https://wiki.unissula.ac.id/index.php?action=history&feed=atom&title=Konstanta_Kepler%E2%80%94Bouwkamp 2026-09-16T00:03:22Z Riwayat revisi halaman ini di wiki MediaWiki 1.46.0 https://wiki.unissula.ac.id/index.php?title=Konstanta_Kepler%E2%80%94Bouwkamp&diff=9827&oldid=prev 2026-08-25T08:59:53Z

<p>Presentation V4: sitasi, referensi, Math, Wikimedia Commons, dan atribusi</p> <table style="background-color: #fff; color: #202122;" data-mw-interface=""> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="id"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisi sebelumnya</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisi per 25 Agustus 2026 08.59</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Baris 1:</td> <td colspan="2" class="diff-lineno">Baris 1:</td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[File:Kepler-constant.gif|thumb|right|280px|Urutan poligon tersurat dan lingkaran]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dalam [[Geometri Euklides]], Konstanta &#039;&#039;&#039;[[Johannes Kepler|Kepler]]–Bouwkamp&#039;&#039;&#039; (atau konstanta &#039;&#039;&#039;poligon tersurat&#039;&#039;&#039;) diperoleh sebagai batas dari urutan berikut ini. Mengambil sebuah lingkaran dengan jari-jari 1. Memasukan segitiga biasa dalam lingkaran ini. Memasukan sebuah lingkaran dalam segitiga ini. Menuliskan sebuah [[persegi]] di dalamnya. Menuliskan sebuah lingkaran, [[Segi lima|pentagon biasa]], lingkaran, [[Heksagon|segi enam biasa]] dan sebagainya.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Dalam [[Geometri Euklides]], Konstanta &#039;&#039;&#039;[[Johannes Kepler|Kepler]]–Bouwkamp&#039;&#039;&#039; (atau konstanta &#039;&#039;&#039;poligon tersurat&#039;&#039;&#039;) diperoleh sebagai batas dari urutan berikut ini. Mengambil sebuah lingkaran dengan jari-jari 1. Memasukan segitiga biasa dalam lingkaran ini. Memasukan sebuah lingkaran dalam segitiga ini. Menuliskan sebuah [[persegi]] di dalamnya. Menuliskan sebuah lingkaran, [[Segi lima|pentagon biasa]], lingkaran, [[Heksagon|segi enam biasa]] dan sebagainya.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Jari-jari yang membatasi lingkaran ini disebut Konstanta Kepler–Bouwkamp (Finch, 2003), konstanta ini merupakan kebalikan dari konstanta &#039;&#039;polygon circumscribing&#039;&#039;.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Jari-jari yang membatasi lingkaran ini disebut Konstanta Kepler–Bouwkamp (Finch, 2003), konstanta ini merupakan kebalikan dari konstanta &#039;&#039;polygon circumscribing&#039;&#039;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Nilai numerik ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Nilai numerik ==</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Perluasan desimal Konstanta Kepler–Bouwkamp adalah</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Perluasan desimal Konstanta Kepler–Bouwkamp adalah  </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt; \prod_{k=3}^\infty \cos\left(\frac\pi k\right) = 0.1149420448\dots.&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt; \prod_{k=3}^\infty \cos\left(\frac\pi k\right) = 0.1149420448\dots.&lt;/math&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Jika produk diambil alih bilangan prima ganjil, konstantanya:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Jika produk diambil alih bilangan prima ganjil, konstantanya:</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt;\prod_{k=3,5,7,11,13,17,\ldots} \cos\left(\frac\pi k\right) =</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: &lt;math&gt;\prod_{k=3,5,7,11,13,17,\ldots} \cos\left(\frac\pi k\right) =  </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>0.312832\ldots&lt;/math&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>0.312832\ldots&lt;/math&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>diperoleh .</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>diperoleh .</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== <del style="font-weight: bold; text-decoration: none;">Referensi </del>==</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>== <ins style="font-weight: bold; text-decoration: none;">Sumber dan atribusi </ins>==</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">*</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">*</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">*</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">*</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Konstanta+Kepler%E2%80%94Bouwkamp&amp;oldid=22950366 Wikipedia bahasa Indonesia], revisi 22950366 (2023-02-14T19:41:54Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Gambar pada artikel ini bersumber dari Wikimedia Commons dan mengikuti ketentuan lisensi masing-masing berkas. Mohon gunakan konten dan media secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;!</ins>-- <ins style="font-weight: bold; text-decoration: none;">WIKI_UNISSULA_PRESENTATION_V4 </ins>--<ins style="font-weight: bold; text-decoration: none;">&gt;</ins></div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">== Sumber dan atribusi ==</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Konstanta+Kepler%E2%80%94Bouwkamp&amp;oldid=22950366 Wikipedia bahasa Indonesia], revisi 22950366 (2023</del>-<del style="font-weight: bold; text-decoration: none;">02</del>-<del style="font-weight: bold; text-decoration: none;">14T19:41:54Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi</del>-<del style="font-weight: bold; text-decoration: none;">BerbagiSerupa (CC BY</del>-<del style="font-weight: bold; text-decoration: none;">SA). Mohon gunakan konten ini secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.</del></div></td><td colspan="2" class="diff-side-added"></td></tr> </table>

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<p>Impor teks terkontrol dari Wikipedia bahasa Indonesia; revisi 22950366; atribusi sumber disertakan.</p> <p><b>Halaman baru</b></p><div>Dalam [[Geometri Euklides]], Konstanta &#039;&#039;&#039;[[Johannes Kepler|Kepler]]–Bouwkamp&#039;&#039;&#039; (atau konstanta &#039;&#039;&#039;poligon tersurat&#039;&#039;&#039;) diperoleh sebagai batas dari urutan berikut ini. Mengambil sebuah lingkaran dengan jari-jari 1. Memasukan segitiga biasa dalam lingkaran ini. Memasukan sebuah lingkaran dalam segitiga ini. Menuliskan sebuah [[persegi]] di dalamnya. Menuliskan sebuah lingkaran, [[Segi lima|pentagon biasa]], lingkaran, [[Heksagon|segi enam biasa]] dan sebagainya.<br /> Jari-jari yang membatasi lingkaran ini disebut Konstanta Kepler–Bouwkamp (Finch, 2003), konstanta ini merupakan kebalikan dari konstanta &#039;&#039;polygon circumscribing&#039;&#039;.<br /> <br /> == Nilai numerik ==<br /> Perluasan desimal Konstanta Kepler–Bouwkamp adalah<br /> : &lt;math&gt; \prod_{k=3}^\infty \cos\left(\frac\pi k\right) = 0.1149420448\dots.&lt;/math&gt;<br /> Jika produk diambil alih bilangan prima ganjil, konstantanya:<br /> : &lt;math&gt;\prod_{k=3,5,7,11,13,17,\ldots} \cos\left(\frac\pi k\right) =<br /> 0.312832\ldots&lt;/math&gt;<br /> diperoleh .<br /> <br /> == Referensi ==<br /> *<br /> *<br /> *<br /> *<br /> <br /> <br /> <br /> == Sumber dan atribusi ==<br /> <br /> Konten artikel ini diadaptasi dari [https://id.wikipedia.org/w/index.php?title=Konstanta+Kepler%E2%80%94Bouwkamp&amp;oldid=22950366 Wikipedia bahasa Indonesia], revisi 22950366 (2023-02-14T19:41:54Z), yang tersedia berdasarkan lisensi Creative Commons Atribusi-BerbagiSerupa (CC BY-SA). Mohon gunakan konten ini secara bijak serta sesuai dengan ketentuan lisensi yang berlaku.</div>

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