{"id":871,"date":"2013-08-07T01:11:28","date_gmt":"2013-08-06T16:11:28","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=871"},"modified":"2021-09-23T09:40:16","modified_gmt":"2021-09-23T00:40:16","slug":"thr201306","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201306\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2013\uff1a\u7b2c6\u554f"},"content":{"rendered":"
\n

\u534a\u5f84 \\(1\\) \u306e\u5186\u3092\u5e95\u9762\u3068\u3059\u308b\u9ad8\u3055 \\(\\dfrac{1}{\\sqrt{2}}\\) \u306e\u76f4\u5186\u67f1\u304c\u3042\u308b.\r\n\u5e95\u9762\u306e\u5186\u306e\u4e2d\u5fc3\u3092 O \u3068\u3057, \u76f4\u5f84\u3092 \\(1\\) \u3064\u3068\u308a AB \u3068\u304a\u304f. AB \u3092\u542b\u307f\u5e95\u9762\u3068 \\(45^{\\circ}\\) \u306e\u89d2\u5ea6\u3092\u306a\u3059\u5e73\u9762\u3067\u3053\u306e\u76f4\u5186\u67f1\u3092 \\(2\\) \u3064\u306e\u90e8\u5206\u306b\u5206\u3051\u308b\u3068\u304d, \u4f53\u7a4d\u306e\u5c0f\u3055\u3044\u65b9\u306e\u90e8\u5206\u3092 \\(V\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u76f4\u5f84 AB \u306b\u76f4\u4ea4\u3057, O \u3068\u306e\u8ddd\u96e2\u304c \\(t \\ ( 0 \\leqq t \\leqq 1 )\\) \u3067\u3042\u308b\u3088\u3046\u306a\u5e73\u9762\u3067 \\(V\\) \u3092\u5207\u3063\u305f\u3068\u304d\u306e\u65ad\u9762\u7a4d \\(S(t)\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(V\\) \u306e\u4f53\u7a4d\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

    \u4e0b\u56f3\u306e\u3088\u3046\u306b, \u70b9 O \u3092\u539f\u70b9\u3068\u3057, AB \u3092 \\(x\\) \u8ef8, \u5e95\u9762\u3092\u5e73\u9762 \\(z = 0\\) \u3068\u3059\u308b\u3088\u3046\u306a\u5ea7\u6a19\u8ef8\u3092\u3068\u308b.<\/p>\r\n\"tohoku_r_2013_06_01\"\r\n

    \u5186\u67f1\u306e\u9ad8\u3055\u306b\u3064\u3044\u3066 \\(\\dfrac{1}{\\sqrt{2}} \\lt 1 \\cdot \\tan 45^{\\circ}\\) \u306a\u306e\u3067, \u90e8\u5206 \\(V\\) \u306f\u4e0a\u9762\u3092\u3082\u3064.
    \r\n\u4e0a\u9762\u306e\u5f27\u3092 CD \u3068\u304a\u304f\u3068, \u6761\u4ef6\u3088\u308a, C \u306e\u5ea7\u6a19\u306f\r\n\\[\r\n\\left( \\dfrac{1}{\\sqrt{2}} , \\dfrac{1}{\\sqrt{2}} , \\dfrac{1}{\\sqrt{2}} \\right) \\ .\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u5e73\u9762 \\(x = t \\ ( 0 \\leqq t \\leqq 1 )\\) \u306b\u3088\u308b \\(V\\) \u306e\u65ad\u9762\u306f, \\(t\\) \u306e\u5024\u306b\u3088\u3063\u3066 \\(2\\) \u3064\u306e\u5834\u5408\u304c\u8003\u3048\u3089\u308c\u308b.<\/p>\r\n

      \r\n
    1. 1*<\/strong>\u3000\\(0 \\leqq t \\leqq \\dfrac{1}{\\sqrt{2}}\\) \u306e\u3068\u304d<\/li>\r\n<\/ol>\r\n\"tohoku_r_2013_06_02\"\r\n

      \u65ad\u9762\u306f\u4e0a\u56f3\u306e\u3088\u3046\u306b\u306a\u308a\r\n\\[\\begin{align}\r\nS(t) & = \\dfrac{1}{2} \\left\\{ \\sqrt{1-t^2} +\\left( \\sqrt{1-t^2} -\\dfrac{1}{\\sqrt{2}} \\right) \\right\\} \\cdot \\dfrac{1}{\\sqrt{2}} \\\\\r\n& = \\dfrac{\\sqrt{2 (1-t^2)}}{2} -\\dfrac{1}{4} \\ .\r\n\\end{align}\\]\r\n

        \r\n
      1. 2*<\/strong>\u3000\\(\\dfrac{1}{\\sqrt{2}} \\lt t \\leqq 1\\) \u306e\u3068\u304d<\/li>\r\n<\/ol>\r\n\"tohoku_r_2013_06_03\"\r\n

        \u65ad\u9762\u306f\u4e0a\u56f3\u306e\u3088\u3046\u306b\u306a\u308a\r\n\\[\\begin{align}\r\nS(t) & = \\dfrac{1}{2} \\left( \\sqrt{1-t^2} \\right)^2 \\\\\r\n& = \\dfrac{1-t^2}{2} \\ .\r\n\\end{align}\\]\r\n

        \u3088\u3063\u3066\r\n\\[\r\nS(t) = \\underline{\\left\\{\\begin{array}{ll} \\dfrac{\\sqrt{2(1-t^2)}}{2} -\\dfrac{1}{4} & \\left( 0 \\leqq t \\leqq \\dfrac{1}{\\sqrt{2}} \\text{\u306e\u3068\u304d} \\right) \\\\ \\dfrac{1-t^2}{2} & \\left( \\dfrac{1}{\\sqrt{2}} \\lt t \\leqq 1 \\text{\u306e\u3068\u304d} \\right) \\end{array}\\right.} \\ .\r\n\\]\r\n

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

        \\(V\\) \u306f\u5e73\u9762 \\(x = 0\\) \u306b\u3064\u3044\u3066\u5bfe\u79f0\u306a\u306e\u3067, \u6c42\u3081\u308b\u4f53\u7a4d \\(W\\) \u306f\r\n\\[\\begin{align}\r\nW & = 2 \\displaystyle\\int _ 0^1 S(t) \\, dt \\\\\r\n& = \\sqrt{2} \\underline{\\displaystyle\\int _ 0^{\\frac{1}{\\sqrt{2}}} \\sqrt{1-t^2} \\, dt} _ {[1]} -\\dfrac{1}{2} \\cdot \\dfrac{1}{\\sqrt{2}} +\\displaystyle\\int _ {\\frac{1}{\\sqrt{2}}}^1 (1-t^2) \\, dt \\ .\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, \u4e0b\u7dda\u90e8 [1] \u306f\u4e0b\u56f3\u306e\u659c\u7dda\u90e8\u306e\u9762\u7a4d\u3092\u8868\u3059\u306e\u3067<\/p>\r\n\"tohoku_r_2013_06_04\"\r\n

        \\[\\begin{align}\r\nW & = \\sqrt{2} \\left\\{ \\dfrac{1}{2} \\left( \\dfrac{1}{\\sqrt{2}} \\right)^2 +\\dfrac{1}{2} \\cdot 1^2 \\cdot \\dfrac{\\pi}{4} \\right\\} -\\dfrac{\\sqrt{2}}{4} +\\left[ t -\\dfrac{t^3}{3} \\right] _ {\\frac{1}{\\sqrt{2}}}^1 \\\\\r\n& = \\underline{\\dfrac{\\sqrt{2} \\pi}{8} -\\dfrac{5 \\sqrt{2}}{12} +\\dfrac{2}{3}} \\ .\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u534a\u5f84 \\(1\\) \u306e\u5186\u3092\u5e95\u9762\u3068\u3059\u308b\u9ad8\u3055 \\(\\dfrac{1}{\\sqrt{2}}\\) \u306e\u76f4\u5186\u67f1\u304c\u3042\u308b. \u5e95\u9762\u306e\u5186\u306e\u4e2d\u5fc3\u3092 O \u3068\u3057, \u76f4\u5f84\u3092 \\(1\\) \u3064\u3068\u308a AB \u3068\u304a\u304f. AB \u3092\u542b\u307f\u5e95\u9762\u3068 \\(45^{\\cir … \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":[96],"tags":[143,111],"class_list":["post-871","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2013","tag-nagoya_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/871","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=871"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/871\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=871"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=871"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}