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<p>Das <b>Moss-Ei</b> (engl. <i>Moss's egg</i>) ist ein aus einem <a href="Halbkreis" title="Halbkreis">Halbkreis</a> und drei weiteren <a href="Kreisbogen" title="Kreisbogen">Kreisbögen</a> bestehendes symmetrisches <a href="Oval" title="Oval">Oval</a>, das dem Profil eines <a href="H%C3%BChnerei" title="Hühnerei">Hühnereis</a> ähnelt.

</p><p>Das Moss-Ei lässt sich mit Zirkel und Lineal wie folgt konstruieren:

</p>

<ul><li>Man beginnt mit einer Strecke <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AB}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle AB}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b04153f9681e5b06066357774475c04aaef3a8bd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle AB}" loading="lazy"></span> und konstruiert deren Mittelsenkrechte und zeichnet den Kreis mit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AB}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle AB}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b04153f9681e5b06066357774475c04aaef3a8bd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle AB}" loading="lazy"></span> als Durchmesser, dessen obere Hälfte schneidet die Mittelsenkrechte in <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy"></span> und die untere Hälfte bildet den ersten Kreisbogen des Ovals.</li>

<li>Man schlägt dann je einen Kreisbogen um die Endpunkte der Strecke <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AB}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle AB}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b04153f9681e5b06066357774475c04aaef3a8bd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle AB}" loading="lazy"></span> mit dem Radius<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |AB|}">

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle |AB|}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fa0bf6dba77a8b8734eb4356cac20b49e9a80c3c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.801ex; height:2.843ex;" alt="{\displaystyle |AB|}" loading="lazy"></span>, so dass dieser vom anderen Ende der Strecke <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AB}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle AB}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b04153f9681e5b06066357774475c04aaef3a8bd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle AB}" loading="lazy"></span> zu den Punkten <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"></span> und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy"></span> auf verlängerten Strecken <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AC}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle AC}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b930d133ca536a071bec52a9acc4b05482890d53.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.509ex; height:2.176ex;" alt="{\displaystyle AC}" loading="lazy"></span> beziehungsweise <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle BC}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle BC}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/74e0f24a49061dcd63874f7d81f395b5f38800f7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.53ex; height:2.176ex;" alt="{\displaystyle BC}" loading="lazy"></span> reicht.</li>

<li>Abschließend zeichnet man einen Kreisbogen von <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"></span> nach <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy"></span> mit <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

<p>Allgemeiner bezeichnet man ein aus Kreisbögen zusammengesetztes Oval mit einer Symmetrieachse auch als <a href="Euklidisches_Ei" title="Euklidisches Ei">euklidisches Ei</a>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>

<ul><li>Robert A. Dixon: <cite style="font-style:italic">Mathographics</cite>. Dover 1991, ISBN 0-486-26639-7, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>5</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Moss-Ei&rft.au=Robert+A.+Dixon&rft.btitle=Mathographics&rft.date=1991&rft.genre=book&rft.isbn=0486266397&rft.pages=5&rft.place=Dover" style="display:none"> </span></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>

<div class="sisterproject" style="margin:0.1em 0 0 0;"><div class="noresize noviewer" style="display:inline-block; line-height:10px; min-width:1.6em; text-align:center;" aria-hidden="true" role="presentation"><span class="mw-default-size" typeof="mw:File"><span title="Commons"></span></span></div><b><span class=""><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Moss%27s_egg_generalized?uselang=de"><span lang="en">Commons</span>: verallgemeinerte Moss-Eier</a></span></b> – Sammlung von Bildern, Videos und Audiodateien</div>

<ul><li><a href="Eric_Weisstein" title="Eric Weisstein">Eric W. Weisstein</a>: <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/MosssEgg.html"><i>Moss's egg</i>.</a> In: <i><a href="MathWorld" title="MathWorld">MathWorld</a></i> (englisch).</li>

<li><span class="cite">Freyja Hreinsdóttir: <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200618202007/https://www.dynamat.oriw.eu/upload_pdf/20121022_154322__0.pdf"><i>Euclidean Eggs.</i></a> Archiviert vom <style data-mw-deduplicate="TemplateStyles:r250917974">

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</style><span class="dewiki-iconexternal"><a class="external text" href="https://redirecter.toolforge.org/?url=https%3A%2F%2Fwww.dynamat.oriw.eu%2Fupload_pdf%2F20121022_154322__0.pdf">Original</a></span> am <span style="white-space:nowrap;">18. Juni 2020</span><span style="display:none">;</span><span class="Abrufdatum" style="display:none"> abgerufen im 1. Januar 1</span> (englisch).</span><span style="display: none;" class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rfr_id=info%3Asid%2Fde.wikipedia.org%3AMoss-Ei&rft.title=Euclidean+Eggs&rft.description=Euclidean+Eggs&rft.identifier=https%3A%2F%2Fweb.archive.org%2Fweb%2F20200618202007%2Fhttps%3A%2F%2Fwww.dynamat.oriw.eu%2Fupload_pdf%2F20121022_154322__0.pdf&rft.creator=Freyja%26%2332%3BHreinsd%C3%B3ttir&rft.date=&rft.source=https://www.dynamat.oriw.eu/upload_pdf/20121022_154322__0.pdf&rft.language=en"> </span></li>

<li><a rel="nofollow" class="external text" href="https://aperiodical.com/2017/04/video-how-to-draw-an-egg/">Video: How to draw an egg</a>, The Aperiodical</li>

<li><a rel="nofollow" class="external text" href="https://www.geogebra.org/m/QQ4wnxAp"><i>Moss Egg or Euclidean Egg</i></a> - interaktieve Illustration</li>

<li><a rel="nofollow" class="external text" href="https://homepages.gac.edu/~hvidsten/gex/gex-examples/projects/ovalExample/index.html"><i>Euclidean Eggs: Over Easy</i></a></li></ul></div><div><div class="zim-footer">

Dieser Artikel wurde von <a class="external text" title="Zuletzt bearbeitet am 2025-12-02" href="https://de.wikipedia.org/wiki/?title=Moss-Ei&oldid=262050585">Wikipedia</a> herausgegeben. Der Text ist unter <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.de">Creative Commons Attribution-Share Alike 4.0</a> verfügbar, sofern nicht anders angegeben. Für die Mediendateien können zusätzliche Bedingungen gelten.

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