /></span> kaj <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/671bd891701e0d6cfa6da0114a5dd64233b58709" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.547ex; height:2.509ex;" alt="{\displaystyle P_{0}}" /></span>, tiaj ke </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {P_{1}}{P_{0}}}={\frac {A_{1}^{2}}{A_{0}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {P_{1}}{P_{0}}}={\frac {A_{1}^{2}}{A_{0}^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4370caec6e9c2a60602f77bdba482e0a9ea51b71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:10.115ex; height:7.009ex;" alt="{\displaystyle {\frac {P_{1}}{P_{0}}}={\frac {A_{1}^{2}}{A_{0}^{2}}}}" /></span>,</dd></dl> <p>do </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{nombro de neperoj}}={\frac {1}{2}}\ln {\frac {P_{1}}{P_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>nombro de neperoj</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{nombro de neperoj}}={\frac {1}{2}}\ln {\frac {P_{1}}{P_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0581c75aff5c9ab387c631a277f3200dfb31b831" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.873ex; height:5.676ex;" alt="{\displaystyle {\text{nombro de neperoj}}={\frac {1}{2}}\ln {\frac {P_{1}}{P_{0}}}}" /></span></dd></dl> <p>Alivorte, unu <b>nepero</b> estas la logaritmo de la <a href="/wiki/Rilatumo" title="Rilatumo">rilatumo</a> inter du povumoj kiu egalas <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {e} ^{2}=7,\!389\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>7</mn> <mo>,</mo> <mspace width="negativethinmathspace"></mspace> <mn>389</mn> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {e} ^{2}=7,\!389\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d355fa8e9d19f07ead648af7f8d38d108aaa2130" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.592ex; height:3.009ex;" alt="{\displaystyle \mathrm {e} ^{2}=7,\!389\cdots }" /></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Konverto_al_aliaj_unuoj">Konverto al aliaj unuoj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nepero&veaction=edit&section=2" title="Redakti sekcion: Konverto al aliaj unuoj" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Nepero&action=edit&section=2" title="Redakti la fontkodo de la sekcio: Konverto al aliaj unuoj"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La <a href="/wiki/Belo_(mezurunuo)" title="Belo (mezurunuo)">belo (mezurunuo)</a> (simbole B) estas mezurunuo, kiu reprezentas la rilatumon inter du amplitudoj kiu egalas <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\ln 10)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mn>10</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\ln 10)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7375fa521e20b924a0b9d4e8713c900149d812ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.786ex; height:2.843ex;" alt="{\displaystyle (\ln 10)/2}" /></span> (aŭ rilatumon inter povumoj de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ln 10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡</mo> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln 10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca0dbe948697e0e07d16f36c6e4dc9a63202532" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.651ex; height:2.176ex;" alt="{\displaystyle \ln 10}" /></span>). </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{nombro de beloj}}={\frac {1}{2}}\ln 10\ln {\frac {A_{1}}{A_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>nombro de beloj</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mn>10</mn> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{nombro de beloj}}={\frac {1}{2}}\ln 10\ln {\frac {A_{1}}{A_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1420ed4db42f2a6c1a0da6ed07deac8227ff9218" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.572ex; height:5.843ex;" alt="{\displaystyle {\text{nombro de beloj}}={\frac {1}{2}}\ln 10\ln {\frac {A_{1}}{A_{0}}}}" /></span></dd></dl> <p>Tial, jen la konverto inter belo kaj nepero: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1\,\mathrm {Np} ={\frac {2}{\ln(10)}}\,\mathrm {B} \approx 8,\!6859\times 10^{-1}\,\mathrm {B} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">p</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>10</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> <mo>≈</mo> <mn>8</mn> <mo>,</mo> <mspace width="negativethinmathspace"></mspace> <mn>6859</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\,\mathrm {Np} ={\frac {2}{\ln(10)}}\,\mathrm {B} \approx 8,\!6859\times 10^{-1}\,\mathrm {B} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e39cdc8b5b9e219540f40c79b205f7bbfdb2a8c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:35.714ex; height:6.009ex;" alt="{\displaystyle 1\,\mathrm {Np} ={\frac {2}{\ln(10)}}\,\mathrm {B} \approx 8,\!6859\times 10^{-1}\,\mathrm {B} }" /></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1\,\mathrm {B} ={\frac {1}{2}}\ln(10)\,\mathrm {Np} \approx 1,\!1513\,\mathrm {Np} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>10</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">p</mi> </mrow> <mo>≈</mo> <mn>1</mn> <mo>,</mo> <mspace width="negativethinmathspace"></mspace> <mn>1513</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">p</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\,\mathrm {B} ={\frac {1}{2}}\ln(10)\,\mathrm {Np} \approx 1,\!1513\,\mathrm {Np} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a519218dd56fb11b5031463589c5f8668538027" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:31.156ex; height:5.176ex;" alt="{\displaystyle 1\,\mathrm {B} ={\frac {1}{2}}\ln(10)\,\mathrm {Np} \approx 1,\!1513\,\mathrm {Np} }" /></span></dd></dl> <p>La <a href="/wiki/Decibelo" title="Decibelo">decibelo</a> (simbole dB) estas mezurunuo, kiu reprezentas la rilatumon inter du amplitudoj kiu egalas <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\ln 10)/20}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mn>10</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>20</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\ln 10)/20}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc5e4ca2a529166d0c9125d2b43b6aedd0b12d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.948ex; height:2.843ex;" alt="{\displaystyle (\ln 10)/20}" /></span> (aŭ rilatumon inter povumoj de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\ln 10)/10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mn>10</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\ln 10)/10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3243704820c1e01039881553a31ce6a89860cb1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.948ex; height:2.843ex;" alt="{\displaystyle (\ln 10)/10}" /></span>). </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{nombro de beloj}}={\frac {1}{20}}\ln 10\ln {\frac {A_{1}}{A_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>nombro de beloj</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>20</mn> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mn>10</mn> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{nombro de beloj}}={\frac {1}{20}}\ln 10\ln {\frac {A_{1}}{A_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/863d8fae586f3761417a6af5665d29afa084316e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:33.735ex; height:5.843ex;" alt="{\displaystyle {\text{nombro de beloj}}={\frac {1}{20}}\ln 10\ln {\frac {A_{1}}{A_{0}}}}" /></span></dd></dl> <p>Tial, jen la konverto inter belo kaj nepero: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1\,\mathrm {Np} ={\frac {20}{\ln(10)}}\,\mathrm {dB} \approx 8,\!6859\,\mathrm {dB} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">p</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>20</mn> <mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>10</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> <mo>≈</mo> <mn>8</mn> <mo>,</mo> <mspace width="negativethinmathspace"></mspace> <mn>6859</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\,\mathrm {Np} ={\frac {20}{\ln(10)}}\,\mathrm {dB} \approx 8,\!6859\,\mathrm {dB} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e8e0f3b7b575f74d37ff2c32c16af10f97d445e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:30.801ex; height:6.009ex;" alt="{\displaystyle 1\,\mathrm {Np} ={\frac {20}{\ln(10)}}\,\mathrm {dB} \approx 8,\!6859\,\mathrm {dB} }" /></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1\,\mathrm {dB} ={\frac {1}{20}}\ln(10)\,\mathrm {Np} \approx 1,\!1513\times 10^{-1}\,\mathrm {Np} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>20</mn> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>10</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">p</mi> </mrow> <mo>≈</mo> <mn>1</mn> <mo>,</mo> <mspace width="negativethinmathspace"></mspace> <mn>1513</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">p</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\,\mathrm {dB} ={\frac {1}{20}}\ln(10)\,\mathrm {Np} \approx 1,\!1513\times 10^{-1}\,\mathrm {Np} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46325f66a6ac7cfb64010cae83cbf54301249322" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:41.109ex; height:5.176ex;" alt="{\displaystyle 1\,\mathrm {dB} ={\frac {1}{20}}\ln(10)\,\mathrm {Np} \approx 1,\!1513\times 10^{-1}\,\mathrm {Np} }" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Historio">Historio</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nepero&veaction=edit&section=3" title="Redakti sekcion: Historio" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Nepero&action=edit&section=3" title="Redakti la fontkodo de la sekcio: Historio"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La nepero estis nomita laŭ <a href="/wiki/John_Napier" title="John Napier">John Napier</a> (Esperantigite, Johano Nepero). La nepero estis difinita en 1922 de la Usona firmao Bell Telephone Laboratories, origine angle literatumita <i><span class="lang-en" lang="en">napier</span></i>;<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><sup class="reference" style="white-space:nowrap;">:191</sup> poste la literumo estis ŝanĝita al <i><span class="lang-en" lang="en">neper</span></i> en 1929.<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><sup class="reference" style="white-space:nowrap;">:2</sup> </p><p>La simbolo de la nepero estas majuskla (Np), pro la ĝenerala regulo ke la simbolo de mezurunuo nomita laŭ propra nomo estas majuskla (malgraŭ ke la nomo de la mezurunuo mem estas minuskla). </p> <div class="noprint" id="aliaj_projektoj" style="float: right; clear: right; width: 250px; border: 1px solid #aaa; padding: 4px; font-size: 90%; background: #f9f9f9;"> <ul class="noarchive"><li class="retavortaro"><a href="https://reta-vortaro.de/revo/art/neper.html" class="extiw" title="revo:neper">Nepero en <span>ReVo</span></a> </li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Referencoj">Referencoj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nepero&veaction=edit&section=4" title="Redakti sekcion: Referencoj" class="mw-editsection-visualeditor"><span>redakti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Nepero&action=edit&section=4" title="Redakti la fontkodo de la sekcio: Referencoj"><span>redakti fonton</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist references-small" style="padding-right: 6px;"> <ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1">↑</a> <span class="reference-text"><a href="/wiki/Nova_Plena_Ilustrita_Vortaro_de_Esperanto" class="mw-redirect" title="Nova Plena Ilustrita Vortaro de Esperanto">Nova Plena Ilustrita Vortaro de Esperanto</a>: <a rel="nofollow" class="external text" href="http://vortaro.net/#nepero">neper/o</a></span> </li> <li id="cite_note-2"><a href="#cite_ref-2">↑</a> <span class="reference-text"><cite style="font-style:normal;">MacKenzie, Donald (1922). “The relative sensitivity of the ear at different levels of loudness”, <i>Proceedings of the National Academy of Sciences of the United States of America</i> (en) <b>8</b> (7), <span style="white-space:nowrap;">p. 188–191</span>. <a href="/wiki/Cifereca_objekta_identigilo" title="Cifereca objekta identigilo">doi</a>:<a href="//doi.org/10.1073/pnas.8.7.188" class="extiw" title="doi:10.1073/pnas.8.7.188">10.1073/pnas.8.7.188</a>.</cite><span style="display:none;"> </span></span> </li> <li id="cite_note-3"><a href="#cite_ref-3">↑</a> <span class="reference-text"><cite style="font-style:normal;">Martin, W. H. (1929-01). “<a rel="nofollow" class="external text" href="https://archive.org/details/bstj8-1-1/">Decibel — the name for the transmission unit</a>”, <i>Bell Systems Technical Journal</i> (en) <b>8</b>, <span style="white-space:nowrap;">p. 1–2</span>.</cite><span style="display:none;"> </span></span> </li> </ol></div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Elŝutita el "<a dir="ltr" href="https://eo.wikipedia.org/w/index.php?title=Nepero&oldid=9028650">https://eo.wikipedia.org/w/index.php?title=Nepero&oldid=9028650</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Speciala%C4%B5o:Kategorioj" title="Specialaĵo:Kategorioj">Kategorio</a>: <ul><li><a href="/wiki/Kategorio:Mezurunuoj" title="Kategorio:Mezurunuoj">Mezurunuoj</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"> Ĉi tiu paĝo estis lastafoje redaktita je 16:32, 21 feb. 2025.</li> <li id="footer-info-copyright">La teksto disponeblas laŭ la permesilo <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.eo">Krea Komunaĵo Atribuite-Samkondiĉe 4.0 Neadaptita</a>; eble aldonaj kondiĉoj aplikeblas. 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