{"id":2012,"date":"2021-12-05T19:24:03","date_gmt":"2021-12-05T10:24:03","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2012"},"modified":"2021-12-05T19:24:03","modified_gmt":"2021-12-05T10:24:03","slug":"thr202102","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr202102\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2021\uff1a\u7b2c2\u554f"},"content":{"rendered":"
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\\(a , b\\) \u3092 \\(0 \\lt a \\lt 1\\) , \\(0 \\lt b \\lt 1\\) \u3092\u6e80\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b.\r\n\u5e73\u9762\u4e0a\u306e\u4e09\u89d2\u5f62 ABC \u3092\u8003\u3048, \u8fba AB \u3092 \\(a : 1-a\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 P , \u8fba BC \u3092 \\(b : 1-b\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 Q , \u8fba CA \u306e\u4e2d\u70b9\u3092 R \u3068\u3057, \u4e09\u89d2\u5f62 ABC \u306e\u9762\u7a4d\u3092 \\(S\\) , \u4e09\u89d2\u5f62 PQR \u306e\u9762\u7a4d\u3092 \\(T\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\dfrac{T}{S}\\) \u3092 \\(a , b\\) \u3067\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a , b\\) \u304c \\(0 \\lt a \\lt \\dfrac{1}{2}\\) , \\(0 \\lt b \\lt \\dfrac{1}{2}\\) \u306e\u7bc4\u56f2\u3092\u52d5\u304f\u3068\u304d, \\(\\dfrac{T}{S}\\) \u304c\u3068\u308a\u3046\u308b\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(p , q\\) \u3092 \\(3\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3057, \\(a = \\dfrac{1}{p}\\) , \\(b = \\dfrac{1}{q}\\) \u3068\u3059\u308b.\r\n\\(\\dfrac{T}{S}\\) \u306e\u9006\u6570 \\(\\dfrac{S}{T}\\) \u304c\u6574\u6570\u3068\u306a\u308b\u3088\u3046\u306a \\(p , q\\) \u306e\u7d44 \\(( p , q )\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

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

    \\[\r\n\\triangle \\text{PBQ} = (1-a) b S \\ , \\ \\triangle \\text{QCR} = \\dfrac{1-b}{2} S \\ , \\ \\triangle \\text{RAP} = \\dfrac{a}{2} S\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nT & = S -\\triangle \\text{PBQ} -\\triangle \\text{QCR} -\\triangle \\text{RAP} \\\\\r\n& = \\left\\{ 1 -(1-a) b -\\dfrac{1-b}{2} -\\dfrac{a}{2} \\right\\} S \\\\\r\n& = \\dfrac{2ab -a -b +1}{2} S\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\dfrac{T}{S} = \\underline{\\dfrac{2ab -a -b +1}{2}}\r\n\\]\r\n

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

    \\[\r\n\\dfrac{T}{S} = \\dfrac{( 2a -1 ) ( 2b -1 ) +1}{4}\r\n\\]\r\n\u6761\u4ef6\u3088\u308a \\(0 \\lt 2a -1 \\lt 1\\) , \\(0 \\lt 2b -1 \\lt 1\\) \u306a\u306e\u3067\r\n\\[\r\n\\underline{\\dfrac{1}{4} \\lt \\dfrac{T}{S} \\lt \\dfrac{1}{2}}\r\n\\]\r\n

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

    \\(p \\geqq 3\\) , \\(q \\geqq 3\\) ... [1] \u306a\u3089\u3070, \\(0 \\lt \\dfrac{1}{p} \\lt \\dfrac{1}{2}\\) , \\(0 \\lt \\dfrac{1}{q} \\lt \\dfrac{1}{2}\\) \u306a\u306e\u3067, (2)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\r\n\\dfrac{1}{4} \\lt \\dfrac{T}{S} \\lt \\dfrac{1}{2}\r\n\\]\r\n\u3086\u3048\u306b\r\n\\[\r\n2 \\lt \\dfrac{S}{T} \\lt 4\r\n\\]\r\n\u306a\u306e\u3067, \\(\\dfrac{S}{T}\\) \u304c\u6574\u6570\u306a\u3089\u3070\r\n\\[\r\n\\dfrac{S}{T} = 3\r\n\\]\r\n\u3053\u308c\u3092\u3068\u304f\u3068\r\n\\[\\begin{align}\r\n\\dfrac{2}{2ab -a -b +1} & = 3 \\\\\r\n\\dfrac{2pq}{pq -p -q +2} & = 3 \\\\\r\npq -3p -3q +6 & = 0 \\\\\r\n( p-3 ) ( q-3 ) & = 3\r\n\\end{align}\\]\r\n[1] \u306b\u6ce8\u610f\u3059\u308c\u3070\r\n\\[\r\n( p , q ) = \\underline{( 6 , 4 ) , ( 4 , 6 )}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(a , b\\) \u3092 \\(0 \\lt a \\lt 1\\) , \\(0 \\lt b \\lt 1\\) \u3092\u6e80\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b. \u5e73\u9762\u4e0a\u306e\u4e09\u89d2\u5f62 ABC \u3092\u8003\u3048, \u8fba AB \u3092 \\(a : 1-a\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 P , \u8fba … \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":[175],"tags":[148,165],"class_list":["post-2012","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2021","tag-tohoku_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2012","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=2012"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2012\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2012"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2012"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}