{"id":1886,"date":"2021-09-18T15:38:51","date_gmt":"2021-09-18T06:38:51","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1886"},"modified":"2021-09-18T15:38:51","modified_gmt":"2021-09-18T06:38:51","slug":"thr201605","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201605\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2016\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\u7a7a\u9593\u5185\u306b, \u76f4\u7dda \\(l\\) \u3067\u4ea4\u308f\u308b \\(2\\) \u5e73\u9762 \\(\\alpha , \\beta\\) \u3068\u4ea4\u7dda \\(l\\) \u4e0a\u306e \\(1\\) \u70b9 O \u304c\u3042\u308b.\r\n\u3055\u3089\u306b, \u5e73\u9762 \\(\\alpha\\) \u4e0a\u306e\u76f4\u7dda \\(m\\) \u3068\u5e73\u9762 \\(\\beta\\) \u4e0a\u306e\u76f4\u7dda \\(n\\) \u3092, \u3069\u3061\u3089\u3082\u70b9 O \u3092\u901a\u308a \\(l\\) \u306b\u5782\u76f4\u306b\u3068\u308b. \\(m , n\\) \u4e0a\u306b\u305d\u308c\u305e\u308c\u70b9 P , Q \u304c\u3042\u308a,\r\n\\[\r\n\\text{OP} = \\sqrt{3} , \\quad \\text{OQ} = 2 , \\quad \\text{PQ} = 1\r\n\\]\r\n\u3067\u3042\u308b\u3068\u3059\u308b.\r\n\u7dda\u5206 PQ \u4e0a\u306e\u52d5\u70b9 T \u306b\u3064\u3044\u3066, \\(\\text{PT} = t\\) \u3092\u304a\u304f. \u70b9 T \u3092\u4e2d\u5fc3\u3068\u3057\u305f\u534a\u5f84 \\(\\sqrt{2}\\) \u306e\u7403\u3092\u8003\u3048\u308b. \u3053\u306e\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

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  1. (1)<\/strong>\u3000\\(S\\) \u306e\u5e73\u9762 \\(\\alpha\\) \u306b\u3088\u308b\u5207\u308a\u53e3\u306e\u9762\u7a4d\u3092 \\(t\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(S\\) \u306e\u5e73\u9762 \\(\\alpha\\) \u306b\u3088\u308b\u5207\u308a\u53e3\u306e\u9762\u7a4d\u3068 \\(S\\) \u306e\u5e73\u9762 \\(\\beta\\) \u306b\u3088\u308b\u5207\u308a\u53e3\u306e\u9762\u7a4d\u306e\u548c\u3092 \\(f(t)\\) \u3068\u304a\u304f. T \u304c\u7dda\u5206 PQ \u4e0a\u3092\u52d5\u304f\u3068\u304d, \\(f(t)\\) \u306e\u6700\u5927\u5024\u3068, \u305d\u306e\u3068\u304d\u306e \\(t\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n\"thr20160501.svg\"\r\n

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

    \u25b3 OPQ \u306f\u4e0a\u56f3\u306e\u3088\u3046\u306a\u76f4\u89d2\u4e09\u89d2\u5f62\u3067, \\(t\\) \u306e\u3068\u308a\u3046\u308b\u5024\u306e\u7bc4\u56f2\u306f \\(0 \\leqq t \\leqq 1\\) ... [1] .
    \r\n\\(S\\) \u306e \\(\\alpha\\) \u306b\u3088\u308b\u5207\u308a\u53e3\u306f\u5186\u3067, \u305d\u306e\u534a\u5f84\u3092 \\(r_t\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nr_t = \\sqrt{2 -t^2} \\ .\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u9762\u7a4d\u306f\r\n\\[\r\n\\underline{\\pi \\left( 2 -t^2 \\right)} \\ .\r\n\\]\r\n

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

    T \u304b\u3089 OQ \u306b\u4e0b\u3057\u305f\u5782\u7dda\u306e\u8db3\u3092 H \u3068\u304a\u304f\u3068, \\(\\triangle \\text{OPQ} \\sim \\triangle \\text{THQ}\\) \u306a\u306e\u3067\r\n\\[\r\n\\text{TH} = \\dfrac{\\sqrt{3} ( 1-t )}{2} \\ .\r\n\\]\r\n\\(S\\) \u306e \\(\\beta\\) \u306b\u3088\u308b\u5207\u308a\u53e3\u306f\u5186\u3067, \u305d\u306e\u534a\u5f84\u3092 \\(R_t\\) \u3068\u304a\u304f\u3068\r\n\\[\r\nR_t = \\sqrt{2 -\\dfrac{3}{4} (1-t)^2} = \\dfrac{1}{2} \\sqrt{5 +6t -3 t^2} \\ .\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\nf(t) & = \\pi \\left( {r_t}^2 +{R_t}^2 \\right) \\\\\r\n& = \\dfrac{\\pi}{4} \\left( 13 +6t -7t^2 \\right) \\\\\r\n& = \\dfrac{\\pi}{4} \\left\\{ -7 \\left( t -\\dfrac{3}{7} \\right)^2 +\\dfrac{100}{7} \\right\\} \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, [1] \u306e\u7bc4\u56f2\u3067, \\(f(t)\\) \u306f \\(t = \\underline{\\dfrac{3}{7}}\\) \u306e\u3068\u304d, \u6700\u5927\u5024\r\n\\[\r\nf \\left( \\dfrac{3}{7} \\right) = \\dfrac{\\pi}{4} \\cdot \\dfrac{100}{7} =\\underline{\\dfrac{25 \\pi}{7}}\r\n\\]\r\n\u3092\u3068\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u7a7a\u9593\u5185\u306b, \u76f4\u7dda \\(l\\) \u3067\u4ea4\u308f\u308b \\(2\\) \u5e73\u9762 \\(\\alpha , \\beta\\) \u3068\u4ea4\u7dda \\(l\\) \u4e0a\u306e \\(1\\) \u70b9 O \u304c\u3042\u308b. \u3055\u3089\u306b, \u5e73\u9762 \\(\\alpha\\) \u4e0a\u306e\u76f4\u7dda \\(m\\) \u3068\u5e73\u9762 … \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":[155],"tags":[148,162],"class_list":["post-1886","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2016","tag-tohoku_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1886","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=1886"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1886\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1886"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1886"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1886"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}