{"id":607,"date":"2022-02-15T14:45:47","date_gmt":"2022-02-15T06:45:47","guid":{"rendered":"https:\/\/codomainstudyspace.com\/?p=607"},"modified":"2022-02-22T21:24:19","modified_gmt":"2022-02-22T13:24:19","slug":"number-of-diagonals-of-a-polygon-%e5%a4%9a%e9%82%8a%e5%bd%a2%e7%9a%84%e5%b0%8d%e8%a7%92%e7%b7%9a%e6%95%b8%e7%9b%ae","status":"publish","type":"post","link":"https:\/\/codomainstudyspace.com\/maths\/combinatorics\/number-of-diagonals-of-a-polygon-%e5%a4%9a%e9%82%8a%e5%bd%a2%e7%9a%84%e5%b0%8d%e8%a7%92%e7%b7%9a%e6%95%b8%e7%9b%ae\/","title":{"rendered":"Number of Diagonals of a polygon
\u591a\u908a\u5f62\u7684\u5c0d\u89d2\u7dda\u6578\u76ee"},"content":{"rendered":"\n

<\/p>\n\n\n\n

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\u5c0d\u89d2\u7dda<\/strong>\u662f\u4e00\u500b\u591a\u908a\u5f62\u5167\u4efb\u4f55\u5169\u500b\u4e0d\u76f8\u9130\u7684\u9802\u9ede\u6240\u9023\u8d77\u7684\u76f4\u7dda\u3002\u6211\u5011\u53ef\u4ee5\u7528 \"C_r^n\" \u627e\u51fa\u4e5d\u908a\u5f62\u7684\u5c0d\u89d2\u7dda\u7684\u6578\u76ee\u3002<\/p>\n

\u5148\u5047\u8a2d\u5728\u4e00\u500b\u5e73\u9762\u4e0a\u6709\u4e5d\u9ede\uff0c\u628a\u4efb\u610f\u5169\u9ede\u9023\u8d77\u5c31\u80fd\u5f97\u51fa\u4e00\u689d\u76f4\u7dda\u3002\u9019\u6a23\u7684\u8a71\uff0c\u6211\u5011\u6703\u6709 \"C_2^9 = 36\" \u689d\u76f4\u7dda\u3002\u6e1b\u53bb\u4e5d\u908a\u5f62\u7684 9 \u689d\u908a\uff0c\u5c31\u6703\u5f97\u51fa \"36 - 9 = 27\" \u689d\u5c0d\u89d2\u7dda\u3002\u628a\u4e0a\u8981\u7684\u6b65\u9a5f\u5408\u4f75\u7684\u8a71\uff0c\u4e5d\u908a\u5f62\u7684\u5c0d\u89d2\u7dda\u6578\u76ee\u662f \"C_2^9-9=27\" \u689d\u3002<\/p>\n

\"nonagon\"<\/p>\n

<\/p>\n

\u7531\u6b64\u53ef\u898b\uff0c\u4e00\u500b \"n\" \u908a\u5f62\u7684\u5c0d\u89d2\u7dda\u6578\u76ee\u53ef\u4ee5\u4ee5\u540c\u4e00\u65b9\u6cd5\u5f97\u51fa\uff1a<\/p>\n

\u5148\u5047\u8a2d\u5728\u4e00\u500b\u5e73\u9762\u4e0a\u6709 \"n\" \u9ede\uff0c\u628a\u4efb\u610f\u5169\u9ede\u9023\u8d77\u6703\u5f97\u51fa\u5171 \"C_2^n\" \u689d\u76f4\u7dda\uff0c\u6e1b\u53bb \"n\" \u908a\u5f62\u7684 \"n\" \u689d\u908a\uff0c\u5c31\u6703\u5f97\u51fa \"n\" \u908a\u5f62\u7684\u5c0d\u89d2\u7dda\u6578\u76ee\uff1a

  <\/span>   <\/span>\"\begin{equation*} C_2^n-n \end{equation*}\"<\/p><\/p>\n

<\/p>\n\n\n

\n\n\n\n

\u5373\u6642\u7df4\u7fd2<\/h4>\n\n\n\n
\n
\n

Which of the following statements about a regular \"15\"-sided polygon are true? 

I. Each interior angle is \"156\degree\".
II. Each exterior angle is \"24\degree\".
III. The number of diagonals is \"15\". 

A. I and II only
B. I and III only
C. II and III only
D. I, II and III<\/p>\n<\/div>\n\n\n\n

\n

\u4e0b\u5217\u6709\u95dc\u6b63 \"15\" \u908a\u5f62\u7684\u654d\u8ff0\uff0c\u4f55\u8005\u6b63\u78ba\uff1f

I. \u6bcf\u4e00\u5167\u89d2\u5747\u70ba \"156\degree\"\u3002
II. \u6bcf\u4e00\u5916\u89d2\u5747\u70ba \"24\degree\"\u3002
III. \u5c0d\u89d2\u7dda\u6578\u76ee\u70ba \"15\"\u3002 

A. \u53ea\u6709 I \u53ca II
B. \u53ea\u6709 I \u53ca III
C. \u53ea\u6709 II \u53ca III
D. I\u3001II \u53ca III<\/p>\n<\/div>\n<\/div>\n\n\n\n

\u984c\u89e3<\/a><\/h5>\n\n\n\n
\n\n\n\n

Past Paper \u53c3\u8003\u984c\u76ee<\/h4>\n\n\n\n

HKDSE Maths 2013 Paper 2 Q21
HKDSE Maths 2015 Paper 2 Q22
HKDSE Maths 2016 Paper 2 Q24<\/h4>\n","protected":false},"excerpt":{"rendered":"

\u5c0d\u89d2\u7dda\u662f\u4e00\u500b\u591a\u908a\u5f62\u5167\u4efb\u4f55\u5169\u500b\u4e0d\u76f8\u9130\u7684\u9802\u9ede\u6240\u9023\u8d77\u7684\u76f4\u7dda\u3002\u6211\u5011\u53ef\u4ee5\u7528 \u627e\u51fa\u4e5d\u908a\u5f62\u7684\u5c0d\u89d2\u7dda\u7684\u6578\u76ee\u3002 \u5148\u5047\u8a2d\u5728\u4e00\u500b\u5e73\u9762 …<\/p>\n

Number of Diagonals of a polygon
\u591a\u908a\u5f62\u7684\u5c0d\u89d2\u7dda\u6578\u76ee<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":681,"comment_status":"open","ping_status":"closed","sticky":false,"template":"elementor_theme","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[25,30,36],"tags":[31,34],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/codomainstudyspace.com\/wp-content\/uploads\/2022\/02\/Ig-Math-DTraning-Post-1.png","_links":{"self":[{"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/posts\/607"}],"collection":[{"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/comments?post=607"}],"version-history":[{"count":31,"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/posts\/607\/revisions"}],"predecessor-version":[{"id":964,"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/posts\/607\/revisions\/964"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/media\/681"}],"wp:attachment":[{"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/media?parent=607"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/categories?post=607"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/codomainstudyspace.com\/wp-json\/wp\/v2\/tags?post=607"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}