{"id":1443,"date":"2017-05-18T23:28:12","date_gmt":"2017-05-18T14:28:12","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1443"},"modified":"2021-09-08T14:51:29","modified_gmt":"2021-09-08T05:51:29","slug":"osr201605","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr201605\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2016\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\u5186\u4e0a\u306e \\(5\\) \u70b9 A, B, C, D, E \u306f\u53cd\u6642\u8a08\u56de\u308a\u306b\u3053\u306e\u9806\u306b\u4e26\u3073, \u5186\u5468\u3092 \\(5\\) \u7b49\u5206\u3057\u3066\u3044\u308b. \\(5\\) \u70b9 A, B, C, D, E \u3092\u9802\u70b9\u3068\u3059\u308b\u6b63\u4e94\u89d2\u5f62\u3092 \\(\\text{R} _ 1\\) \u3068\u3059\u308b. \\(\\overrightarrow{\\text{AB}} = \\overrightarrow{a}\\) , \\(\\overrightarrow{\\text{CD}} = \\overrightarrow{c}\\) \u3068\u304a\u304d, \\(\\overrightarrow{a}\\) \u306e\u5927\u304d\u3055\u3092 \\(x\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\overrightarrow{\\text{AC}}\\) \u306e\u5927\u304d\u3055\u3092 \\(y\\) \u3068\u3059\u308b\u3068\u304d, \\(x^2 = y (y-x)\\) \u304c\u306a\u308a\u305f\u3064\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\overrightarrow{\\text{BC}}\\) \u3092 \\(\\overrightarrow{a} , \\overrightarrow{c}\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(\\text{R} _ 1\\) \u306e\u5bfe\u89d2\u7dda\u306e\u4ea4\u70b9\u3068\u3057\u3066\u5f97\u3089\u308c\u308b \\(\\text{R} _ 1\\) \u306e\u5185\u90e8\u306e \\(5\\) \u3064\u306e\u70b9\u3092\u9802\u70b9\u3068\u3059\u308b\u6b63\u4e94\u89d2\u5f62\u3092 \\(\\text{R} _ 2\\) \u3068\u3059\u308b. \\(\\text{R} _ 2\\) \u306e\u4e00\u8fba\u306e\u9577\u3055\u3092 \\(x\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  4. (4)<\/strong>\u3000\\(n = 1, 2, 3, \\cdots\\) \u306b\u5bfe\u3057\u3066, \\(\\text{R} _ n\\) \u306e\u5bfe\u89d2\u7dda\u306e\u4ea4\u70b9\u3068\u3057\u3066\u5f97\u3089\u308c\u308b \\(\\text{R} _ n\\) \u306e\u5185\u90e8\u306e \\(5\\) \u3064\u306e\u70b9\u3092\u9802\u70b9\u3068\u3059\u308b\u6b63\u4e94\u89d2\u5f62\u3092 \\(\\text{R} _ {n+1}\\) \u3068\u3057, \\(\\text{R} _ n\\) \u306e\u9762\u7a4d\u3092 \\(S _ n\\) \u3068\u3059\u308b.\r\n\\[\r\n\\displaystyle\\lim _ {n \\rightarrow \\infty} \\dfrac{1}{S _ 1} \\textstyle\\sum\\limits _ {k=1}^{n} (-1)^{k+1} S _ k\r\n\\]\r\n\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

    \"\"<\/p>\r\n

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

    \u5186\u5468\u89d2\u306e\u5b9a\u7406\u3088\u308a, \u6761\u4ef6\u304b\u3089\r\n\\[\r\n\\angle \\text{BAC} = \\angle \\text{ACB} = \\angle \\text{ABE} = \\dfrac{\\pi}{5} \\quad ... [1]\r\n\\]\r\nAC \u3068 BE \u306e\u4ea4\u70b9\u3092 F \u3068\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\angle \\text{BFC} & = \\angle \\text{BAC} +\\angle \\text{ABE} = \\dfrac{2 \\pi}{5} \\\\\r\n\\angle \\text{BFC} & = \\pi -\\angle \\text{ACB} -\\angle \\text{BFC} = \\dfrac{2 \\pi}{5}\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, \\(\\triangle \\text{BCF}\\) \u306f\u4e8c\u7b49\u8fba\u4e09\u89d2\u5f62\u3067\r\n\\[\r\n\\text{FC} = \\text{BC} = x \\quad ... [2]\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(\\text{AF} = y-x\\) .
    \r\n\u307e\u305f, [1] \u3088\u308a, \\(\\triangle \\text{ABC} \\sim \\triangle \\text{BFA}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\text{BC} : \\text{CA} & = \\text{FA} : \\text{AB} \\\\\r\nx : y & = (y-x) : x \\\\\r\n\\text{\u2234} \\quad x^2 & = y (y-x)\r\n\\end{align}\\]\r\n

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

    \\[\\begin{align}\r\n\\overrightarrow{\\text{BC}} & = \\overrightarrow{\\text{BE}} +\\overrightarrow{\\text{EC}} \\\\\r\n& = \\dfrac{y}{x} \\overrightarrow{c} +\\dfrac{y}{x} \\overrightarrow{a}\r\n\\end{align}\\]\r\n\\(x \\neq 0\\) \u306a\u306e\u3067, (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\\begin{align}\r\ny^2 -xy -x^2 & = 0 \\\\\r\n\\left( \\dfrac{y}{x} \\right)^2 -\\dfrac{y}{x} -1 & = 0 \\\\\r\n\\text{\u2234} \\quad \\dfrac{y}{x} & = \\dfrac{1 +\\sqrt{5}}{2}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\overrightarrow{\\text{BC}} = \\underline{\\dfrac{1 +\\sqrt{5}}{2} \\left( \\overrightarrow{a} +\\overrightarrow{c} \\right)}\r\n\\]\r\n

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

    \u6c42\u3081\u308b\u4e00\u8fba\u306e\u9577\u3055\u306f\r\n\\[\\begin{align}\r\ny -2(y-x) & = 2x-y \\\\\r\n& = \\left( 2 -\\dfrac{1 +\\sqrt{5}}{2} \\right) x \\\\\r\n& = \\underline{\\dfrac{3 -\\sqrt{5}}{2} x}\r\n\\end{align}\\]\r\n

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

    \\(p = \\dfrac{3 -\\sqrt{5}}{2}\\) \u3068\u304a\u304f\u3068, \\(0 \\lt p \\lt 1\\) .
    \r\n\\(\\text{R} _n\\) \u3068 \\(\\text{R} _{n+1}\\) \u306e\u76f8\u4f3c\u6bd4\u306f \\(1 : p\\) \u306a\u306e\u3067, \u9762\u7a4d\u6bd4\u306f \\(1 : p^2 \\) .
    \r\n\u3053\u3053\u3067\r\n\\[\r\np^2 = \\dfrac{14 -6 \\sqrt{5}}{4} = \\dfrac{7 -3 \\sqrt{5}}{2}\r\n\\]\r\n\u6c42\u3081\u308b\u5024 \\(I\\) \u306f, \u521d\u9805\\(1\\) , \u516c\u6bd4 \\(-p^2\\) \u306e\u7121\u9650\u7b49\u6bd4\u7d1a\u6570\u306e\u548c\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nI & = \\dfrac{1}{1 -(-p^2)} = \\dfrac{2}{2 +(7 -3 \\sqrt{5})} \\\\\r\n& = \\dfrac{2}{9 -3 \\sqrt{5}} = \\dfrac{2 ( 9 +3 \\sqrt{5} )}{81 -45} \\\\\r\n& = \\underline{\\dfrac{3 +\\sqrt{5}}{6}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u5186\u4e0a\u306e \\(5\\) \u70b9 A, B, C, D, E \u306f\u53cd\u6642\u8a08\u56de\u308a\u306b\u3053\u306e\u9806\u306b\u4e26\u3073, \u5186\u5468\u3092 \\(5\\) \u7b49\u5206\u3057\u3066\u3044\u308b. \\(5\\) \u70b9 A, B, C, D, E \u3092\u9802\u70b9\u3068\u3059\u308b\u6b63\u4e94\u89d2\u5f62\u3092 \\(\\text{R} _ 1\\) … \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":[152],"tags":[142,162],"class_list":["post-1443","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2016","tag-osaka_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1443","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=1443"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1443\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1443"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1443"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1443"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}