{"id":298,"date":"2012-02-11T21:47:19","date_gmt":"2012-02-11T12:47:19","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=298"},"modified":"2021-09-16T06:45:03","modified_gmt":"2021-09-15T21:45:03","slug":"ngr200802","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr200802\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2008\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u4e09\u89d2\u5f62 ABC \u3067\u8fba AC \u3092 \\(s : 1-s\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 P , \u8fba BC \u3092 \\(t : 1-t\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 Q , \u7dda\u5206 AQ \u3068\u7dda\u5206 BP \u306e\u4ea4\u70b9\u3092 R \u3068\u3059\u308b. \u3053\u306e\u3068\u304d,\r\n\\[\r\n\\text{\u25b3APR \u306e\u9762\u7a4d} = 2 \\times ( \\text{\u25b3BQR \u306e\u9762\u7a4d} )\n\\]\r\n\u304c\u6210\u308a\u7acb\u3063\u3066\u3044\u308b\u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(s\\) \u3092 \\(t\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u6975\u9650 \\(\\displaystyle\\lim _ {t \\rightarrow +0} \\dfrac{s}{t}\\) \u3092\u6c42\u3081\u3088. \u305f\u3060\u3057, \\(t\\) \u304c\u6b63\u306e\u7bc4\u56f2\u3067 \\(0\\) \u306b\u9650\u308a\u306a\u304f\u8fd1\u3065\u304f\u3068\u304d, \\(t \\rightarrow +0\\) \u3068\u8868\u3059.<\/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

    \u30e1\u30cd\u30e9\u30a6\u30b9\u306e\u5b9a\u7406\u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{\\text{AP}}{\\text{PC}} \\cdot \\dfrac{\\text{CB}}{\\text{BQ}} \\cdot \\dfrac{\\text{QR}}{\\text{RA}} = \\dfrac{s}{1-s} \\cdot \\dfrac{1}{t} \\cdot \\dfrac{\\text{QR}}{\\text{RA}} & = 1 \\\\\r\n\\text{\u2234} \\quad \\dfrac{\\text{QR}}{\\text{RA}} = \\dfrac{t(1-s)}{s} & \\\\\r\n\\dfrac{\\text{BQ}}{\\text{QC}} \\cdot \\dfrac{\\text{CA}}{\\text{AP}} \\cdot \\dfrac{\\text{PR}}{\\text{RB}} = \\dfrac{t}{1-t} \\cdot \\dfrac{1}{s} \\cdot \\dfrac{\\text{PR}}{\\text{RB}} & = 1 \\\\\r\n\\text{\u2234} \\quad \\dfrac{\\text{PR}}{\\text{RB}} = \\dfrac{s(1-t)}{t} &\n\\end{align}\\]\r\n\u3053\u308c\u3089\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\dfrac{\\triangle \\text{APR}}{\\triangle \\text{BQR}} & = \\dfrac{\\text{PR} \\cdot \\text{RA}}{\\text{RB} \\cdot \\text{RQ}} \\\\\r\n& = \\dfrac{s(1-t)}{t} \\cdot \\dfrac{s}{t(1-s)} \\\\\r\n& = \\dfrac{s^2(1-t)}{t^2(1-s)} =2 \\\\\r\n\\text{\u2234} \\quad & (1-t)s^2 +2t^2 s -2t^2 = 0 \\\\\n\\end{align}\\]\r\n\\(0 \\lt t \\lt 1 , \\ 0 \\lt s \\lt 1\\) \u306a\u306e\u3067, \u3053\u308c\u3092\u89e3\u304f\u3068\r\n\\[\\begin{align}\r\ns & =\\dfrac{-t^2 +\\sqrt{t^4 +2t^2(1-t)}}{1-t} \\\\\r\n& =\\underline{\\dfrac{t \\left( \\sqrt{t^2-2t+2} -t \\right)}{1-t}}\n\\end{align}\\]\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\\begin{align}\r\n\\dfrac{s}{t} & = \\dfrac{\\sqrt{t^2-2t+2} -t}{1-t} \\\\\r\n& = \\dfrac{-2t+2}{(1-t) \\left( \\sqrt{t^2-2t+2} +t \\right)} \\\\\r\n& \\rightarrow \\dfrac{2}{1 \\cdot \\sqrt{2}} \\quad ( t \\rightarrow +0 \\text{\u306e\u3068\u304d} ) \\\\\r\n& = \\sqrt{2}\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\displaystyle\\lim _ {t \\rightarrow +0} \\dfrac{s}{t} =\\underline{\\sqrt{2}}\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4e09\u89d2\u5f62 ABC \u3067\u8fba AC \u3092 \\(s : 1-s\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 P , \u8fba BC \u3092 \\(t : 1-t\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3092 Q , \u7dda\u5206 AQ \u3068\u7dda\u5206 BP \u306e\u4ea4\u70b9\u3092 R \u3068\u3059\u308b. \u3053\u306e\u3068\u304d, \\[ \\text … \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":[53],"tags":[143,16],"class_list":["post-298","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2008","tag-nagoya_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/298","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=298"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/298\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=298"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=298"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}