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id="content" class="mw-body"> <div class="banner-container"> <div id="siteNotice"></div> </div> <div class="pre-content heading-holder"> <div class="page-heading"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Octaeteris</span></h1> <div class="tagline"></div> </div> <ul id="p-associated-pages" class="minerva__tab-container"> <li class="minerva__tab selected"><a class="minerva__tab-text" href="https://en-m-wikipedia-org.translate.goog/wiki/Octaeteris?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" rel="" data-event-name="tabs.subject">Article</a></li> <li class="minerva__tab "><a class="minerva__tab-text" href="https://en-m-wikipedia-org.translate.goog/wiki/Talk:Octaeteris?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" rel="discussion" data-event-name="tabs.talk">Talk</a></li> </ul> <nav class="page-actions-menu"> <ul id="p-views" class="page-actions-menu__list"> <li id="language-selector" class="page-actions-menu__list-item"><a role="button" 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class="page-actions-menu__list-item"><a role="button" id="ca-edit" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Octaeteris&action=edit&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" data-event-name="menu.edit" data-mw="interface" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet edit-page menu__item--page-actions-edit"> <span class="minerva-icon minerva-icon--edit"></span> <span>Edit</span> </a></li> </ul> </nav> <div id="mw-content-subtitle"></div> </div> <div id="bodyContent" class="content"> <div id="mw-content-text" class="mw-body-content"> <script>function mfTempOpenSection(id){var block=document.getElementById("mf-section-"+id);block.className+=" open-block";block.previousSibling.className+=" open-block";}</script> <div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"> <section class="mf-section-0" id="mf-section-0"> <p>In <a href="https://en-m-wikipedia-org.translate.goog/wiki/Astronomy?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Astronomy">astronomy</a>, an <b>octaeteris</b> (<a href="https://en-m-wikipedia-org.translate.goog/wiki/Greek_language?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Greek language">Greek</a>: <span lang="el">ὀκταετηρίς</span>, plural: <b>octaeterides</b>) is the period of eight <a href="https://en-m-wikipedia-org.translate.goog/wiki/Solar_year?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Solar year">solar years</a> after which the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Moon_phase?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Moon phase">moon phase</a> occurs on the same day of the year plus one or two days.</p> <p>This period is also in a very good synchronicity with five <a href="https://en-m-wikipedia-org.translate.goog/wiki/Venus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Venus">Venusian</a> visibility cycles (the Venusian <a href="https://en-m-wikipedia-org.translate.goog/wiki/Synodic_period?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Synodic period">synodic period</a>) and thirteen Venusian revolutions around the Sun (Venusian <a href="https://en-m-wikipedia-org.translate.goog/wiki/Sidereal_period?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Sidereal period">sidereal period</a>). This means, that if <a href="https://en-m-wikipedia-org.translate.goog/wiki/Venus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Venus">Venus</a> is visible beside the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Moon?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Moon">Moon</a>, after eight years the two will be again close together near the same date of the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Calendar?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Calendar">calendar</a>.</p> <dl> <dd> <table class="wikitable"> <caption> Comparison of differing parts of the octaeteris </caption> <tbody> <tr> <th>Astronomical period</th> <th>Number in an<br> octaeteris</th> <th>Overall duration<br> (<a href="https://en-m-wikipedia-org.translate.goog/wiki/Earth?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Earth">Earth</a> days)</th> </tr> <tr> <td><a href="https://en-m-wikipedia-org.translate.goog/wiki/Tropical_year?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Tropical year">Tropical year</a></td> <td align="right">8 </td> <td>  2 921.93754</td> </tr> <tr> <td><a href="https://en-m-wikipedia-org.translate.goog/wiki/Synodic_month?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Synodic month">Synodic lunar month</a></td> <td align="right">99 </td> <td>  2 923.528230</td> </tr> <tr> <td><a href="https://en-m-wikipedia-org.translate.goog/wiki/Sidereal_month?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Sidereal month">Sidereal lunar month</a></td> <td align="right">107 </td> <td>  2 923.417787</td> </tr> <tr> <td><a href="https://en-m-wikipedia-org.translate.goog/wiki/Venus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Venus">Venusian</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Synodic_period?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Synodic period">synodic period</a></td> <td align="right">5 </td> <td>  2 919.6</td> </tr> <tr> <td>Venusian <a href="https://en-m-wikipedia-org.translate.goog/wiki/Sidereal_period?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Sidereal period">sidereal period</a></td> <td align="right">13 </td> <td>  2 921.07595</td> </tr> </tbody> </table> </dd> </dl> <p>The octaeteris, also known as <i>oktaeteris</i>, was noted by <a href="https://en-m-wikipedia-org.translate.goog/wiki/Cleostratus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Cleostratus">Cleostratus</a> in <a href="https://en-m-wikipedia-org.translate.goog/wiki/Ancient_Greece?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Ancient Greece">ancient Greece</a> as a <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠2 923<span class="sr-only">+</span><span class="tion"><span class="num"> 1 </span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> day cycle. The octaeteris is the calendar used for the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Ancient_Olympic_Games?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Ancient Olympic Games">Olympic games</a>; if one <a href="https://en-m-wikipedia-org.translate.goog/wiki/Olympiad?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Olympiad">Olympiad</a> was 50 months long, the next would be 49 lunar months long. This octaeteris calendar is used for the Olympic dial of the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Antikythera_mechanism?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Antikythera mechanism">Antikythera mechanism</a>, to determine the time of the Olympic games and other Greek festivities.</p> <p>The 8 year short lunisolar cycle was probably known to many ancient cultures. The mathematical proportions of the octaeteris cycles were <span class="citation-needed-content" style="padding-left:0.1em; padding-right:0.1em; color:var(--color-subtle, #54595d); border:1px solid var(--border-color-subtle, #c8ccd1);">noted in Classic Vernal rock art in northeastern <a href="https://en-m-wikipedia-org.translate.goog/wiki/Utah?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Utah">Utah</a> by J.Q. Jacobs in 1990.</span><sup class="noprint Inline-Template Template-Fact" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="https://en-m-wikipedia-org.translate.goog/wiki/Wikipedia:Citation_needed?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2020)">citation needed</span></a></i>]</sup> The Three Kings panel also contains more accurate ratios, ratios related to other planets, and apparent astronomical symbolism<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="https://en-m-wikipedia-org.translate.goog/wiki/Wikipedia:Please_clarify?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (January 2020)">clarification needed</span></a></i>]</sup>.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="See_also">See also</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Octaeteris&action=edit&section=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> <ul> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Metonic_cycle?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Metonic cycle">Metonic cycle</a></li> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Eclipse_cycle?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Eclipse cycle">Eclipse cycle</a></li> </ul> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="References">References</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Octaeteris&action=edit&section=2&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Edit section: References" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <ul> <li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMeeus1997" class="citation book cs1"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Jean_Meeus?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Jean Meeus">Meeus, Jean</a> (1997). <i>Mathematical Astronomy Morsels</i>. Willmann-Bell. 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