{"id":528,"date":"2012-12-25T08:21:38","date_gmt":"2012-12-24T23:21:38","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=528"},"modified":"2021-10-31T06:50:38","modified_gmt":"2021-10-30T21:50:38","slug":"tkb201202","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201202\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2012\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\u5b9f\u6570 \\(t\\) \u306f \\(0 \\lt t \\lt 1\\) \u3092\u6e80\u305f\u3059\u3068\u3057, \u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(4\\) \u70b9O \\((0,0)\\) , A \\((0,1)\\) , B \\((1,0)\\) , C \\((t,0)\\) \u3092\u8003\u3048\u308b.\r\n\u307e\u305f\u7dda\u5206 AB \u4e0a\u306e\u70b9 D \u3092 \\(\\angle \\text{ACO} = \\angle \\text{BCD}\\) \u3068\u306a\u308b\u3088\u3046\u306b\u5b9a\u3081\u308b. \\(t\\) \u3092\u52d5\u304b\u3057\u305f\u3068\u304d\u306e\u4e09\u89d2\u5f62 ACD \u306e\u9762\u7a4d\u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tokyo_b_2012_02_01.png\" alt=\"tokyo_b_2012_02_01\" class=\"aligncenter size-full\" \/>\r\n<p>AC \u306e\u50be\u304d\u306f \\(-\\dfrac{1}{t}\\) \u306a\u306e\u3067, CD \u306e\u50be\u304d\u306f \\(\\dfrac{1}{t}\\) \u3067\u3042\u308b.<br \/>\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\n\\text{CD} : \\ y = \\dfrac{1}{t} (x-t)\r\n\\]\r\n\u3053\u308c\u3068 \\(\\text{AB} : \\ y = 1-x\\) \u3068\u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{1}{t} (x-t) & = 1-x \\\\\r\nx-t & = t -tx \\\\\r\n\\text{\u2234} \\quad x & = \\dfrac{2t}{1+t}\r\n\\end{align}\\]\r\nAB \u306e\u5f0f\u3088\u308a\r\n\\[\r\ny = 1-\\dfrac{2t}{1+t} = \\dfrac{1-t}{1+t}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, D \\(\\left( \\dfrac{2t}{1+t} , \\dfrac{1-t}{1+t} \\right)\\) .<br \/>\r\n\u25b3ACD \u306e\u9762\u7a4d\u3092 \\(S(t)\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nS(t) &= \\dfrac{1}{2} (1-t) \\left( 1 -\\dfrac{1-t}{1+t} \\right) \\\\\r\n& = \\dfrac{1-t^2 -(1-t)^2}{2(1+t)} \\\\\r\n& = \\dfrac{t-t^2}{1+t} \\\\\r\n& = -t+2 -\\dfrac{2}{1+t} \\\\\r\n& = 3 -\\left( 1+t +\\dfrac{2}{1+t} \\right)\r\n\\end{align}\\]\r\n\u3053\u3053\u3067\u76f8\u52a0\u76f8\u4e57\u5e73\u5747\u306e\u95a2\u4fc2\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\nS(t) & \\leqq 3 -2 \\sqrt{(1+t) \\cdot \\dfrac{2}{1+t}} \\\\\r\n& =3-2 \\sqrt{2}\r\n\\end{align}\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f,\r\n\\[\\begin{align}\r\n1+t & = \\dfrac{2}{1+t} \\\\\r\n\\text{\u2234} \\quad t & = \\sqrt{2} -1 \\quad ( \\ \\text{\u2235} \\ 0 \\lt t \\lt 1\\ )\r\n\\end{align}\\]\r\n\u306e\u3068\u304d\u3067\u3042\u308b.<br \/>\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6700\u5927\u5024\u306f\r\n\\[\r\n\\underline{3 -2 \\sqrt{2}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5b9f\u6570 \\(t\\) \u306f \\(0 \\lt t \\lt 1\\) \u3092\u6e80\u305f\u3059\u3068\u3057, \u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(4\\) \u70b9O \\((0,0)\\) , A \\((0,1)\\) , B \\((1,0)\\) , C \\((t,0)\\) \u3092\u8003\u3048\u308b. &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkb201202\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[78],"tags":[68,149],"class_list":["post-528","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2012","tag-68","tag-tokyo_b"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/528","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=528"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/528\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=528"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=528"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}