{"id":32744,"date":"2024-01-05T17:06:46","date_gmt":"2024-01-05T17:06:46","guid":{"rendered":"https:\/\/science-hub.click\/%E7%9C%81%E7%95%A5%E8%A8%98%E5%8F%B7%28%E6%95%B0%E5%AD%A6%29%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-01-05T17:06:46","modified_gmt":"2024-01-05T17:06:46","slug":"%E7%9C%81%E7%95%A5%E8%A8%98%E5%8F%B7%28%E6%95%B0%E5%AD%A6%29%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=32744","title":{"rendered":"\u7701\u7565\u8a18\u53f7 (\u6570\u5b66)\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"
\n\"\u5186\u9310\u307e\u305f\u306f\u5186\u306e\u6295\u5f71\u306e\u65ad\u9762\"<\/figure>
\u5186\u9310\u307e\u305f\u306f\u5186\u306e\u6295\u5f71\u306e\u65ad\u9762<\/div><\/div><\/div>

\u6570\u5b66\u3067\u306f\u3001\u6955\u5186\u306f\u3001<\/strong>\u5186\u3092\u5272\u5e73\u9762\u306b\u6295\u5f71\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u307e\u305f\u306f\u76f4\u5186\u9310\u3068\u305d\u306e\u8ef8\u306b\u5782\u76f4\u3067<\/a><\/span>\u306a\u3044\u5e73\u9762\u3068\u306e\u4ea4\u70b9\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u9589\u5e73\u9762\u66f2\u7dda\u3067\u3059\u3002\u5186\u306f<\/a><\/span>\u6955\u5186\u306e\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\u3068\u307f\u306a\u3055\u308c\u307e\u3059\u3002<\/p>

\u3057\u305f\u304c\u3063\u3066\u3001\u305d\u308c\u306f\u5186\u3092\u9060\u8fd1\u6cd5\u3067\u898b\u305f\u3068\u304d\u306b\u77e5\u899a\u3055\u308c\u308b\u5f62\u72b6\u3001\u307e\u305f\u306f\u5e73\u9762<\/a><\/span>\u4e0a<\/a><\/span>\u306e\u5186\u76e4<\/span>\u306e\u5f71\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u56f3\u5f62\u3067\u3059\u3002<\/p>

\u5e7e\u4f55\u5b66<\/a><\/span>\u3067\u306f\u3001\u7126\u70b9\u3068\u547c\u3070\u308c\u308b 2 \u3064\u306e\u56fa\u5b9a\u70b9\u307e\u3067\u306e\u8ddd\u96e2\u306e\u5408\u8a08\u304c\u4e00\u5b9a\u3068\u306a\u308b\u3088\u3046\u306a\u5404\u70b9\u304c\u5b58\u5728\u3059\u308b\u5834\u6240\u3067\u3059 (\u5ead\u5e2b\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u305f\u305d\u306e\u69cb\u7bc9\u306f\u975e\u5e38\u306b\u7c21\u5358\u3067\u3059)\u3002<\/p>

\u6052\u661f<\/a><\/span>\u3084\u5225\u306e\u60d1\u661f<\/a><\/span>\u3092\u5468\u56de\u3059\u308b<\/a><\/span>\u5929\u4f53 (\u60d1\u661f\u3001\u5f57\u661f\u3001\u4eba\u5de5\u885b\u661f<\/a><\/span>) \u306e\u8ecc\u9053\u306f\u3001\u4e00\u6b21\u8fd1\u4f3c<\/a><\/span>\u3067\u306f\u6955\u5186\u306b\u306a\u308a\u307e\u3059 (2 \u4f53\u554f\u984c\u3068N<\/a><\/span>\u4f53\u554f\u984c\u3092\u53c2\u7167)\u3002<\/p>

\u6955\u5186<\/strong>\u306f\u3001\u96e2\u5fc3\u7387<\/a><\/span>\u304c\u53b3\u5bc6\u306b 0 \u3068 1 \u306e\u9593\u306e\u5186\u9310\u66f2\u7dda<\/a><\/span>\u3067\u3059\u3002<\/p>

\u5e7e\u4f55\u5b66\u7684\u5b9a\u7fa9<\/span><\/h2>

\u5186\u9310\u306e\u65ad\u9762<\/span><\/h3>

\u6955\u5186<\/strong>\u306f\u5186\u9310\u30d5\u30a1\u30df\u30ea\u30fc\u306e\u4e00\u90e8\u3067\u3042\u308b\u5e73\u9762\u66f2\u7dda<\/a><\/span>\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u5e73\u9762\u304c\u56de\u8ee2\u5186\u9310\u3092\u901a\u904e\u3059\u308b<\/span>\u3068\u304d\u306b\u3001\u5e73\u9762\u3068\u56de\u8ee2\u5186\u9310\u304c\u4ea4\u5dee\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u5186\u306f\u6955\u5186\u306e\u7279\u6b8a\u306a\u30b1\u30fc\u30b9 (\u5782\u76f4\u306a\u5207\u65ad\u9762) \u306b\u306a\u308a\u307e\u3059\u3002<\/p>

\u9662\u9577\u3068\u4e16\u5e2f\u4e3b<\/span><\/h3>
\n\"\u30d5\u30a9\u30fc\u30ab\u30b9\u3068\u30c7\u30a3\u30ec\u30af\u30bf\u30fc\u306b\u3088\u308b\u6955\u5186\u306e\u69cb\u7bc9\u3002\u504f\u5fc31\/2\"<\/figure>
\u30d5\u30a9\u30fc\u30ab\u30b9\u3068\u30c7\u30a3\u30ec\u30af\u30bf\u30fc\u306b\u3088\u308b\u6955\u5186\u306e\u69cb\u7bc9\u3002\u504f\u5fc31\/2<\/i><\/small><\/div><\/div><\/div>

\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u306f\u6b21\u5143<\/a><\/span>2 \u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30a2\u30d5\u30a3\u30f3\u7a7a\u9593<\/a><\/span>\u3067\u3059\u3002 ( d<\/i> ) \u3092<\/span>\u76f4\u7dda\u3001 F \u3092<\/i><\/span>( d<\/i> )<\/span>\u306b\u5c5e\u3055\u306a\u3044\u70b9<\/a><\/span>\u3001 e \u3092<\/i><\/span>]0,1[<\/span>\u306e\u5b9f\u6570\u3068\u3057\u307e\u3059\u3002 ( d<\/i> )<\/span>\u3068F<\/i><\/span>\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u308b\u30a2\u30d5\u30a3\u30f3<\/a><\/span>\u5e73\u9762\u3092P<\/i>\u3068\u3057\u307e\u3059\u3002\u5e73\u9762<\/i>P<\/i>\u306e\u70b9<\/i><\/span>M<\/i><\/span>\u306e\u96c6\u5408<\/i><\/span>\u306f<\/a><\/span>\u6b21\u306e\u3053\u3068\u3092\u691c\u8a3c\u3057\u307e\u3059<\/i>\u3002<\/i><\/span> <\/p>

$$ {\\frac{d(M,F)}{d(M,(d))} = e} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001 d<\/i> ( M<\/i> , F<\/i> ) \u306f<\/span>\u70b9M<\/i>\u304b\u3089\u70b9F<\/i>\u307e\u3067\u306e\u8ddd\u96e2\u3092\u8868\u3057\u3001 d<\/i> ( M<\/i> ,( d<\/i> )) = d<\/i> ( M<\/i> , H<\/i> )<\/span>\u306fM<\/i>\u304b\u3089\u7dda(d)<\/i>\u307e\u3067\u306e\u8ddd\u96e2\u3092\u8868\u3057\u307e\u3059\u3002<\/p>

K \u3092<\/i><\/span>( d<\/i> )<\/span>\u4e0a\u306eF<\/i><\/span>\u306e\u6b63\u5c04\u5f71\u3068\u3057\u307e\u3059\u3002 ( K<\/i> F<\/i> ) \u306f<\/span>\u660e\u3089\u304b\u306b\u3001\u7126\u70b9\u8ef8<\/strong>\u3068\u547c\u3070\u308c\u308b\u6955\u5186\u306e\u5bfe\u79f0<\/a><\/span>\u8ef8\u3067\u3059\u3002<\/p>

\u6955\u5186\u306e\u4e8c\u7126\u70b9\u5b9a\u7fa9<\/a><\/span><\/span><\/h3>

F<\/i><\/span>\u3068F<\/i> ‘ \u3092<\/span>\u5e73\u9762\u4e0a\u306e 2 \u3064\u306e\u7570\u306a\u308b\u70b9\u3068\u3057\u307e\u3059\u3002\u7126\u70b9F<\/i><\/span>\u304a\u3088\u3073F<\/i> ‘<\/span>\u306e\u6955\u5186\u3092\u547c\u3073\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6b21\u306e\u7279\u6027\u3092\u691c\u8a3c\u3059\u308b\u5e73\u9762\u306e\u70b9M<\/i><\/span>\u306e\u30bb\u30c3\u30c8\u3067\u3059\u3002 <\/p>

$$ {d(M,F) + d(M,F’) =2a=2\\sqrt{c^2+b^2} \\qquad a \\in\\mathbb{R}^*_+,\\quad b \\in\\mathbb{R}^*_+} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001 2a \u306f<\/i><\/span>\u9577\u8ef8<\/a><\/span>\u306e\u9577\u3055<\/a><\/span>\u3001 2c<\/i> = d<\/i> ( F<\/i> , F<\/i> ‘)<\/span> \u3001 2b \u306f<\/i><\/span>\u77ed\u8ef8<\/a><\/span>(\u9577\u8ef8\u306b\u5782\u76f4\u306a) \u306e\u9577\u3055\u3067\u3059\u3002<\/p>

\u89aa\u548c\u6027\u306b\u3088\u308b\u5186\u306e\u30a4\u30e1\u30fc\u30b8<\/span><\/h3>
\n\"\u6955\u5186\u3068<\/figure>
\u6955\u5186\u3068 2 \u3064\u306e\u89aa\u548c\u5186<\/div><\/div><\/div>

( C<\/i> 1)<\/span>\u3092\u4e2d\u5fc3O<\/i><\/span> \u3001\u534a\u5f84a<\/i><\/span>\u306e\u5186\u3001 ( C<\/i> 2) \u3092<\/span>\u4e2d\u5fc3O<\/i><\/span> \u3001\u534a\u5f84b<\/i><\/span> ( b<\/i> < a<\/i><\/span> ) \u306e\u5186\u3001 ( x<\/i> x<\/i> ‘)<\/span> O<\/i><\/span>\u3092\u901a\u308b\u76f4\u7dda\u3068\u3057\u307e\u3059\u3002\u4e2d\u5fc3O<\/i><\/span> \u3001\u9577\u534a\u5f84a<\/i><\/span> \u3001\u77ed\u534a\u5f84 b \u3092\u6301\u3064\u6955\u5186\u3092\u3001\u8ef8( x<\/i> x<\/i> ‘ )<\/span>\u3068( x<\/i> x<\/i> ‘ )<\/span>\u306b\u5782\u76f4\u306a\u65b9\u5411\u306e\u89aa\u548c\u6027\u304a\u3088\u3073b \u306e<\/i><\/span>\u5186<\/i><\/span>\u306e\u753b\u50cf( C<\/i> 1 )<\/span>\u3068\u547c\u3073\u307e\u3059\u3002 \/\u6bd4\u7387<\/i><\/span>\u3002<\/p>

\u5927\u5186<\/a><\/span>\u306e\u70b9m<\/i> 1<\/sub><\/span>\u306e\u30a4\u30e1\u30fc\u30b8\u3067\u3042\u308b\u6955\u5186\u306e\u70b9M \u3092<\/i><\/span>\u69cb\u7bc9\u3059\u308b\u306b\u306f\u3001 [ O<\/i> m<\/i> 1<\/sub> ]<\/span>\u4e0a\u306b\u4f4d\u7f6e\u3059\u308b\u5186\u306e\u70b9m<\/i> 2<\/sub><\/span> ( C<\/i> 2)<\/span>\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002 ( x<\/i> x<\/i> ‘)<\/span>\u306b\u5782\u76f4\u306am<\/i> 1<\/sub><\/span> a \u3068( x<\/i> x<\/i> ‘)<\/span>\u306b\u5e73\u884c\u306am<\/i> 2 a<\/sub><\/span>\u306b\u3088\u3063\u3066\u5c0e\u304d\u307e\u3059\u3002\u7dda\u306fM<\/i><\/span>\u3067\u4ea4\u5dee\u3057\u307e\u3059\u3002\u5b9f\u969b\u3001 m<\/i> ‘ \u304c<\/span>m<\/i> 1<\/sub><\/span>\u306e( x<\/i> x<\/i> ‘)<\/span>\u3078\u306e\u6b63\u5c04\u5f71\u3067\u3042\u308b\u5834\u5408\u3001\u30bf\u30ec\u30b9\u306e\u5b9a\u7406<\/a><\/span>\u306b\u3088\u308c\u3070\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {\\frac{m’M}{m’m_1} = \\frac{Om_2}{ Om_1 } = \\frac{b}{a}} $$<\/div><\/dd><\/dl>

\u30b9\u30c6\u30a2\u30ea\u30f3\u30b0\u30b5\u30fc\u30af\u30eb\u306b\u3088\u308b\u65bd\u5de5<\/span><\/h3>
\n\"\u6955\u5186\u3068\u305d\u306e\u8a98\u5c0e\u5186\u306e\u4e00\u90e8\"<\/figure>
\u6955\u5186\u3068\u305d\u306e\u8a98\u5c0e\u5186\u306e\u4e00\u90e8<\/div><\/div><\/div>

F \u3068 F’ \u3092 2 \u3064\u306e\u7570\u306a\u308b\u70b9\u3001(C) \u4e2d\u5fc3 F’ \u304a\u3088\u3073\u534a\u5f84 2a (2a > FF’) \u306e\u5186\u3068\u3057\u307e\u3059\u3002<\/p>

\u30c7\u30a3\u30ec\u30af\u30bf\u30fc\u5186 (C) \u3068\u7126\u70b9 F \u3092\u6301\u3064\u6955\u5186\u3001(C) \u306b\u63a5\u3057 F \u3092\u901a\u904e\u3059\u308b\u5186\u306e\u4e2d\u5fc3\u306e\u30bb\u30c3\u30c8\u3092\u547c\u3073\u307e\u3059\u3002<\/p>

m \u3067 (C) \u306b\u63a5\u3059\u308b\u5186\u306e\u4e2d\u5fc3\u3067\u3042\u308b\u70b9 M \u3092\u4f5c\u6210\u3059\u308b\u306b\u306f\u3001\u7dda\u5206 [Fm] \u306e\u4e8c\u7b49\u5206\u7dda<\/a><\/span>\u3092\u30c8\u30ec\u30fc\u30b9\u3057\u307e\u3059<\/a><\/span>\u3002\u3053\u308c\u306f M \u306e\u534a\u5f84 [F’m] \u3068\u4e00\u81f4\u3057\u307e\u3059\u3002<\/p>

\u5e7e\u4f55\u5b66\u7684\u7279\u6027<\/span><\/h2>

\u5bfe\u79f0\u6027\u306e\u8981\u7d20<\/span><\/h3>

\u300c\u7126\u70b9\u8ef8\u300d\u306f\u300c\u9577\u8ef8\u300d\u3068\u3082\u547c\u3070\u308c\u3001\u7126\u70b9\u3092\u901a\u308a\u3001\u6e96\u7dda\u306b\u5782\u76f4\u3067\u3042\u308a\u3001\u6955\u5186\u306e\u5bfe\u79f0\u8ef8\u3067\u3059\u3002\u77ed\u8ef8\u3082\u540c\u69d8\u3067\u3001\u9577\u8ef8\u306b\u5782\u76f4\u3067\u3001[FF’] \u306e\u4e2d\u70b9\u3067\u3042\u308b\u300c\u6955\u5186\u306e\u4e2d\u5fc3\u300d\u3092\u901a\u904e\u3057\u307e\u3059\u3002\u9577\u8ef8\u3068\u77ed\u8ef8\u306e\u4ea4\u70b9\u3001\u3064\u307e\u308a\u6955\u5186\u306e\u4e2d\u5fc3\u304c\u5bfe\u79f0\u306e\u4e2d\u5fc3\u3068\u306a\u308a\u307e\u3059\u3002<\/p>

\u6955\u5186\u3068\u305d\u306e\u9577\u8ef8\u3068\u306e\u4ea4\u70b9\u306f\u4e3b\u9802\u70b9<\/i>\u3068\u547c\u3070\u308c\u3001\u6955\u5186\u3068\u305d\u306e\u77ed\u8ef8\u3068\u306e\u4ea4\u70b9\u306f\u526f\u9802\u70b9<\/i>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>

\u63a5\u7dda\u3068\u4e8c\u7b49\u5206\u7dda<\/a><\/span><\/span><\/h3>
\n\"\u6955\u5186\u306e\u70b9\u3068\u7126\u70b9\u3092\u7d50\u3076\u7dda\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u6247\u5f62\u306e\u4e8c\u7b49\u5206\u7dda\u306f\u3001\u3053\u306e\u70b9\u306e\u63a5\u7dda\u306b\u5782\u76f4\u3067\u3059\u3002\"<\/figure>
\u6955\u5186\u306e\u70b9\u3068\u7126\u70b9\u3092\u7d50\u3076\u7dda\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u6247\u5f62\u306e\u4e8c\u7b49\u5206\u7dda\u306f\u3001\u3053\u306e\u70b9\u306e\u63a5\u7dda\u306b\u5782\u76f4\u3067\u3059\u3002<\/i><\/small><\/div><\/div><\/div>

\u7126\u70b9\u304cF<\/i>\u304a\u3088\u3073F’<\/i>\u3067\u3042\u308b\u6955\u5186\u306b\u3064\u3044\u3066\u8003\u3048\u307e\u3059\u3002\u3053\u306e\u6955\u5186\u306e\u70b9M<\/i>\u3067\u3001\u6247\u5f62\u306e\u4e8c\u7b49\u5206\u7dda ( FMF’<\/i> ) \u3092\u8003\u3048\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u3053\u306e\u4e8c\u7b49\u5206\u7dda\u306fM<\/i>\u3067\u306e\u63a5\u7dda\u306b\u5782\u76f4\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

\u3053\u306e\u7279\u6027\u306f\u3001\u5e7e\u4f55\u5149\u5b66\u306e<\/a><\/span>\u6955\u5186\u93e1\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u7126\u70b9\u306e 1 \u3064\u3092\u901a\u904e\u3059\u308b\u5149\u7dda\u306f\u3001\u53cd\u5c04\u3055\u308c\u308b\u3068\u3082\u3046 1 \u3064\u306e\u7126\u70b9\u3092\u901a\u904e\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6955\u5186\u93e1<\/a><\/span>\u306e\u4e00\u65b9\u306e\u7126\u70b9\u306b\u96fb\u7403\u3092\u7f6e\u304f\u3068\u3001\u5149\u7dda\u306f\u3082\u3046\u4e00\u65b9\u306e\u7126\u70b9\u306b\u7126\u70b9\u3092\u5408\u308f\u305b\u307e\u3059\u3002<\/p>

\u3053\u308c\u306f\u3001\u30d1\u30ea\u306e\u5730\u4e0b\u9244<\/a><\/span>\u5185\u3067\u3001\u3042\u308b\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u304b\u3089\u5225\u306e\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u306b\u97f3\u304c\u975e\u5e38\u306b\u3088\u304f\u4f1d\u64ad\u3059\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u3082\u8aac\u660e\u3057\u307e\u3059\u3002\u5b9f\u969b\u3001\u307b\u3068\u3093\u3069\u306e\u99c5\u306f\u6955\u5186\u5f62\u3092\u3057\u3066\u3044\u307e\u3059\u3002\u97f3\u306e\u767a\u751f\u6e90\u304c\u3044\u305a\u308c\u304b\u306e\u4e2d\u5fc3\u306b\u3042\u308b\u5834\u5408\u3001\u3059\u3079\u3066\u306e\u53cd\u5c04\u97f3\u306f\u4ed6\u306e\u4e2d\u5fc3\uff08\u4ed6\u306e\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0a\uff09\u306b\u5411\u304b\u3063\u3066\u53ce\u675f\u3057\u307e\u3059\u3002\u6955\u5186\u304c\u6301\u3064\u3053\u306e\u6027\u8cea\u306f\u300c\u53cd\u5c04\u7279\u6027\u300d\u3068\u3082\u547c\u3070\u308c\u3001\u6955\u5186\u306e\u70b9\u306b\u304a\u3051\u308b\u63a5\u7dda\u3092\u4f7f\u3063\u3066\u8aac\u660e\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u4e00\u65b9\u306e\u7126\u70b9\u304b\u3089\u767a\u305b\u3089\u308c\u305f\u97f3\u3084\u5149\u7dda\u306f\u3001\u3082\u3046\u4e00\u65b9\u306e\u7126\u70b9\u3067\u53cd\u5c04\u3055\u308c\u307e\u3059\u3002 \u3002\u3053\u306e\u7279\u6027\u306f\u3001\u7279\u5b9a\u306e\u5149\u5b66<\/a><\/span>\u6a5f\u5668\u306e\u8a2d\u8a08\u306b\u5229\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u305d\u308c\u306f\u660e\u3089\u304b\u306b\u30a8\u30b3\u30fc \u30ae\u30e3\u30e9\u30ea\u30fc\u3001\u3064\u307e\u308a\u5929\u4e95<\/a><\/span>\u304c\u6955\u5186\u5f62\u3067\u3042\u308b\u305f\u3081\u3001\u7126\u70b9\u306e 1 \u3064\u3067\u3055\u3055\u3084\u304f\u4eba\u304c\u3082\u3046 1 \u3064\u306e\u7126\u70b9\u3067\u805e\u3053\u3048\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u90e8\u5c4b\u306b\u5b58\u5728\u3057\u307e\u3059\u3002\u30ef\u30b7\u30f3\u30c8\u30f3\u306e\u30ad\u30e3\u30d4\u30bf\u30eb \u30d3\u30eb\u30c7\u30a3\u30f3\u30b0\u306e\u30ed\u30bf\u30f3\u30c0\u3084\u30bd\u30eb\u30c8\u30ec\u30fc\u30af \u30b7\u30c6\u30a3\u306e\u30e2\u30eb\u30e2\u30f3\u30bf\u30d0\u30ca\u30af\u30eb\u306f\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u30ae\u30e3\u30e9\u30ea\u30fc\u306e\u4f8b\u3067\u3059\u3002 (SWOKOWSKI \u8457\u300eAnalytics \u7b2c 5 \u7248\u300f\u306e\u66f8\u7c4d\u304b\u3089\u306e\u629c\u7c8b\u3001 Micheline<\/a><\/span> Citta \u306b\u3088\u308b\u82f1\u8a9e\u304b\u3089\u306e\u7ffb\u8a33)\u3002<\/p>

\u30b5\u30a4\u30ba\u9593\u306e\u95a2\u4fc2<\/span><\/h2>

\u6955\u5186\u304c\u305d\u306e\u96e2\u5fc3\u7387e<\/i><\/span>\u3068\u7126\u70b9\u3068\u6e96\u7dda\u306e\u9593\u306e\u8ddd\u96e2h<\/i><\/span>\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u5834\u5408\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

p<\/i> = e<\/i> h<\/i><\/span>\u3053\u3053\u3067\u3001 p \u306f<\/i><\/span>\u6955\u5186\u306e\u30d1\u30e9\u30e1\u30fc\u30bf<\/a><\/span>\u3067\u3059\u3002 <\/dd>
$$ {a = {p \\over 1-e^2}} $$<\/div>\u3053\u3053\u3067\u3001 a \u306f<\/i><\/span>\u9577\u534a\u5f84\u306e\u9577\u3055\u3067\u3059\u3002 <\/dd>
$$ {b = {p \\over \\sqrt{1-e^2}}} $$<\/div>\u3053\u3053\u3067\u3001 b \u306f<\/i><\/span>\u77ed\u534a\u5f84\u306e\u9577\u3055\u3067\u3059\u3002 <\/dd>
$$ {c = ae = {ep\\over 1 – e^2}} $$<\/div>\u3053\u3053\u3067\u3001 c \u306f<\/i><\/span>\u7126\u70b9\u3068\u4e2d\u5fc3\u306e\u9593\u306e\u8ddd\u96e2\u3067\u3059\u3002<\/dd><\/dl>

\u6955\u5186\u304c\u534a\u8ef8a<\/i><\/span>\u3068b<\/i><\/span>\u3067\u4e0e\u3048\u3089\u308c\u308b<\/span>\u5834\u5408<\/p>

$$ {c = \\sqrt{a^2-b^2}} $$<\/div>\u3053\u3053\u3067\u3001 c \u306f<\/i><\/span>\u7126\u70b9\u3068\u4e2d\u5fc3\u306e\u9593\u306e\u8ddd\u96e2\u3067\u3059\u3002 <\/dd>
$$ {e = {c\\over a}} $$<\/div>\u3053\u3053\u3067\u3001 e \u306f<\/i><\/span>\u96e2\u5fc3\u7387\u3067\u3042\u308a\u3001 e \u306f<\/i><\/span>\u53b3\u5bc6\u306b 0 \u3068 1 \u306e\u9593\u3067\u3059\u3002 <\/dd>
$$ {p = {b^2\\over a}} $$<\/div>\u3053\u3053\u3067\u3001 p \u306f<\/i><\/span>\u6955\u5186\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3059\u3002 <\/dd>
$$ {h = {p\\over e}={b^2\\over c}} $$<\/div>\u3053\u3053\u3067\u3001 h \u306f<\/i><\/span>\u7126\u70b9\u3068\u30c7\u30a3\u30ec\u30af\u30bf\u30fc\u306e\u9593\u306e\u8ddd\u96e2\u3067\u3059\u3002<\/dd><\/dl>

\u7279\u6027\u65b9\u7a0b\u5f0f<\/span><\/h2>

\u30c7\u30ab\u30eb\u30c8\u65b9\u7a0b\u5f0f<\/span><\/h3>

\u6955\u5186\u306e\u9577\u8ef8\u3068\u77ed\u8ef8\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u30d5\u30ec\u30fc\u30e0\u3067\u306f\u3001\u305d\u306e\u65b9\u7a0b\u5f0f<\/a><\/span>\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1} $$<\/div><\/dd><\/dl>

\u6955\u5186\u306e\u4e2d\u5fc3\u304cx<\/i> \u2013 y<\/i>\u5ea7\u6a19\u7cfb<\/a><\/span>\u306e\u539f\u70b9\u306b\u306a\u3044\u304c\u3001\u305d\u306e\u9577\u8ef8\u3068\u77ed\u8ef8\u304c\u5ea7\u6a19\u8ef8\u306b\u5e73\u884c\u306a\u307e\u307e\u3067\u3042\u308b\u5834\u5408\u3001\u3053\u308c\u306f\u6b21\u306e\u65b9\u7a0b\u5f0f\u3067\u6307\u5b9a\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {\\frac{(x-h)^2}{a^2} + \\frac{(y-k)^2}{b^2} = 1} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001\u30d1\u30e9\u30e1\u30fc\u30bf h \u3068 k \u306f\u6955\u5186\u306e\u4e2d\u5fc3\u306e\u5ea7\u6a19\u3067\u3059\u3002<\/p>

\u30d1\u30e9\u30e1\u30fc\u30bf\u5316<\/span><\/h3>
$$ {(lien) \\qquad \\begin{cases}x = a\\cos t \\\\ y = b\\sin t \\end{cases} \\quad t \\in\\R} $$<\/div><\/dd><\/dl>

\u9577\u8ef8\u3068\u77ed\u8ef8\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u57fa\u6e96\u30d5\u30ec\u30fc\u30e0\u5185\u3067\u3002<\/p>

\u6975\u65b9\u7a0b\u5f0f<\/span><\/h3>
$$ {[3a] \\qquad r = \\frac{p}{1+e \\cos \\theta} \\qquad \\theta \\in\\R} $$<\/div><\/dd><\/dl>

\u7126\u70b9\u3068\u7126\u70b9\u8ef8\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u57fa\u6e96\u30d5\u30ec\u30fc\u30e0\u5185\u3002<\/p>

\u307e\u305f\u306f<\/p>

$$ {[3b] \\qquad r^2 = \\frac{b^2}{1-e^2 \\cos ^2 \\theta} \\qquad \\theta \\in\\R} $$<\/div><\/dd><\/dl>

\u4e2d\u5fc3\u3068\u7126\u70b9\u8ef8\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u57fa\u6e96\u30d5\u30ec\u30fc\u30e0\u5185\u3002<\/p>

\u5468<\/span><\/h2>

\u6955\u5186\u306e\u5186\u5468\u306f 4 aE<\/i> ( e<\/i> ) \u3067\u3059\u3002\u3053\u3053\u3067E \u306f<\/i>\u7b2c 2\u7a2e<\/a><\/span>\u5b8c\u5168\u6955\u5186\u7a4d\u5206<\/a><\/span>\u3067\u3059\u3002<\/p>

\u30b7\u30ea\u30fc\u30ba\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>

$$ {c = 2\\pi a \\left[{1 – \\left({1\\over 2}\\right)^2e^2 – \\left({1\\cdot 3\\over 2\\cdot 4}\\right)^2{e^4\\over 3} – \\left({1\\cdot 3\\cdot 5\\over 2\\cdot 4\\cdot 6}\\right)^2{e^6\\over5} – \\dots}\\right]} $$<\/div><\/dd><\/dl>

\u9069\u5207\u306a\u8fd1\u4f3c\u306f\u3001\u30e9\u30de\u30cc\u30b8\u30e3\u30f3\u306e\u516c\u5f0f\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ {c \\approx \\pi \\left[3(a+b) – \\sqrt{(3a+b)(a+3b)}\\right]} $$<\/div><\/dd><\/dl>

\u6b21\u306e\u3088\u3046\u306b\u3082\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {c \\approx \\pi a \\left[ 3 (1+\\sqrt{1-e^2}) – \\sqrt{(3+ \\sqrt{1-e^2})(1+3 \\sqrt{1-e^2})} \\right]} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001a \u306f\u9577\u8ef8\u306e\u534a\u5206\u306e\u9577\u3055\u3001b \u306f\u77ed\u8ef8\u306e\u534a\u5206\u306e\u9577\u3055\u3067\u3059\u3002<\/p>

\u3088\u308a\u4e00\u822c\u7684\u306b\u306f\u3001\u5186\u5f27\u306e\u9577\u3055\u306f\u3001\u7bc4\u56f2\u3092\u5b9a\u3081\u305f\u89d2\u5ea6<\/a><\/span>\u306e\u95a2\u6570\u3068\u3057\u3066\u3001\u7b2c 2<\/a><\/span>\u7a2e\u4e0d\u5b8c\u5168\u6955\u5186\u7a4d\u5206<\/a><\/span>\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002\u9006<\/a><\/span>\u95a2\u6570\u3001\u3064\u307e\u308a\u5186\u5f27\u306e\u9577\u3055\u306e\u95a2\u6570\u3068\u3057\u3066\u5b9a\u3081\u3089\u308c\u308b\u89d2\u5ea6\u306f\u3001\u6955\u5186\u95a2\u6570\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<\/p>

\u6955\u5186\u306e\u5185\u9818\u57df\u306e\u9762\u7a4d<\/span><\/h2>

\u6955\u5186\u306e\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u6955\u5186\u306e\u65b9\u7a0b\u5f0f\u304c\u8a18\u8ff0\u3055\u308c\u3066\u3044\u308b\u8ef8\u306b\u3088\u3063\u3066\u904b\u3070\u308c\u308b\u53c2\u7167\u30d5\u30ec\u30fc\u30e0\u306b\u81ea\u5206\u81ea\u8eab\u3092\u7f6e\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1} $$<\/div><\/dd><\/dl>

\u4e0a\u8a18\u3067\u78ba\u7acb\u3055\u308c\u305f\u5bfe\u79f0\u6027\u306b\u3088\u308a\u3001\u305f\u3068\u3048\u3070\u3001\u3053\u306e\u57fa\u6e96\u3092\u57fa\u6e96\u306b\u3057\u3066\u5e73\u9762\u306e\u53f3\u4e0a 4 \u5206\u306e 1 \u306b\u3042\u308b\u6955\u5186\u306e\u90e8\u5206\u306e\u9762\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002\u5bfe\u5fdc\u3059\u308b\u6955\u5186\u90e8\u5206\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>

$$ {y= b \\sqrt{1 – \\left(\\frac xa\\right)^2}} $$<\/div><\/dd><\/dl>

[0, a<\/i> ]<\/span>\u306ex<\/i><\/span>\u306e\u5834\u5408\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6955\u5186\u306e\u53f3\u4e0a4\u5206\u306e1\u306e\u9762\u7a4d\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {I = \\int_0^a b \\sqrt{1-\\left(\\frac xa\\right)^2}\\,\\mathrm dx = ab \\int_0^1 \\sqrt{1- t^2}\\,\\mathrm dt = ab \\int_0^{\\frac\\pi2} \\cos^2 u\\,\\mathrm du} $$<\/div><\/dd><\/dl>

\u5909\u6570<\/a><\/span>\u306e\u5909\u66f4\u306b\u3088\u3063\u3066\u53d6\u5f97\u3055\u308c\u305f\u6700\u5f8c\u306e\u30ea\u30e9\u30a4\u30c8

$$ {u \\mapsto \\sin u = t} $$<\/div> [0,\u03c0 \/ 2]<\/span>\u304b\u3089[0,1]<\/span>\u307e\u3067\u3002 cos 2<\/sup> u \u3092<\/i><\/span>\u7dda\u5f62\u5316\u3057\u3066\u3001\u6955\u5186\u306e\u9762\u7a4d\u306e 4 \u5206\u306e 1 \u3092\u898b\u3064\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>
$$ {I= ab \\int_0^{\\frac\\pi2} \\frac{1+ \\cos 2u}2\\,\\mathrm du = \\frac{\\pi ab}4} $$<\/div><\/dd><\/dl>

\u305d\u3057\u3066\u6955\u5186\u5168\u4f53\u306e\u9762\u7a4d\u306b\u3064\u3044\u3066\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>

S<\/i> = \u03c0 a<\/i> b<\/i><\/span><\/dd><\/dl>

a<\/i> = b<\/i><\/span>\u306e\u5834\u5408\u3001\u5186\u306e\u9762\u7a4d\u304c\u6c42\u3081\u3089\u308c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>

\u6955\u5186\u3092\u63cf\u304f<\/span><\/h2>