{"id":944,"date":"2013-09-20T23:10:45","date_gmt":"2013-09-20T14:10:45","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=944"},"modified":"2021-10-23T03:24:52","modified_gmt":"2021-10-22T18:24:52","slug":"wsr201305","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201305\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52013\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\u7a7a\u9593\u5185\u306b\u5e73\u9762 \\(P\\) \u304c\u3042\u308b.\r\n\u7a7a\u9593\u5185\u306e\u56f3\u5f62 \\(A\\) \u306b\u5bfe\u3057, \\(A\\) \u306e\u5404\u70b9\u304b\u3089 \\(P\\) \u306b\u4e0b\u308d\u3057\u305f\u5782\u7dda\u3068 \\(P\\) \u3068\u306e\u4ea4\u70b9\u306e\u5168\u4f53\u3092, \\(A\\) \u306e \\(P\\) \u3078\u306e\u6b63\u5c04\u5f71\u3068\u3088\u3076. \u6b21\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u5e73\u9762 \\(Q\\) \u304c\u5e73\u9762 \\(P\\) \u3068\u89d2 \\(\\theta \\ ( 0 \\lt \\theta \\lt \\dfrac{\\pi}{2} )\\) \u3067\u4ea4\u308f\u3063\u3066\u3044\u308b\u3068\u3059\u308b. \u3059\u306a\u308f\u3061, \\(P\\) \u3068 \\(Q\\) \u306e\u4ea4\u7dda\u306b\u5782\u76f4\u306a\u5e73\u9762\u3067 \\(P , Q\\) \u3092\u5207\u3063\u3066\u3067\u304d\u308b \\(2\\) \u76f4\u7dda\u306e\u306a\u3059\u89d2\u304c \\(\\theta\\) \u3067\u3042\u308b\u3068\u3059\u308b. \\(Q\\) \u4e0a\u306e\u9577\u3055 \\(1\\) \u306e\u7dda\u5206\u306e \\(P\\) \u3078\u306e\u6b63\u5c04\u5f71\u306e\u9577\u3055\u306e\u6700\u5927\u5024\u3068\u6700\u5c0f\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000(1)<\/strong> \u306e \\(Q\\) \u3092\u8003\u3048\u308b. \\(Q\\) \u4e0a\u306e \\(1\\) \u8fba\u306e\u9577\u3055\u304c \\(1\\) \u3067\u3042\u308b\u6b63\u4e09\u89d2\u5f62\u306e \\(P\\) \u3078\u306e\u6b63\u5c04\u5f71\u306e\u9762\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(1\\) \u8fba\u306e\u9577\u3055\u304c \\(1\\) \u3067\u3042\u308b\u6b63\u56db\u9762\u4f53 \\(T\\) \u306e \\(P\\) \u3078\u306e\u6b63\u5c04\u5f71 \\(T'\\) \u306f\u3069\u3093\u306a\u5f62\u304b. \u307e\u305f, \\(T'\\) \u306e\u9762\u7a4d\u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong><\/p>\r\n

    \\(P\\) \u3068 \\(Q\\) \u306e\u4ea4\u7dda\u3092 \\(x\\) \u8ef8, \\(P\\) \u3092 \\(xy\\) \u5e73\u9762\u3068\u306a\u308b\u3088\u3046\u306b\u7a7a\u9593\u5ea7\u6a19\u3092\u3068\u308b.<\/p>\r\n\"waseda_r_2013_05_01\"\r\n

    \\(Q\\) \u4e0a\u306b \\(x\\) \u8ef8\u3068\u306a\u3059\u89d2\u304c \\(\\phi \\ \\left( -\\dfrac{\\pi}{2} \\leqq \\phi \\leqq \\dfrac{\\pi}{2} \\right) \\quad ... [1]\\) \u3067\u3042\u308b\u9577\u3055 \\(1\\) \u306e\u7dda\u5206 OX \u3092\u3068\u308b\u3068\r\n\\[\r\n\\text{X} \\left( \\cos \\phi , \\sin \\phi \\cos \\theta , \\sin \\phi \\sin \\theta \\right)\r\n\\]\r\n\u306a\u306e\u3067, OX \u306e \\(P\\) \u3078\u306e\u6b63\u5c04\u5f71 OX' \u306e\u9577\u3055\u306f\r\n\\[\\begin{align}\r\n\\text{OX'} & = \\sqrt{\\cos^2 \\phi +( \\sin \\phi \\cos \\theta )^2} \\\\\r\n& = \\sqrt{1 -\\left( 1 -\\cos^2 \\theta \\right) \\sin^2 \\phi} \\\\\r\n& = \\sqrt{1 -\\sin^2 \\phi \\sin^2 \\theta}\r\n\\end{align}\\]\r\n\\(0 \\leqq \\sin^2 \\phi \\leqq 1\\) \u306a\u306e\u3067\r\n\\[\r\n\\sqrt{1 -\\sin^2 \\theta} = \\cos \\theta \\leqq \\text{OX'} \\leqq 1\r\n\\]\r\n\u3088\u3063\u3066, \u6700\u5927\u5024\u306f \\(\\underline{1}\\) , \u6700\u5c0f\u5024\u306f \\(\\underline{\\cos \\theta}\\) .<\/p>\r\n

    (2)<\/strong><\/p>\r\n

    \\(1\\) \u8fba\u3092 OX \u3068\u8003\u3048\u308c\u3070, \u4ed6\u306e \\(1\\) \u8fba OY \u306f \\(x\\) \u8ef8\u3068\u89d2 \\(\\phi +\\dfrac{\\pi}{3}\\) \u3092\u306a\u3059\u3068\u8003\u3048\u3089\u308c\u308b.
    \r\n(1)<\/strong> \u306e\u7d4c\u904e\u3088\u308a\r\n\\[\r\n\\text{X} \\left( \\cos \\phi , \\sin \\left( \\phi +\\dfrac{\\pi}{3} \\right) \\cos \\theta , \\sin \\left( \\phi +\\dfrac{\\pi}{3} \\right) \\sin \\theta \\right)\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u9762\u7a4d \\(S\\) \u306f\r\n\\[\\begin{align}\r\nS & = \\dfrac{1}{2} \\left| \\cos \\phi \\cdot \\sin \\left( \\phi +\\dfrac{\\pi}{3} \\right) \\cos \\theta -\\cos \\phi \\cdot \\sin \\phi \\cos \\theta \\right| \\\\\r\n& = \\dfrac{1}{2} \\left| \\cos \\theta \\sin \\left\\{ \\left( \\phi +\\dfrac{\\pi}{3} \\right) -\\phi \\right\\} \\right| \\\\\r\n& = \\dfrac{1}{2} \\cdot \\dfrac{\\sqrt{3}}{2} \\cos \\theta \\quad ( \\ \\text{\u2235} \\ [1] \\ ) \\\\\r\n& = \\underline{\\dfrac{\\sqrt{3}}{4} \\cos \\theta}\r\n\\end{align}\\]\r\n

    (3)<\/strong><\/p>\r\n

    \\(T'\\) \u306e\u9762\u7a4d\u3092 \\(|T'|\\) \u3068\u304a\u304f.
    \r\n\\(T\\) \u306e \\(4\\) \u3064\u306e\u9762\u306e\u3046\u3061 \\(1\\) \u3064\u3092\u5e95\u9762 \\(B\\) , \u3053\u308c\u306b\u542b\u307e\u308c\u306a\u3044\u70b9\u3092\u9802\u70b9 A \u3068\u8868\u3059.
    \r\n\\(B\\) , A \u306e\u6b63\u5c04\u5f71\u3092\u305d\u308c\u305e\u308c \\(B'\\) , A'\u3068\u304a\u304f\u3068<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000A' \u304c \\(B'\\) \u306e\u5468\u304a\u3088\u3073\u5185\u90e8\u306b\u542b\u307e\u308c\u308b\u3068\u304d, \\(T'\\) \u306f\u4e09\u89d2\u5f62<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000A' \u304c \\(B'\\) \u306e\u5916\u90e8\u306b\u3042\u308b\u3068\u304d, \\(T'\\) \u306f\u56db\u89d2\u5f62<\/p><\/li>\r\n<\/ol>\r\n

      \u305d\u308c\u305e\u308c\u306e\u5834\u5408\u306b\u3064\u3044\u3066\u8003\u3048\u308b.<\/p>\r\n

        \r\n

      1. 1*<\/strong>\u3000\u4e09\u89d2\u5f62\u306e\u5834\u5408
        \r\n(2)<\/strong> \u306e\u7d50\u679c\u304b\u3089\r\n\\[\r\n|T'| = \\dfrac{\\sqrt{3}}{4} \\cos \\theta \\leqq \\dfrac{\\sqrt{3}}{4}\r\n\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \\(\\theta = 0\\) \u306e\u3068\u304d, \u3059\u306a\u308f\u3061, \\(1\\) \u3064\u306e\u9762\u304c \\(P\\) \u3068\u5e73\u884c\u3067\u3042\u308b\u3068\u304d.<\/p><\/li>\r\n

      2. 2*<\/strong>\u3000\u56db\u89d2\u5f62\u306e\u5834\u5408
        \r\n\u56db\u89d2\u5f62\u306e\u5bfe\u89d2\u7dda\u306e\u9577\u3055\u3092 \\(p , q\\) , \u5bfe\u89d2\u7dda\u3069\u3046\u3057\u306e\u306a\u3059\u89d2\u3092 \\(\\alpha\\) \u3068\u304a\u304f\u3068\r\n\\[\r\n|T'| = \\dfrac{1}{2} pq \\sin \\alpha \\leqq \\dfrac{1}{2}\r\n\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \\(p = q = 1 , \\ \\alpha = \\dfrac{\\pi}{2} \\quad ... [2]\\) \u306e\u3068\u304d.\r\n\"waseda_r_2013_05_02\"\r\n\u3053\u3053\u3067, \\(1\\) \u7d44\u306e\u5bfe\u8fba\u304c \\(P\\) \u3068\u5e73\u884c\u3067\u3042\u308b\u3068\u304d\u306b\u3064\u3044\u3066\u8003\u3048\u308b\u3068, \u5bfe\u8fba\u306f\u5782\u76f4\u3067\u3042\u308b\u304b\u3089, \\(\\alpha = \\dfrac{\\pi}{2}\\) , (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \\(p = q = 1\\) \u306a\u306e\u3067, [2] \u306e\u5834\u5408\u3092\u307f\u305f\u3057\u3066\u3044\u308b.<\/p><\/li>\r\n<\/ol>\r\n

        \u4ee5\u4e0a\u3088\u308a, \\(T'\\) \u306e\u5f62\u306f \\(\\underline{\\text{\u4e09\u89d2\u5f62, \u56db\u89d2\u5f62}}\\) \u3067\u3042\u308a,\r\n\\(\\dfrac{\\sqrt{3}}{4} \\lt \\dfrac{1}{2}\\) \u306a\u306e\u3067, \u9762\u7a4d\u306e\u6700\u5927\u5024\u306f \\(\\underline{\\dfrac{1}{2}}\\) .<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u7a7a\u9593\u5185\u306b\u5e73\u9762 \\(P\\) \u304c\u3042\u308b. \u7a7a\u9593\u5185\u306e\u56f3\u5f62 \\(A\\) \u306b\u5bfe\u3057, \\(A\\) \u306e\u5404\u70b9\u304b\u3089 \\(P\\) \u306b\u4e0b\u308d\u3057\u305f\u5782\u7dda\u3068 \\(P\\) \u3068\u306e\u4ea4\u70b9\u306e\u5168\u4f53\u3092, \\(A\\) \u306e \\(P\\) \u3078\u306e\u6b63\u5c04\u5f71\u3068\u3088\u3076. \u6b21\u306e\u554f\u306b\u7b54\u3048\u3088 … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[100],"tags":[147,111],"class_list":["post-944","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2013","tag-waseda_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/944","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=944"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/944\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=944"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=944"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=944"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}