{"id":54621,"date":"2024-06-08T01:01:50","date_gmt":"2024-06-08T01:01:50","guid":{"rendered":"https:\/\/science-hub.click\/%E5%86%86%E5%91%A8%E7%8E%87-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-06-08T01:01:50","modified_gmt":"2024-06-08T01:01:50","slug":"%E5%86%86%E5%91%A8%E7%8E%87-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=54621","title":{"rendered":"\u5186\u5468\u7387 – \u5b9a\u7fa9"},"content":{"rendered":"

\u5c0e\u5165<\/h2>
\n\"\"<\/figure>
\u5186\u306e\u76f4\u5f84\u304c 1 \u306e\u5834\u5408\u3001\u5186\u5468\u306f \u03c0 \u3067\u3059\u3002<\/div><\/div><\/div>

\u5186\u5468\u7387<\/b>(\u307e\u305f\u306f\u30a2\u30eb\u30ad\u30e1\u30c7\u30b9\u306e\u5b9a\u6570<\/b>) \u306f\u3001\u901a\u5e38\u306f\u540c\u3058\u540d\u524d\u306e\u30ae\u30ea\u30b7\u30e3\u6587\u5b57\u03c0<\/span><\/b>\u3067\u8868\u3055\u308c\u308b\u6570\u5024\u3067\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5e7e\u4f55\u5b66<\/a><\/span>\u3067\u306f\u4e00\u822c\u306b\u5186<\/a><\/span>\u306e\u5186\u5468\u3068\u305d\u306e\u76f4\u5f84<\/a><\/span>\u306e\u6bd4\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u5186\u306e\u9762\u7a4d<\/a><\/span>\u3068\u305d\u306e\u534a\u5f84\u306e\u4e8c\u4e57<\/a><\/span>\u306e\u6bd4\u3068\u3057\u3066\u3082\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 10^ -6<\/sup>\u306b\u56db\u6368\u4e94\u5165\u3055\u308c\u305f\u5186\u5468\u7387\u306e\u5024\u306f\u300110 \u9032\u8868\u8a18\u3067 3.141593 \u306b\u306a\u308a\u307e\u3059\u3002\u7269\u7406\u5b66<\/a><\/span>\u3001\u5de5\u5b66<\/span>\u3001\u305d\u3057\u3066\u3082\u3061\u308d\u3093\u6570\u5b66<\/a><\/span>\u306a\u3069\u306e\u5206\u91ce\u306e\u591a\u304f\u306e\u516c\u5f0f\u306b\u306f\u3001\u6570\u5b66\u3067\u6700\u3082\u91cd\u8981\u306a\u5b9a\u6570\u306e 1 \u3064\u3067\u3042\u308b \u03c0 \u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/p>

\u03c0 \u306f\u7121\u7406\u6570<\/a><\/span>\u3067\u3059\u3002\u3064\u307e\u308a\u30012 \u3064\u306e\u6574\u6570\u306e\u6bd4\u3068\u3057\u3066\u8868\u3059\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001\u305d\u306e 10 \u9032\u8868\u8a18\u304c\u6709\u9650\u3067\u3082\u5468\u671f\u7684\u3067\u3082\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u8d85\u8d8a\u6570<\/a><\/span>\u3067\u3082\u3042\u308a\u3001\u03c0 \u304c\u6839\u3067\u3042\u308b\u6574\u6570\u4fc2\u6570\u3092\u6301\u3064\u975e\u30bc\u30ed\u591a\u9805\u5f0f<\/a><\/span>\u306f\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u306e\u7d50\u679c\u306f 1882 \u5e74\u306b\u30d5\u30a7\u30eb\u30c7\u30a3\u30ca\u30f3\u30c8 \u30d5\u30a9\u30f3 \u30ea\u30f3\u30c7\u30de\u30f3\u306b\u3088\u3063\u3066\u8a3c\u660e\u3055\u308c\u307e\u3057\u305f\u3002\u5341\u5206\u306b\u6b63\u78ba\u306a \u03c0 \u306e\u8fd1\u4f3c\u5024\u3092\u6c7a\u5b9a\u3057\u3001\u305d\u306e\u6027\u8cea\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u306f\u3001\u6570\u5b66\u306e\u6b74\u53f2\u306b\u308f\u305f\u308b\u554f\u984c\u3067\u3059\u3002\u4e00\u90e8\u306e\u4eba\u304c\u3053\u306e\u6570\u5b57<\/a><\/span>\u306b\u5bfe\u3057\u3066\u8868\u73fe\u3057\u305f\u9b45\u529b\u306f\u3001\u3053\u306e\u6570\u5b57\u3092\u5927\u8846\u6587\u5316<\/a><\/span>\u306b\u6301\u3061\u8fbc\u3093\u3060\u3053\u3068\u3055\u3048\u3042\u308a\u307e\u3059\u3002<\/p>

\u300c \u03c0\u03b5\u03c1\u03af\u03bc\u03b5\u03c4\u03c1\u03bf\u03c2<\/span> \u300d\uff08\u30ae\u30ea\u30b7\u30e3\u8a9e\u3067\u5468\u56f2<\/i>\uff09\u306e\u6700\u521d\u306e\u6587\u5b57\u3067\u3042\u308b\u30ae\u30ea\u30b7\u30e3\u6587\u5b57 \u03c0 \u304c\u3053\u306e\u610f\u5473<\/a><\/span>\u3067\u4f7f\u7528\u3055\u308c\u308b\u3088\u3046\u306b\u306a\u3063\u305f<\/a><\/span>\u306e\u306f18<\/span>\u4e16\u7d00<\/sup>\u306b\u306a\u3063\u3066\u304b\u3089\u3067\u3059\u3002<\/p>

\n\"\u5186\u5468\u7387<\/figure>

\u5b9a\u7fa9\u3068\u6700\u521d\u306e\u30d7\u30ed\u30d1\u30c6\u30a3<\/h2>

\u610f\u5473<\/span><\/h3>
\n\"\"<\/figure>
\u5186\u5468 = \u03c0 \u00d7 \u76f4\u5f84<\/div><\/div><\/div>

\u8f9e\u66f8\u3084\u4e00\u822c\u7684\u306a\u66f8\u7c4d\u3067\u306f\u3001\u03c0 \u306f\u5186\u306e\u5186\u5468\u3068\u305d\u306e\u76f4\u5f84 (\u5fc5\u7136\u7684\u306b\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5e73\u9762\u3067\u3042\u308b\u901a\u5e38\u306e\u5e73\u9762\u5185) \u306e\u9593\u306e\u4e00\u5b9a\u306e\u6bd4\u7387\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002 <\/p>

$$ { \\pi = \\frac{C}{d}. } $$<\/div><\/dd><\/dl>

\u3053\u306e\u6bd4\u7387\u306f\u3001\u9078\u629e\u3057\u305f\u5186\u3001\u7279\u306b\u305d\u306e\u30b5\u30a4\u30ba\u306b\u306f\u4f9d\u5b58\u3057\u307e\u305b\u3093\u3002\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5e73\u9762\u5185\u306e\u3059\u3079\u3066\u306e\u5186\u306f\u76f8\u4f3c\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u3042\u308b\u5186\u306e\u76f4\u5f84d \u304c<\/i>\u5225\u306e\u5186\u306e 2 \u500d\u3067\u3042\u308b\u5834\u5408\u3001\u305d\u306e\u5186\u5468C<\/i>\u3082 2 \u500d\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

\u03c0 \u306f\u5186\u306e\u8868\u9762\u7a4d\u3068\u305d\u306e\u534a\u5f84\u306e\u4e8c\u4e57\u306e\u6bd4\u3067\u3082\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>

$$ { \\pi = \\frac{A}{r^2}. } $$<\/div><\/dd><\/dl>

\u3053\u306e\u5e7e\u4f55\u5b66\u7684\u306a\u5b9a\u7fa9\u306f\u3001\u6b74\u53f2\u7684\u306b\u521d\u3081\u3066\u306e\u3082\u306e\u3067\u3042\u308a\u3001\u975e\u5e38\u306b\u76f4\u89b3\u7684\u306a\u3082\u306e\u3067\u3059\u304c\u3001\u6570\u5b66\u8005\u304c \u03c0 \u3092\u53b3\u5bc6\u306b\u5b9a\u7fa9\u3057\u305f\u3044\u5834\u5408\u306b\u306f\u3001\u6700\u3082\u76f4\u63a5\u7684\u306a\u3082\u306e\u3067\u306f\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u3088\u308a\u5c02\u9580\u7684\u306a\u7814\u7a76\u3067\u306f\u3001\u5e7e\u4f55\u5b66\u3092<\/a><\/span>\u53c2\u7167\u305b\u305a\u306b\u5c0e\u5165\u3055\u308c\u305f\u4e09\u89d2\u95a2\u6570\u81ea\u4f53\u3092\u4f7f\u7528\u3057\u305f\u5b9f\u969b\u306e\u89e3\u6790\u306b\u3088\u3063\u3066 \u03c0 \u3092\u5b9a\u7fa9\u3057\u307e\u3059 (\u4ee5\u4e0b\u3092\u53c2\u7167)\u3002<\/p>

\u4ee3\u66ff\u306e\u5b9a\u7fa9<\/span><\/h3>

\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u9078\u629e\u306f\u3001cos( x<\/i> ) = 0 \u3068\u306a\u308b\u6700\u5c0f\u306e\u6b63\u306e\u6570x<\/i>\u306e 2 \u500d\u3068\u3057\u3066 \u03c0 \u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u5225\u306e\u53ef\u80fd\u306a\u5b9a\u7fa9\u306f\u3001\u30d7\u30ed\u30d1\u30c6\u30a3 exp(z+w)=exp(z)exp(w) \u3068 \u3092\u8003\u616e\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002 exp(0)=1 \u3053\u308c\u306f\u6307\u6570\u95a2\u6570\u306e\u5206\u6790\u7684\u5b9a\u7fa9\u304b\u3089\u5f97\u3089\u308c\u3001\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002

$$ {\\scriptstyle t \\mapsto \\exp(it)} $$<\/div>\u7fa4\u306e\u9023\u7d9a\u7fa4\u5c04\u3067\u3059\u3002
$$ {\\scriptstyle (\\R,+)} $$<\/div>\u30b0\u30eb\u30fc\u30d7\u306b
$$ {\\scriptstyle (\\mathbb{U},\\times)} $$<\/div> \uff08\u307e\u305f\u306f
$$ {\\scriptstyle \\mathbb{U}} $$<\/div>\u306f 1 \u306b\u7b49\u3057\u3044\u4fc2\u6570\u3092\u6301\u3064\u8907\u5408\u4f53\u306e\u30bb\u30c3\u30c8\u3067\u3059)\u3002\u6b21\u306b\u3001exp(it) = 1 \u3068\u306a\u308b\u5b9f\u6570 t \u306e\u96c6\u5408\u304c\u6b21\u306e\u5f62\u5f0f\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002
$$ {\\scriptstyle a\\Z} $$<\/div>\u3053\u3053\u3067\u3001 a \u306f<\/i>\u53b3\u5bc6\u306b\u6b63\u306e\u5b9f\u6570\u3067\u3059\u3002\u6b21\u306b\u3001 \u03c0 = a<\/i> \/ 2<\/span>\u3092\u8a2d\u5b9a\u3057\u307e\u3059\u3002\u7a4d\u5206\u8a08\u7b97<\/a><\/span>\u306b\u3088\u308a\u3001\u3053\u306e\u62bd\u8c61\u5b9a\u7fa9\u304c\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5e7e\u4f55\u5b66\u306e\u5b9a\u7fa9\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u691c\u8a3c\u3067\u304d\u307e\u3059\u3002<\/p>

\u30d6\u30eb\u30d0\u30ad\u306e\u30b0\u30eb\u30fc\u30d7\u306f\u3001\u6b21\u306e\u9023\u7d9a\u7fa4f<\/i>\u5c04\u306e\u5b58\u5728\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u975e\u5e38\u306b\u3088\u304f\u4f3c\u305f\u5225\u306e<\/a><\/span>\u5b9a\u7fa9\u3092\u63d0\u6848\u3057\u3066\u3044\u307e\u3059\u3002

$$ {\\scriptstyle (\\R,+)} $$<\/div>\u306b\u5411\u304b\u3063\u3066
$$ {\\scriptstyle (\\mathbb{U},\\times)} $$<\/div> f<\/i> (1\/4) = i<\/i>\u3068\u306a\u308a\u307e\u3059\u3002\u5f7c\u306f\u3001\u3053\u306e\u5c04\u304c\u5468\u671f 1 \u3067\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308a\u3001\u3059\u3079\u3066\u306e<\/a><\/span>\u5b9f\u6570 x \u306b\u5bfe\u3057\u3066f'(x) = 2iaf(x)<\/i>\u3068\u306a\u308b\u3088\u3046\u306a\u5b9f\u6570a<\/i>\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f\u3002\u5f7c\u306f \u03c0 \u3092\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u6c42\u3081\u3089\u308c\u305f\u5b9f\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>

\u524d\u306e 2 \u3064\u306e\u65b9\u6cd5\u306f\u5b9f\u969b\u306b\u306f\u3001\u95a2\u6570\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3057\u305f\u5186\u306e\u5468\u56f2\u9577\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002

$$ {\\scriptstyle t \\mapsto e^{it},} $$<\/div>\u307e\u305f\u306f\u95a2\u6570
$$ {\\scriptstyle t \\mapsto e^{2i\\pi t}} $$<\/div><\/p>

\u3057\u304b\u3057\u3001\u6b21\u306e\u3088\u3046\u306b\u3057\u3066\u7a4d\u5206\u8a08\u7b97\u3092\u4f7f\u7528\u3057\u3066 \u03c0 \u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ { {\\pi \\over 4} =\\int_0^1 \\sqrt{1-x^2}\\ dx\\,} $$<\/div><\/dd><\/dl>

\u3053\u308c\u306f\u3001\u534a\u5f84 1 \u306e\u5186\u76e4<\/span>\u306e 4 \u5206\u306e 1 \u306e\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

\u307e\u305f\u306f\u3001\u547c\u3073\u51fa\u3057\u3066\u30ab\u30a6\u30f3\u30c8\u3092\u4f7f\u7528\u3059\u308b

$$ {\\scriptstyle \\varphi(n)} $$<\/div>\u6b21\u306e\u3088\u3046\u306a\u81ea\u7136\u6570\u306e\u30da\u30a2 (k, p) \u306e\u6570\u3002
$$ {\\scriptstyle k^2+p^2 \\le n^2} $$<\/div>\u305d\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002 <\/p>
$$ {\\frac{\\pi}{4}= \\lim_{n \\mapsto \\infty} \\frac{\\varphi(n)}{n^2}} $$<\/div><\/dd><\/dl>

\u3053\u308c\u306f\u30014\u5206\u306e1\u5186\u677f\u306e\u9762\u7a4d<\/a><\/span>\u3092\u8a08\u7b97\u3059\u308b\u5225\u306e\u65b9\u6cd5\u3067\u3059\u3002<\/p>

\u4e0d\u5408\u7406<\/span><\/h3>

\u03c0 \u306f\u7121\u7406\u6570\u3067\u3059\u3002\u3064\u307e\u308a\u3001 p<\/i>\u3068q \u304c<\/i>\u6574\u6570\u3067\u3042\u308b\u5834\u5408\u306b\u03c0=p\/q<\/i>\u3068\u66f8\u304f\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002 9 \u4e16\u7d00<\/span>\u306e\u30a2\u30eb\u30fb\u30cf\u30ef\u30ea\u30ba\u30df\u306f<\/a><\/span>\u3001<\/sup> \u03c0 \u304c\u7121\u7406\u6570\u3067\u3042\u308b\u3068\u78ba\u4fe1\u3057\u307e\u3057\u305f\u3002\u30e2\u30fc\u30bc\u30b9 \u30de\u30a4\u30e2\u30cb\u30c7\u30b9<\/a><\/span>\u3082 12\u4e16\u7d00<\/sup>\u306b\u3053\u306e\u8003\u3048\u306b\u3064\u3044\u3066\u8a00\u53ca\u3057\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u30e8\u30cf\u30f3\u30fb\u30cf\u30a4\u30f3\u30ea\u30d2\u30fb\u30e9\u30f3\u30d9\u30eb\u30c8\u304c<\/a><\/span>\u3053\u306e\u7d50\u679c\u3092\u8a3c\u660e\u3057\u305f\u306e\u306f17<\/sup>\u4e16\u7d00\u306b\u306a\u3063\u3066\u304b\u3089\u3067\u3057\u305f\u3002<\/p>

\u5f8c\u8005\u304c\u8457\u66f8\u300e\u8d85\u8d8a\u5186\u5468\u91cf\u304a\u3088\u3073\u5bfe\u6570\u91cf\u306e\u3044\u304f\u3064\u304b\u306e\u9855\u8457\u306a\u6027\u8cea\u306b\u95a2\u3059\u308b\u56de\u60f3\u9332<\/i>\u300f\u306e\u4e2d\u3067\u3001\u4e09\u89d2\u95a2\u6570<\/a><\/span>\u306e\u9023\u5206\u6570<\/a><\/span>tan\u306e\u767a\u5c55\u3092\u7814\u7a76\u3057\u3001tan(m \/ n) \u306f\u3001m \u304a\u3088\u3073 n \u306e\u30bc\u30ed\u4ee5\u5916\u306e\u6574\u6570\u3067\u3001\u7121\u5236\u9650\u3067\u3059\u3002\u3082\u3063\u3068\u8a73\u3057\u304f\u66f8\u3044\u3066\u3042\u308b\u3088<\/p>

$$ {\\tan \\left(\\frac mn\\right) = \\frac{m \\mid}{\\mid n} – \\frac{m^2 \\mid}{\\mid 3n} – \\frac{m^2 \\mid}{\\mid 5n} – \\frac{m^2 \\mid}{\\mid 7n} + \\cdots } $$<\/div><\/dd><\/dl>

\u305f\u3060\u3057\u3001\u9023\u5206\u6570\u3068\u3057\u3066\u306e\u5c55\u958b\u304c\u7121\u9650\u3067\u3042\u308b\u6570\u306f\u7121\u7406\u6570\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u305f\u3081\u3001x \u304c\u30bc\u30ed\u4ee5\u5916\u306e\u6709\u7406\u6570\u306e\u5834\u5408\u3001tan(x) \u306f\u7121\u7406\u6570\u306b\u306a\u308a\u307e\u3059\u3002\u3055\u3066\u3001tan(\u03c0\/4) \u306f 1 \u3067\u3042\u308a\u3001\u6709\u7406\u6570\u3067\u3059\u3002\u5bfe\u5076\u306b\u3088\u3063\u3066\u3001\u03c0\/4\u3001\u3064\u307e\u308a \u03c0 \u304c\u6709\u7406\u6570\u3067\u306f\u306a\u3044\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u307e\u3059\u3002<\/p>

20<\/sup>\u4e16\u7d00\u306b\u306f\u3001\u7a4d\u5206\u5fae\u7a4d\u5206\u306e\u77e5\u8b58\u3088\u308a\u9ad8\u5ea6\u306a\u77e5\u8b58\u3092\u5fc5\u8981\u3068\u3057\u306a\u3044\u4ed6\u306e\u5b9f\u8a3c\u3082\u898b\u3064\u304b\u308a\u307e\u3057\u305f\u3002\u305d\u306e\u3046\u3061\u306e 1 \u3064\u306f\u3001Ivan Niven \u306e\u304a\u304b\u3052\u3067\u975e\u5e38\u306b\u5e83\u304f\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u540c\u69d8\u306e\u8a3c\u62e0\u306f\u30e1\u30a2\u30ea\u30fc\u30fb\u30ab\u30fc\u30c8\u30e9\u30a4\u30c8\u306b\u3088\u3063\u3066\u4ee5\u524d\u306b<\/a><\/span>\u767a\u898b\u3055\u308c\u3066\u3044\u305f\u3002<\/p>

\u8d85\u8d8a\u6027<\/span><\/h3>

\u03c0 \u306f\u8d85\u8d8a\u6570\u3067\u3082\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u03c0 \u3092\u6839\u3068\u3059\u308b\u6709\u7406\u4fc2\u6570\u3092\u6301\u3064\u591a\u9805\u5f0f\u306f\u5b58\u5728\u3057\u307e\u305b\u3093\u3002<\/p>

\u3053\u306e\u7d50\u679c\u304c\u5b9f\u8a3c\u3055\u308c\u305f\u306e\u306f 19\u4e16\u7d00<\/sup>\u306b\u306a\u3063\u3066\u304b\u3089\u3067\u3059\u3002 1873 \u5e74\u3001\u30c1\u30e3\u30fc\u30eb\u30ba \u30a8\u30eb\u30df\u30c3\u30c8\u306f<\/a><\/span>\u81ea\u7136\u5bfe\u6570\u306e\u5e95<\/span>\u3067\u3042\u308b\u6570\u5024 e \u304c\u8d85\u8d8a\u7684\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u305f\u3002 1882 \u5e74\u3001\u30d5\u30a7\u30eb\u30c7\u30a3\u30ca\u30f3\u30c9 \u30d5\u30a9\u30f3 \u30ea\u30f3\u30c7\u30de\u30f3\u306f\u3001\u81ea\u5206\u306e\u63a8\u8ad6\u3092\u5b9a\u7406<\/span>(\u30a8\u30eb\u30df\u30fc\u30c8 \u30ea\u30f3\u30c7\u30de\u30f3\u306e\u5b9a\u7406) \u306b\u4e00\u822c\u5316\u3057\u307e\u3057\u305f\u3002\u3053\u306e\u5b9a\u7406\u3067\u306f\u3001x \u304c\u4ee3\u6570\u7684\u3067\u30bc\u30ed<\/a><\/span>\u3068\u7570\u306a\u308b\u5834\u5408\u3001 e x \u306f<\/sup>\u8d85\u8d8a\u7684\u3067\u3042\u308b\u3068\u8ff0\u3079\u3089\u308c\u3066<\/a><\/span>\u3044\u307e\u3059\u3002\u3053\u3053\u3067 e i\u03c0<\/sup> = -1 \u3057\u305f\u304c\u3063\u3066\u3001e i\u03c0 \u306f<\/sup>\u8d85\u8d8a\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5bfe\u5076\u3068\u306f\u3001i\u03c0 \u306f\u4ee3\u6570\u7684\u3067\u306f\u306a\u304f\u3001\u03c0 \u306f\u8d85\u8d8a\u7684\u3067\u3059\u3002<\/p>

\u03c0 \u306e\u8d85\u8d8a\u306e\u91cd\u8981\u306a\u7d50\u679c\u306f\u3001\u305d\u308c\u304c\u69cb\u6210<\/a><\/span>\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u5b9f\u969b\u3001 Wantzel \u306e\u5b9a\u7406\u306f\u3001<\/span>\u69cb\u6210\u53ef\u80fd\u306a\u3059\u3079\u3066\u306e\u6570<\/a><\/span>\u304c\u4ee3\u6570\u7684\u3067\u3042\u308b\u3068\u7279\u306b\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002\u5b9a\u898f\u3068\u30b3\u30f3\u30d1\u30b9\u3067\u4f5c\u6210\u3067\u304d\u308b\u3059\u3079\u3066\u306e\u70b9\u306e\u5ea7\u6a19\u306f\u4f5c\u6210\u53ef\u80fd\u306a\u6570\u5024\u3067\u3042\u308b\u305f\u3081\u3001\u5186\u3092\u6b63\u65b9\u5f62\u306b\u3059\u308b\u3053\u3068\u306f\u4e0d\u53ef\u80fd\u3067\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u5b9a\u898f\u3068\u30b3\u30f3\u30d1\u30b9\u3060\u3051\u3092\u4f7f\u3063\u3066\u3001\u4e0e\u3048\u3089\u308c\u305f\u5186\u306e\u8868\u9762\u7a4d\u3068\u7b49\u3057\u3044\u8868\u9762\u7a4d\u3092\u6301\u3064\u6b63\u65b9\u5f62\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u306f\u4e0d\u53ef\u80fd\u3067\u3059\u3002<\/p>

10\u9032\u6570\u8868\u73fe<\/span><\/h3>

\u03c0 \u306e 10 \u9032\u8868\u8a18\u306e\u6700\u521d\u306e 100 \u6841\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>

3,141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067\u306e\u5834\u5408\u3001\u5c0f\u6570\u70b9\u4ee5\u4e0b\u306e\u6841\u6570\u306b\u3064\u3044\u3066\u306f\u300c \u300d\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/i><\/dd><\/dl>

2007 \u5e74\u6642\u70b9\u3067\u306f\u3001\u03c0 \u306e\u5c0f\u6570\u70b9\u4ee5\u4e0b 10 12<\/sup>\u6841\u4ee5\u4e0a\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u304c\u3001\u5186\u5468\u306e\u63a8\u5b9a\u306a\u3069\u3001\u591a\u304f\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f 10 \u6841\u7a0b\u5ea6\u3057\u304b\u5fc5\u8981\u3042\u308a\u307e\u305b\u3093<\/a><\/span>\u3002\u305f\u3068\u3048\u3070\u3001\u5c0f\u6570\u70b9\u4ee5\u4e0b 39 \u6841\u306b\u5207\u308a\u6368\u3066\u3089\u308c\u305f \u03c0 \u306e 10 \u9032\u8868\u73fe\u306f\u3001\u6c34\u7d20<\/a><\/span>\u539f\u5b50<\/a><\/span>\u306e\u534a\u5f84\u306b\u5339\u6575\u3059\u308b\u7cbe\u5ea6\u3067\u89b3\u6e2c\u53ef\u80fd\u306a\u5b87\u5b99<\/a><\/span>\u306e\u5bf8\u6cd5<\/a><\/span>\u3067\u3042\u308b\u5186\u306e\u5186\u5468\u3092\u63a8\u5b9a\u3059\u308b\u306e\u306b\u5341\u5206\u3067\u3059\u3002<\/p>

\u03c0 \u306f\u7121\u7406\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u306e 10 \u9032\u8868\u73fe\u306f\u5468\u671f\u7684\u3067\u306f\u306a\u304f\u3001\u7d42\u308f\u308a\u307e\u305b\u3093\u3002 \u03c0 \u306e\u5c0f\u6570\u70b9\u4ee5\u4e0b\u306e\u6841\u6570\u306f\u5e38\u306b\u6570\u5b66\u8005\u3084\u30a2\u30de\u30c1\u30e5\u30a2\u3092\u9b45\u4e86\u3057\u3066\u304a\u308a\u3001\u3088\u308a\u591a\u304f\u306e\u5c0f\u6570\u70b9\u4ee5\u4e0b\u306e\u6841\u6570\u3092\u53d6\u5f97\u3057\u3001\u305d\u306e\u7279\u5b9a\u306e\u7279\u6027\u3092\u8abf\u67fb\u3059\u308b\u305f\u3081\u306b\u591a\u5927\u306a\u52aa\u529b\u304c\u6255\u308f\u308c\u3066\u304d\u307e\u3057\u305f\u3002\u5e83\u7bc4\u306a\u5206\u6790\u4f5c\u696d\u304c\u5b9f\u65bd\u3055\u308c\u3001\u03c0 \u306e\u5c0f\u6570\u70b9\u4ee5\u4e0b 2,000 \u5104\u6841\u4ee5\u4e0a\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u305f\u8a08\u7b97\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u3053\u308c\u3089\u306e\u6570\u5024\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u8aac\u660e\u3059\u308b\u5358\u7d14\u306a\u30e2\u30c7\u30eb\u306f\u898b\u3064\u304b\u3063\u3066\u3044\u307e\u305b\u3093\u3002 \u03c0 \u306e\u5c0f\u6570\u8868\u73fe\u306e\u6570\u5024\u306f\u591a\u304f\u306e Web \u30da\u30fc\u30b8\u3067\u5165\u624b\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u3001\u03c0 \u306e\u5c0f\u6570\u70b9\u4ee5\u4e0b\u306e\u6841\u6570\u3092\u8a08\u7b97\u3059\u308b\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u304c\u3042\u308a\u3001\u6570\u5341\u5104\u500b\u306e\u6570\u5024\u3092\u751f\u6210\u3067\u304d\u3001\u30d1\u30fc\u30bd\u30ca\u30eb \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc<\/a><\/span>\u306b\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3067\u304d\u307e\u3059\u3002<\/p>

\u3055\u3089\u306b\u3001\u03c0 \u309210 \u9032\u6570\u5c55\u958b\u3059\u308b\u3068<\/a><\/span>\u3001\u4ed6\u306e\u7591\u554f\u3001\u7279\u306b \u03c0 \u304c\u6b63\u898f\u6570<\/a><\/span>\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3001\u3064\u307e\u308a 10 \u9032\u6570\u8868\u8a18\u306e\u6841\u304c\u5747\u7b49\u306b\u5206\u5e03\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u77e5\u308b\u5206\u91ce<\/a><\/span>\u304c\u958b\u304b\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u03c0 \u304c\u5b87\u5b99<\/a><\/span>\u6570\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5c0b\u306d\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u305d\u306e 10 \u9032\u5c55\u958b\u3067\u4efb\u610f\u306e\u6570\u5b57\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 2006 \u5e74\u73fe\u5728\u3001\u3053\u308c\u3089\u306e\u8cea\u554f\u306b\u5bfe\u3059\u308b\u7b54\u3048\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>

\u5206\u6570\u8868\u73fe<\/span><\/h3>

\u6b21\u306e\u6574\u6570\u5206\u6570\u306f\u3001\u8a08\u7b97\u3067 Pi \u3092\u4fdd\u5b58\u307e\u305f\u306f\u8fd1\u4f3c\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059 (\u62ec\u5f27\u5185\u306e\u6709\u52b9\u6570\u5b57\u306e\u6570<\/i>): 3\/1( 1<\/i> ); 22\/7 ( 3<\/i> ); 333 \/ 106 ( 5<\/i> ); 355\/113 ( 7<\/i> )<\/b> ; 103993\/33102( 9<\/i> ); 104348 \/ 33215 ( 10<\/i> ); 208341 \/ 66317 ( 10<\/i> )\u3001PI= 3.141 592 653<\/i> 589 793 238 462 … \u3068\u6bd4\u8f03\u3057\u307e\u3059\u3002<\/p>

\u4ed6\u306e\u5206\u6570\u306e\u30a2\u30d7\u30ed\u30fc\u30c1 (\u5c65\u6b74\u3001\u6570\u5024<\/span>\u8fd1\u4f3c<\/a><\/span>\u3001\u9023\u5206\u6570\u3001Pi#Memorizing \u03c0) \u306b\u3064\u3044\u3066\u306f\u4ee5\u4e0b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>

\u03c0\u306e\u8fd1\u4f3c<\/span><\/h3>

\u03c0 \u306e\u8fd1\u4f3c\u5024\u306f\u3001\u5186\u3092\u63cf\u304d\u3001\u305d\u306e\u76f4\u5f84\u3068\u5186\u5468\u3092\u6e2c\u5b9a\u3057\u3001\u5186\u5468\u3092\u76f4\u5f84\u3067\u5272\u308b\u3053\u3068\u306b\u3088\u308a\u7d4c\u9a13\u7684\u306b\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30a2\u30eb\u30ad\u30e1\u30c7\u30b9<\/a><\/span>\u306b\u3088\u308b\u5225\u306e\u5e7e\u4f55\u5b66\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u3001 n<\/i>\u500b\u306e\u8fba\u3092\u6301\u3064\u6b63\u591a\u89d2\u5f62<\/a><\/span>\u306e\u5468\u56f2\u9577P n \u3092<\/sub><\/i>\u8a08\u7b97\u3057\u3001\u305d\u306e\u5916\u63a5\u5186\u307e\u305f\u306f\u5185\u63a5\u5186\u306e\u76f4\u5f84d<\/i>\u3092\u6e2c\u5b9a\u3059\u308b\u3053\u3068\u304b\u3089\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u591a\u89d2\u5f62<\/a><\/span>\u306e\u8fba\u306e\u6570\u304c\u5897\u3048\u308b\u307b\u3069\u3001\u03c0 \u306e\u5024\u306e\u7cbe\u5ea6\u304c\u5411\u4e0a\u3057\u307e\u3059\u3002<\/p>

\u30a2\u30eb\u30ad\u30e1\u30c7\u30b9\u306f\u3001\u8fba\u306e\u6570\u304c\u540c\u3058\u3067\u3001\u4e00\u65b9\u306e\u5186\u306f\u5916\u63a5\u5186\u3001\u3082\u3046\u4e00\u65b9\u306e\u5186\u306f\u5185\u63a5\u5186\u3067\u3042\u308b 2 \u3064\u306e\u6b63\u591a\u89d2\u5f62\u3092\u4f7f\u7528\u3057\u3066\u3001\u516c\u5f0f\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u305f\u7d50\u679c\u3092\u6bd4\u8f03\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306e\u7cbe\u5ea6\u3092\u5224\u65ad\u3057\u307e\u3057\u305f\u3002\u5f7c\u306f\u300196 \u89d2\u5f62\u306e\u591a\u89d2\u5f62\u3092\u4f7f\u7528\u3057\u3066\u3001 3 + 10<\/sup> \u2044<\/big> 71<\/sub><\/span> < \u03c0 < 3 + 1<\/sup> \u2044<\/big> 7<\/sub><\/span>\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u307e\u3057\u305f\u3002<\/p>

\u7d14\u7c8b\u306b\u6570\u5b66\u7684\u306a\u65b9\u6cd5\u306e\u307f\u3092\u5b9f\u88c5\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u03c0 \u306e\u8fd1\u4f3c\u5024\u3092\u53d6\u5f97\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 \u03c0 \u306e\u8a08\u7b97\u306b\u4f7f\u7528\u3055\u308c\u308b\u516c\u5f0f\u306e\u307b\u3068\u3093\u3069\u306f\u305d\u306e\u6570\u5b66\u7684\u7279\u6027\u306b\u57fa\u3065\u3044\u3066\u304a\u308a\u3001\u305d\u308c\u3089\u3092\u7406\u89e3\u3059\u308b\u306b\u306f\u4e09\u89d2\u6cd5<\/a><\/span>\u3068\u7a4d\u5206\u306e\u77e5\u8b58\u304c\u5fc5\u8981\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u30e9\u30a4\u30d7\u30cb\u30c3\u30c4\u306e\u516c\u5f0f\u306e\u3088\u3046\u306b\u3001\u3053\u306e\u6b20\u9665\u304c\u306a\u3044\u3082\u306e\u3082\u3042\u308a\u307e\u3059\u3002 <\/p>

$$ {\\pi = 4\\sum^\\infty_{k=0} \\frac{(-1)^k}{2k+1} = \\frac{4}{1}-\\frac{4}{3}+\\frac{4}{5}-\\frac{4}{7}+\\frac{4}{9}-\\frac{4}{11}\\cdots.\\! } $$<\/div><\/dd><\/dl>

\u3053\u306e\u7d1a\u6570\u306f\u53ce\u675f\u304c\u975e\u5e38\u306b\u9045\u3044\u305f\u3081\u3001\u03c0 \u3092\u5c0f\u6570\u70b9\u4ee5\u4e0b 2 \u6841\u307e\u3067\u8a08\u7b97\u3059\u308b\u306b\u306f\u307b\u307c 300 \u306e\u9805\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u6b21\u306e\u3088\u3046\u306b\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u65e9\u304f \u03c0 \u306b\u53ce\u675f\u3059\u308b\u540c\u69d8\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {\\pi_{0,1} = \\frac{4}{1},\\ \\pi_{0,2} =\\frac{4}{1}-\\frac{4}{3},\\ \\pi_{0,3} =\\frac{4}{1}-\\frac{4}{3}+\\frac{4}{5},\\ \\pi_{0,4} =\\frac{4}{1}-\\frac{4}{3}+\\frac{4}{5}-\\frac{4}{7}, \\cdots\\! } $$<\/div><\/dd><\/dl>

\u305d\u3057\u3066\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002 <\/p>

$$ {\\pi_{i,j} = \\frac{\\pi_{i-1,j}+\\pi_{i-1,j+1}}{2}\\text{ pour tout }i,j\\ge 1} $$<\/div> \u3002<\/dd><\/dl>

\u03c0 10.10<\/sub><\/span>\u306e\u8a08\u7b97\u306b\u306f\u3001\u521d\u671f\u7d1a\u6570\u306e\u6700\u521d\u306e 150 \u9805\u3092\u8a08\u7b97\u3059\u308b\u306e\u306b\u5fc5\u8981\u306a\u6642\u9593\u3068\u540c\u69d8\u306e\u6642\u9593\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001\u7cbe\u5ea6\u306f\u306f\u308b\u304b\u306b\u512a\u308c\u3066\u3044\u307e\u3059\u3002<\/span> $$ {\\pi_{10,10}=3.141592653\\ldots} $$<\/p><\/div> \u03c0 \u3092\u5c0f\u6570\u70b9\u4ee5\u4e0b 9 \u6841\u307e\u3067\u8fd1\u3065\u3051\u307e\u3059\u3002<\/div>\n

\u53c2\u8003\u8cc7\u6599<\/h2>\n
  1. Pi\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020afrikaans<\/a><\/li>
  2. Pi (Mathematik)\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020al\u221a\u00a9manique<\/a><\/li>
  3. \u00b7\u00e7\u00ec\u00b7\u00e3\u2260\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020amharique<\/a><\/li>
  4. Numero \u0153\u00c4\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020aragonais<\/a><\/li>
  5. \u00ff\u2211 (\u00ff\u00b1\u0178\u00e4\u00ff\u00df\u00ff\u2202\u0178\u00e4\u00ff\u00df\u00ff\u2122)\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020arabe<\/a><\/li>
  6. \u00ff\u00ae\u00ff\u00df\u0178\u00e2 (\u00ff\u00b1\u0178\u00e4\u00ff\u00df\u00ff\u2202\u0178\u00e4\u00ff\u00df\u00ff\u2122)\u00ac\u2020\u201a\u00c4\u00ec\u00ac\u2020arabe \u221a\u00a9gyptien<\/a><\/li><\/ol>\n
    \n

    \n \u5186\u5468\u7387 – \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n