{"id":1905,"date":"2021-09-22T21:22:23","date_gmt":"2021-09-22T12:22:23","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1905"},"modified":"2021-09-22T21:22:23","modified_gmt":"2021-09-22T12:22:23","slug":"tbr201605","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tbr201605\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2016\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(\\triangle \\text{PQR}\\) \u306b\u304a\u3044\u3066 \\(\\angle \\text{RPQ} = \\theta\\) , \\(\\angle \\text{PQR} = \\dfrac{\\pi}{2}\\) \u3068\u3059\u308b. \u70b9 \\(\\text{P} {} _ n \\ ( n = 1, 2, 3, \\cdots )\\) \u3092\u6b21\u3067\u5b9a\u3081\u308b.\r\n\\[\r\n\\text{P} {} _ 1 = \\text{P} , \\quad \\text{P} {} _ 2 = \\text{Q} , \\quad \\text{P} {} _ n \\text{P} {} _ {n+2} = \\text{P} {} _ n \\text{P} {} _ {n+1}\r\n\\]\r\n\u305f\u3060\u3057, \u70b9 \\(\\text{P} {} _ {n+2}\\) \u306f\u7dda\u5206 \\(\\text{P} {} _ n \\text{R}\\) \u4e0a\u306b\u3042\u308b\u3082\u306e\u3068\u3059\u308b. \u5b9f\u6570 \\(\\theta _ n \\ ( n = 1, 2, 3, \\cdots )\\) \u3092\r\n\\[\r\n\\theta _ n = \\angle \\text{P} {} _ {n+1} \\text{P} {} _ n \\text{P} {} _ {n+2} \\quad ( 0 \\lt \\theta _ n \\lt \\pi )\r\n\\]\r\n\u3067\u5b9a\u3081\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\theta _ 2 , \\theta _ 3\\) \u3092 \\(\\theta\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\theta _ {n+1} +\\dfrac{\\theta _ n}{2} \\ ( n = 1, 2, 3, \\cdots )\\) \u306f \\(n\\) \u306b\u3088\u3089\u306a\u3044\u5b9a\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(\\displaystyle\\lim _ {n \\rightarrow \\infty} \\theta _ n\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n\"tbr20160501.svg\"\r\n

    \r\n\r\n

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

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

    \\[\\begin{align}\r\n\\theta _ 2 & = \\dfrac{\\pi}{2} -\\dfrac{\\pi -\\theta}{2} = \\underline{\\dfrac{\\theta}{2}} \\ , \\\\\r\n\\theta _ 3 & = \\pi -\\dfrac{\\pi -\\theta}{2} -\\dfrac{\\pi -\\frac{\\theta}{2}}{2}= \\underline{\\dfrac{3 \\theta}{4}} \\ .\r\n\\end{align}\\]\r\n

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

    \u300c \\(\\theta _ {n+1} +\\dfrac{\\theta _ n}{2} = \\theta\\) \u300d ... [A] \u3068\u3059\u308b.<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(n = 1\\) \u306e\u3068\u304d\r\n\\[\r\n\\theta _ 2 +\\dfrac{\\theta _ 1}{2} = \\dfrac{\\theta}{2} +\\dfrac{\\theta}{2} = \\theta\r\n\\]\r\n\u3067, [A] \u304c\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(n = k\\) \u306e\u3068\u304d\r\n[A] \u304c\u6210\u7acb\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\theta _ {k+2} & = \\angle \\text{P} {} _ {k+4} \\text{P} {} _ {k+2} \\text{P} {} _ {k+3} \\\\\r\n& = \\pi -\\angle \\text{P} {} _ {k+1} \\text{P} {} _ {k+2} \\text{P} {} _ {k+3} -\\angle \\text{P} {} _ {k} \\text{P} {} _ {k+2} \\text{P} {} _ {k+1} \\\\\r\n& = \\pi -\\dfrac{\\pi -\\theta _ {k}}{2} -\\dfrac{\\pi -\\theta _ {k+1}}{2} \\\\\r\n& = \\dfrac{\\theta _ {k}}{2} +\\dfrac{\\theta _ {k+1}}{2} \\ .\r\n\\end{align}\\]\r\n\u4e21\u8fba\u306b \\(\\dfrac{\\theta _ {k+1}}{2}\\) \u3092\u52a0\u3048\u308c\u3070\r\n\\[\r\n\\theta _ {k+2} +\\dfrac{\\theta _ {k+1}}{2} = \\theta _ {k+1} +\\dfrac{\\theta _ {k}}{2} = \\theta \\ .\r\n\\]\r\n\u3086\u3048\u306b, \\(n = k+1\\) \u306e\u3068\u304d\u3082, [A] \u304c\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n

      1*<\/strong> 2*<\/strong> \u304b\u3089, \u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u306b\u3088\u308a, \u3059\u3079\u3066\u306e\u81ea\u7136\u6570 \\(n\\) \u306b\u3064\u3044\u3066, [A] \u304c\u6210\u7acb\u3059\u308b\u3053\u3068\u304c\u793a\u3055\u308c, \u984c\u610f\u3082\u793a\u3055\u308c\u305f.<\/p>\r\n

      (3)<\/strong><\/p>\r\n[A] \u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\n\\theta _ {n+1} -\\dfrac{2 \\theta}{3} = -\\dfrac{1}{2} \\left( \\theta _ {n} -\\dfrac{2 \\theta}{3} \\right) \\ .\r\n\\]\r\n\u3064\u307e\u308a, \u6570\u5217 \\(\\left\\{ \\theta _ {n} -\\dfrac{2 \\theta}{3} \\right\\}\\) \u306f, \u521d\u9805 \\(\\theta _ 1 -\\dfrac{2 \\theta}{3} = \\dfrac{\\theta}{3}\\) , \u516c\u6bd4 \\(-\\dfrac{1}{2}\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\theta _ {n} -\\dfrac{2 \\theta}{3} & = \\dfrac{\\theta}{3} \\left( -\\dfrac{1}{2} \\right)^{n-1} \\\\\r\n\\text{\u2234} \\quad \\theta _ {n} = \\dfrac{2 \\theta}{3} & +\\dfrac{\\theta}{3} \\left( -\\dfrac{1}{2} \\right)^{n-1} \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\displaystyle\\lim _ {n \\rightarrow \\infty} \\theta _ n = \\underline{\\dfrac{2 \\theta}{3}} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(\\triangle \\text{PQR}\\) \u306b\u304a\u3044\u3066 \\(\\angle \\text{RPQ} = \\theta\\) , \\(\\angle \\text{PQR} = \\dfrac{\\pi}{2}\\) \u3068\u3059\u308b. \u70b9 \\ … \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":[158],"tags":[144,162],"class_list":["post-1905","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2016","tag-tsukuba_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1905","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=1905"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1905\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1905"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1905"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1905"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}