tag:blogger.com,1999:blog-1312731134849572982024-03-14T02:16:42.777-07:00У світі многокутниківТут ви можете знайти всю необхідну інформацію для вивчення та розв'язування многокутниківAnonymoushttp://www.blogger.com/profile/04072122242133573490noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-131273113484957298.post-89830952530276506162015-12-06T01:13:00.001-08:002015-12-06T01:39:54.130-08:00Многокутники<div dir="ltr" style="text-align: left;" trbidi="on">
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<strong style="color: #333333; font-size: 0.9em; line-height: 1.6em; text-align: left;">Многокутник</strong><span style="color: #333333; font-size: 0.9em; line-height: 1.6em; text-align: left;"> — фігура, утворена на площині замкнутою ламаною лінією. Говорять також, що многокутник — частина площини, обмежена замкненою ламаною лінією.</span></div>
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Ланки ламаної називаються <strong>сторонами многокутника</strong>. Точки, в яких сходяться дві сусідні ланки, називаються <strong>вершинами многокутника</strong>.</div>
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Кути, внутрішня область яких належить многокутнику і які складені двома сусідніми сторонами, називаються <strong>внутрішніми кутами многокутника</strong>. Кути, суміжні з внутрішніми кутами многокутника, називаються його <strong>зовнішніми </strong><strong>кутами</strong>, тобто зовнішній кут — це кут, утворений стороною многокутника, і продовженням сусідньої сторони.</div>
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Кожному внутрішньому кутові можна поставити у відповідність лише один зовнішній кут многокутника.</div>
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Сума довжин всіх сторін многокутника називається його <strong>периметром</strong> і позначається буквою <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-1-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-1" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.987em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 0.813em;"><span style="border: 0px; clip: rect(1.623em 1000em 2.665em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.486em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">P<span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.119em;"></span></span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.491em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0.976em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.066em; width: 0px;"></span></span></nobr></span> або <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-2-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-4" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 1.276em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 1.045em;"><span style="border: 0px; clip: rect(1.913em 1000em 3.128em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.775em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-5" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mn" id="MathJax-Span-6" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">2</span><span class="mi" id="MathJax-Span-7" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">p</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.781em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1.184em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.274em; width: 0px;"></span></span></nobr></span> , де <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-3-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-8" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.639em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 0.524em;"><span style="border: 0px; clip: rect(1.855em 1000em 2.839em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.486em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-9" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-10" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">p</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.491em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0.906em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.274em; width: 0px;"></span></span></nobr></span> — півсума всіх його сторін (<strong>півпериметр</strong>).</div>
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Многокутник називається <strong>опуклим</strong>, якщо він розміщений по одну сторону від будь-якої своєї сторони, необмежено продовженої.</div>
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<strong>Простим многокутником</strong> називається такий многокутник, контур якого не має самоперетинів.</div>
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Якщо сторони многокутника мають самоперетини, він називається <strong>непростим </strong>(зірчастим). Сума внутрішніх кутів будь-якого простого многокутника дорівнює <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-4-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-11" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 4.459em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 3.707em;"><span style="border: 0px; clip: rect(1.855em 1000em 3.186em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.775em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-12" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-13" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">π<span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-14" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">(</span><span class="mi" id="MathJax-Span-15" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-16" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.234em; position: static; transition: none; vertical-align: 0px;">−</span><span class="mn" id="MathJax-Span-17" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.234em; position: static; transition: none; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-18" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">)</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.781em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1.323em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.344em; width: 0px;"></span></span></nobr></span> радіанів, тобто <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-5-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-19" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 5.038em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 4.17em;"><span style="border: 0px; clip: rect(1.855em 1000em 3.186em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.775em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-20" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mn" id="MathJax-Span-21" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">2</span><span class="mi" id="MathJax-Span-22" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">d<span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-23" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">(</span><span class="mi" id="MathJax-Span-24" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-25" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.234em; position: static; transition: none; vertical-align: 0px;">−</span><span class="mn" id="MathJax-Span-26" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.234em; position: static; transition: none; vertical-align: 0px;">2</span><span class="mo" id="MathJax-Span-27" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">)</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.781em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1.323em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.344em; width: 0px;"></span></span></nobr></span>.</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Arial, Helvetica, sans-serif; font-size: 0.9em; font-stretch: inherit; line-height: 1.6em; margin-bottom: 1em; padding: 0px; vertical-align: baseline;">
Сума зовнішніх кутів опуклого многокутника дорівнює <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-6-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-28" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 1.334em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 1.102em;"><span style="border: 0px; clip: rect(1.913em 1000em 2.954em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.775em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-29" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mn" id="MathJax-Span-30" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">2</span><span class="mi" id="MathJax-Span-31" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">π<span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.781em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0.976em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.066em; width: 0px;"></span></span></nobr></span> радіанів, тобто <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-7-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-32" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 1.276em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 1.045em;"><span style="border: 0px; clip: rect(1.913em 1000em 2.954em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.775em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-33" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mn" id="MathJax-Span-34" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">4</span><span class="mi" id="MathJax-Span-35" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">d<span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.781em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0.976em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.066em; width: 0px;"></span></span></nobr></span>.</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Arial, Helvetica, sans-serif; font-size: 0.9em; font-stretch: inherit; line-height: 1.6em; margin-bottom: 1em; padding: 0px; vertical-align: baseline;">
Два многокутники називаються <strong>рівними</strong>, якщо їх можна сумістити накладанням.</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Arial, Helvetica, sans-serif; font-size: 0.9em; font-stretch: inherit; line-height: 1.6em; margin-bottom: 1em; padding: 0px; vertical-align: baseline;">
Залежно від числа кутів (сторін) многокутник називається <strong>трикутником</strong>, <strong>чотирикутником</strong> тощо.</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Arial, Helvetica, sans-serif; font-size: 0.9em; font-stretch: inherit; line-height: 1.6em; margin-bottom: 1em; padding: 0px; vertical-align: baseline;">
Многокутник називається <strong>правильним</strong>, якщо всі його сторони і всі кути рівні між собою.</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Arial, Helvetica, sans-serif; font-size: 0.9em; font-stretch: inherit; line-height: 1.6em; margin-bottom: 1em; padding: 0px; vertical-align: baseline;">
Многокутник часто називають також <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-8-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-36" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.813em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 0.639em;"><span style="border: 0px; clip: rect(1.855em 1000em 2.665em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.486em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-37" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-38" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.491em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0.698em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.066em; width: 0px;"></span></span></nobr></span>-кутником, де <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-9-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-39" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.813em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 0.639em;"><span style="border: 0px; clip: rect(1.855em 1000em 2.665em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.486em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-40" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-41" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.491em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0.698em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.066em; width: 0px;"></span></span></nobr></span> — число сторін (вершин, кутів). Очевидно, що <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-10-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-42" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 3.012em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 2.491em;"><span style="border: 0px; clip: rect(1.97em 1000em 3.07em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.775em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-43" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-44" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-45" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.292em; position: static; transition: none; vertical-align: 0px;">≥</span><span class="mn" id="MathJax-Span-46" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.292em; position: static; transition: none; vertical-align: 0px;">3</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.781em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1.115em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.205em; width: 0px;"></span></span></nobr></span>.</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Arial, Helvetica, sans-serif; font-size: 0.9em; font-stretch: inherit; line-height: 1.6em; margin-bottom: 1em; padding: 0px; vertical-align: baseline;">
Кожний кут правильного многокутника дорівнює <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-11-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-47" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 3.244em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 2.665em;"><span style="border: 0px; clip: rect(1.623em 1000em 3.417em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.833em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-48" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mstyle" id="MathJax-Span-49" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-50" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-51" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px 0.119em; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 1.739em;"><span style="border: 0px; clip: rect(3.244em 1000em 4.17em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 15.0156px; margin: 0px 0px 0px -0.807em; padding: 0px; position: absolute; top: -4.453em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-52" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-53" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 14.6707px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-54" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: 14.6707px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">−</span><span class="mn" id="MathJax-Span-55" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: 14.6707px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">2</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 3.996em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.475em 1000em 4.17em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 15.0156px; margin: 0px 0px 0px -0.229em; padding: 0px; position: absolute; top: -3.585em; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-56" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 14.6707px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 3.996em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.871em 1000em 1.276em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -1.386em; transition: none; vertical-align: 0px;"><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 1.739em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1.25px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0.003em; width: 0px;"></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1.102em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mi" id="MathJax-Span-57" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: 20.736px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">π<span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.003em;"></span></span></span></span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.839em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1.948em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.552em; width: 0px;"></span></span></nobr></span> радіанів.</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Arial, Helvetica, sans-serif; font-size: 0.9em; font-stretch: inherit; line-height: 1.6em; margin-bottom: 1em; padding: 0px; vertical-align: baseline;">
<strong>Діагоналями</strong> многокутника називаються відрізки, що з’єднують дві вершини многокутника, які не належать одній його стороні.</div>
<div style="background-color: white; border: 0px; color: #333333; font-family: Arial, Helvetica, sans-serif; font-size: 0.9em; font-stretch: inherit; line-height: 1.6em; margin-bottom: 1em; padding: 0px; vertical-align: baseline;">
Для будь-якого <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-12-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-58" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.813em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 0.639em;"><span style="border: 0px; clip: rect(1.855em 1000em 2.665em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.486em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-59" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-60" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.491em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0.698em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.066em; width: 0px;"></span></span></nobr></span>-кутника число <span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><span class="MathJax" id="MathJax-Element-13-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-size: 14.4px; font-stretch: inherit; font-variant: inherit; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-61" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 1.045em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 17.28px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 0.871em;"><span style="border: 0px; clip: rect(1.623em 1000em 2.665em -999.997em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.003em; margin: 0px; padding: 0px; position: absolute; top: -2.486em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-62" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-63" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">N<span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.061em;"></span></span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.491em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0.976em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.066em; width: 0px;"></span></span></nobr></span> його діагоналей визначається за формулою:</div>
<div class="formula" style="background-color: white; border: 0px; color: #333333; font-family: Tahoma, Arial, Helvetica, sans-serif, 'Lucida Sans'; font-size: 16px; font-stretch: inherit; margin: 0px; padding: 0px; text-align: center; vertical-align: baseline;">
<span class="MathJax_Preview" style="border: 0px; color: inherit; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; padding: 0px; vertical-align: baseline;"></span><br />
<div class="MathJax_Display" style="border: 0px; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 1em 0em; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; position: relative; vertical-align: baseline; width: 689px;">
<span class="MathJax" id="MathJax-Element-14-Frame" style="border: 0px; direction: ltr; display: inline; float: none; font-family: inherit; font-stretch: inherit; font-variant: inherit; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; text-align: left; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none; vertical-align: 0px;"><span class="math" id="MathJax-Span-64" role="math" style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 7.939em;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: 20.16px; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 6.302em;"><span style="border: 0px; clip: rect(1.044em 1000em 3.524em -999.998em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.002em; margin: 0px; padding: 0px; position: absolute; top: -2.676em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-65" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-66" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">N<span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0.102em;"></span></span><span class="mo" id="MathJax-Span-67" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.3em; position: static; transition: none; vertical-align: 0px;">=</span><span class="mfrac" id="MathJax-Span-68" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.3em; position: static; transition: none; vertical-align: 0px;"><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 0px; margin: 0px 0.102em; padding: 0px; position: relative; transition: none; vertical-align: 0px; width: 3.772em;"><span style="border: 0px; clip: rect(3.127em 1000em 4.417em -999.998em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 38.0156px; margin: 0px 0px 0px -1.833em; padding: 0px; position: absolute; top: -4.71em; transition: none; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-69" style="border: 0px; display: inline; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-70" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-71" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">(</span><span class="mi" id="MathJax-Span-72" style="border: 0px; display: inline; font-family: MathJax_Math-italic; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-73" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.201em; position: static; transition: none; vertical-align: 0px;">−</span><span class="mn" id="MathJax-Span-74" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px 0px 0px 0.201em; position: static; transition: none; vertical-align: 0px;">3</span><span class="mo" id="MathJax-Span-75" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">)</span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 4.02em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(3.227em 1000em 4.169em -999.998em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 38.0156px; margin: 0px 0px 0px -0.246em; padding: 0px; position: absolute; top: -3.321em; transition: none; vertical-align: 0px;"><span class="mn" id="MathJax-Span-76" style="border: 0px; display: inline; font-family: "mathjax_main"; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px;">2</span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 4.02em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(0.846em 1000em 1.193em -999.998em); font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; left: 0.002em; margin: 0px; padding: 0px; position: absolute; top: -1.238em; transition: none; vertical-align: 0px;"><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 3.772em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1.25px; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: 0.002em; width: 0px;"></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 1.044em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.681em; margin: 0px; padding: 0px; position: static; transition: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-color: initial; border-left-style: solid; border-width: 0px 0px 0px 0.003em; display: inline-block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-style: inherit; font-variant: inherit; font-weight: inherit; height: 2.816em; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none; vertical-align: -0.934em; width: 0px;"></span></span></nobr></span></div>
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