[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21168#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21168","headline":"\u516c\u5f0f\u306e\u8868\u793a – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","name":"\u516c\u5f0f\u306e\u8868\u793a – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 \u6570\u5b66\u3067\u306f\u3001 Vi\u00e8te\u30d5\u30a9\u30fc\u30df\u30e5\u30e9 \u3001\u3053\u308c\u306f\u3001\u30d5\u30e9\u30f3\u30bd\u30ef\u30f4\u30a3\u30a8\u30c6\u306b\u3088\u308b\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u7121\u9650\u306e\u88fd\u54c1\u3068\u3057\u3066\u6570\u5024\u03c0\u3092\u8868\u73fe\u3059\u308b 2\u03c0= 12de 12+1212de 12+1212+1212de 12+1212+1212+1212\u22ef {displaystyle {frac {2}{pi }}={sqrt {tfrac {1}{2}}}cdot {sqrt {{tfrac {1}{2}}+{tfrac {1}{2}}{sqrt {tfrac","datePublished":"2021-09-09","dateModified":"2021-09-09","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/7ddfb1c04fdf044ae1cc61a47d451cc8ce31a627","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/7ddfb1c04fdf044ae1cc61a47d451cc8ce31a627","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21168","wordCount":3910,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u6570\u5b66\u3067\u306f\u3001 Vi\u00e8te\u30d5\u30a9\u30fc\u30df\u30e5\u30e9 \u3001\u3053\u308c\u306f\u3001\u30d5\u30e9\u30f3\u30bd\u30ef\u30f4\u30a3\u30a8\u30c6\u306b\u3088\u308b\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u7121\u9650\u306e\u88fd\u54c1\u3068\u3057\u3066\u6570\u5024\u03c0\u3092\u8868\u73fe\u3059\u308b 2\u03c0= 12de 12+1212de 12+1212+1212de 12+1212+1212+1212\u22ef {displaystyle {frac {2}{pi }}={sqrt {tfrac {1}{2}}}cdot {sqrt {{tfrac {1}{2}}+{tfrac {1}{2}}{sqrt {tfrac {1}{2}}}}}cdot {sqrt {{tfrac {1}{2}}+{tfrac {1}{2}}{sqrt {{tfrac {1}{2}}+{tfrac {1}{2}}{sqrt {tfrac {1}{2}}}}}}}cdot {sqrt {{tfrac {1}{2}}+{tfrac {1}{2}}{sqrt {{tfrac {1}{2}}+{tfrac {1}{2}}{sqrt {{tfrac {1}{2}}+{tfrac {1}{2}}{sqrt {tfrac {1}{2}}}}}}}}}cdots }         (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u53e4\u4ee3\u3067\u7ba1\u7406\u3055\u308c\u3066\u3044\u308b\u5408\u7406\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u3068\u306f\u7570\u306a\u308a\u3001\u6570\u5024\u03c0\u306e\u6b63\u78ba\u306a\u6b63\u78ba\u306a\u8868\u73fe\u306e\u6700\u521d\u306e\u65e2\u77e5\u306e\u4f8b\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u524d\u306e\u5f0f\u306b\u306f\u7279\u5225\u306a\u95a2\u9023\u6027\u304c\u3042\u308a\u307e\u3059\u3002  2\u306e\u30dd\u30ea\u30b4\u30f3\u306e\u9762\u7a4d n \u534a\u5f841\u306e\u5186\u306b\u767b\u9332\u3055\u308c\u3066\u3044\u308b\u5074\u9762\u306f2\u3067\u3059 n -\u521d\u3081 \u305d\u306e\uff08\u03c0\/2 n -\u521d\u3081 \uff09\u3002 \u4ee5\u524d\u306e\u5f0f\u306f\u03c0\u306e\u6700\u521d\u306e\u5206\u6790\u5f0f\u3092\u63d0\u4f9b\u3057\u307e\u3059\u304c\u3001\u5186\u306e\u6b63\u65b9\u5f62\u306e\u554f\u984c\u306b\u95a2\u9023\u3059\u308b\u5e7e\u4f55\u5b66\u7684\u63a8\u8ad6\u306b\u4e09\u89d2\u6cd5\u306e\u30a2\u30a4\u30c7\u30f3\u30c6\u30a3\u30c6\u30a3\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u306f\u3001\u534a\u5f841\u306e\u8f2a\u306e\u767b\u9332\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002 2 n{displaystyle 2^{n}} \u9762\u7a4d\u306e\u7d99\u627f\u304c\u5186\u9818\u57df\u3078\u306e\u9023\u7d9a\u3057\u305f\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3042\u308b\u8fba\u304c\u03c0\u306b\u7b49\u3057\u3044\u3088\u3046\u306b\u3002 \u3068 a n{displaystyle a_ {n}} 2\u306e\u523b\u307e\u308c\u305f\u30dd\u30ea\u30b4\u30f3\u306e\u9818\u57df\u3067\u3059 n \u305d\u306e\u5f8c\u3001\u5074\u9762        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4an= 2n\u22121\u7f6a \u2061 (\u03c02n\u22121){displaystyle a_ {n} = 2^{n-1} sin left\uff08{tfrac {pi} {2^{n-1}}}}}} \u3002 \u4e00\u65b9\u3001\u4e8c\u91cd\u89d2\u306e\u4e73\u623f\u51e6\u65b9\u306f\u305d\u308c\u3092\u78ba\u7acb\u3057\u307e\u3059 \u7f6a \u2061 \uff08 2 th \uff09\uff09 = 2 \u7f6a \u2061 th cos \u2061 th }  \u3057\u305f\u304c\u3063\u3066 \u7f6a \u2061 (\u03c02n\u22121)= 2 \u7f6a \u2061 (\u03c02n)cos \u2061 (\u03c02n){displaystyle sin left\uff08{tfrac {pi} {2^{n-1}}}\u53f3\uff09= 2sin\u5de6\uff08{tfrac {pi} {2^{n}}}\u53f3\uff09 \u3002 \u4e21\u65b9\u306e\u7d50\u679c\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u3001\u5f0f\u306b\u5230\u9054\u3057\u307e\u3059\u3002 a2= a3cos \u2061 (\u03c022){displaystyle a_ {2} = a_ {3} cos left\uff08{tfrac {pi} {2^{2}}}\u53f3\uff09}  =a4cos\u2061(\u03c022)cos\u2061(\u03c023){displaystyle quad = a_ {4} cos left\uff08{tfrac {pi} {2^{2}}}\u53f3\uff09cos\u5de6\uff08{tfrac {pi} {2^{3}}}\u53f3\uff09} =a5cos\u2061(\u03c022)cos\u2061(\u03c023)cos\u2061(\u03c024){displaystyle quad = a_ {5} cos left\uff08{tfrac {pi} {2^{2}}}\u53f3\uff09cos\u5de6\uff08{tfrac {pi} {2^{3}}}\u53f3\uff09cos\u5de6\uff08{tfrac {pi} {2^{4}}}}}} =\u2026{displaystyle quad = ldots} \u306e\u5024\u3068\u3057\u3066 a n{displaystyle a_ {n}} \uff08\u30dd\u30ea\u30b4\u30f3\u306e\u9818\u57df\uff09\u03c0\u306e\u4fa1\u5024\u304c\u3042\u308b\u5186\u306e\u9818\u57df\u306b\u8fd1\u3065\u3044\u3066\u3044\u307e\u3059\u3001\u79c1\u305f\u3061\u306f\u6301\u3063\u3066\u3044\u307e\u3059 a2= pi (cos\u2061(\u03c022)cos\u2061(\u03c023)cos\u2061(\u03c024)cos\u2061(\u03c025)\u22ef){displaystyle a_ {2} = pi left\uff08cos left\uff08{tfrac {pi} {2^{2}}}\u53f3\uff09cos\u5de6\uff08{tfrac {pi} {2^{3}}}\u53f3\uff09cos\u5de6\uff08{tfrac {pi} {{4^{4} {4} {{4}} {{4}} {{4}}} {4} {5}}}\u53f3\uff09cdots\u53f3\uff09}  \u306e\u9818\u57df a 2{displaystyle a_ {2}} \u305d\u308c\u306f\u534a\u5f841\u306e\u5186\u306b\u767b\u9332\u3055\u308c\u3066\u3044\u308b\u6b63\u65b9\u5f62\u306e\u9818\u57df\u306a\u306e\u3067\u3001\u3060\u304b\u3089 a 2= 2 {displaystyle a_ {2} = 2} \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u305d\u308c\u306f\u53d6\u5f97\u3055\u308c\u307e\u3059 2\u03c0= cos \u2061 (\u03c022)cos \u2061 (\u03c023)cos \u2061 (\u03c024)cos \u2061 (\u03c025)\u22ef {displaystyle {frac {2} {pi}} = cos left\uff08{tfrac {pi} {2^{2}}}\u53f3\uff09cos\u5de6\uff08{tfrac {pi} {2^{3}}}\u53f3\uff09 } {2^{5}}}\u53f3\uff09cdots}  \u6700\u5f8c\u306b\u3001\u30b3\u30b5\u30a4\u30f3\u306e\u4e8c\u91cd\u89d2\u5ea6\u5f0f\u306f cos \u2061 (\u03b82)= 1+cos\u2061\u03b82= 12+12cos\u2061\u03b8{displaystyle cos left\uff08{tfrac {theta} {2}}\u53f3\uff09= {sqrt {frac {1+cos theta} {2}}} = {sqrt {{frac {1} {2}}+{frac {1} {2}}}}}}}}}} \u3002 \u305d\u3057\u3066\u3088\u3046\u306b \u03c022= 45 \u2218{displaystyle {tfrac {pi} {2^{2}}} = 45^{circ}} \u6e80\u305f\u3055\u308c\u3066\u3044\u307e\u3059 cos \u2061 (\u03c022)= 12{displaystyle cos\u5de6\uff08{tfrac {pi} {2^{2}}}\u53f3\uff09= {sqrt {tfrac {1} {2}}}}} \u3002 \u8868\u73fe\u306e\u7e70\u308a\u8fd4\u3057\u7f6e\u63db 2\u03c0{displaystyle {tfrac {2} {pi}}} \u30c6\u30b9\u30c8\u304c\u7d42\u4e86\u3057\u307e\u3059\u3002 \u305f\u3060\u3057\u3001\u4ee5\u524d\u306e\u30c6\u30b9\u30c8\u306f\u5e7e\u4f55\u5b66\u7684\u306b\u76f4\u611f\u7684\u3067\u3059\u304c\u3001\u53b3\u5bc6\u306a\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u306f\u3001\u7121\u9650\u306e\u88fd\u54c1\u306e\u53ce\u675f\u3092\u5b9f\u8a3c\u3059\u308b\u3053\u3068\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001Vi\u00e8te\u306e\u6642\u4ee3\u306b\u306f\u5229\u7528\u3067\u304d\u306a\u304b\u3063\u305f\u6570\u5b66\u30c4\u30fc\u30eb\u3067\u3042\u308b\u305f\u3081\u3001Euler\u304c\u6b63\u5f0f\u306a\u30c6\u30b9\u30c8\u3092\u63d0\u4f9b\u3057\u305f1\u4e16\u7d00\u5f8c\u306b\u306f\u3042\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u3002 \u53c2\u7167 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5916\u90e8\u30ea\u30f3\u30af [ \u7de8\u96c6\u3057\u307e\u3059 ]           (adsbygoogle = window.adsbygoogle || 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