{"id":192,"date":"2011-12-02T23:04:34","date_gmt":"2011-12-02T14:04:34","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=192"},"modified":"2021-09-10T07:43:15","modified_gmt":"2021-09-09T22:43:15","slug":"osr200902","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr200902\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2009\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u884c\u5217 \\(A = \\left( \\begin{array}{cc} \\cos \\dfrac{\\pi}{3} & -\\sin \\dfrac{\\pi}{3} \\\\ \\sin \\dfrac{\\pi}{3} & \\cos \\dfrac{\\pi}{3} \\end{array} \\right)\\) \u306e\u8868\u3059 \\(1\\) \u6b21\u5909\u63db\u3092 \\(f\\) \u3068\u3059\u308b.\r\n\u70b9 P \\(( 16\\sqrt{3}, 16 )\\) \u3092\u3068\u308a, \\(\\text{P} _ 1 = f( \\text{P} )\\) , \\(\\text{P} _ {n+1} = f( \\text{P} _ n )\\) \uff08 \\(n=1, 2, 3, \\cdots\\) \uff09\u3068\u3059\u308b.\r\n\u6b63\u306e\u6574\u6570 \\(k\\) \u306b\u5bfe\u3057\u3066, \u6b21\u306e\u6761\u4ef6\u3092\u307f\u305f\u3059\u9818\u57df\u3092 \\(D _ k\\) \u3068\u3059\u308b.\r\n\\[\r\nx \\lt 0 , \\ y \\lt 0 , \\ \\sqrt{3}x +y \\leqq -2^{-k}\r\n\\]\r\n\u3053\u306e\u3068\u304d \\(D _ k\\) \u306b\u542b\u307e\u308c\u308b \\(\\text{P} _ n\\) \u306e\u500b\u6570\u3092 \\(k\\) \u3067\u8868\u305b.<\/p>\r\n

\r\n\r\n

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

\\(A = \\left( \\begin{array}{cc} \\cos \\dfrac{\\pi}{3} & -\\sin \\dfrac{\\pi}{3} \\\\ \\sin \\dfrac{\\pi}{3} & \\cos \\dfrac{\\pi}{3} \\end{array} \\right)\\) \u306a\u306e\u3067\r\n\\[\r\n\\angle \\text{P} _ n\\text{OP} _ {n+1} =\\dfrac{\\pi}{3} , \\quad \\text{OP} _ {n+1} =\\dfrac{1}{2} \\text{OP} _ n\n\\]\r\nB \\(( 1, 0 )\\) \u3068\u304a\u3051\u3070,\r\n\\[\r\n\\angle \\text{BOP} = \\dfrac{\\pi}{6} , \\quad \\text{OP} =32\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\angle \\text{BOP} _ n & = \\dfrac{(2n+1) \\pi}{6} , \\\\\r\n\\quad \\text{OP} _ n & = 32 \\cdot \\left( \\dfrac{1}{2} \\right)^n = 2^{-n+5}\n\\end{align}\\]\r\n\"\"\r\n

\u3057\u305f\u304c\u3063\u3066, \\(\\text{P} _ n\\) \u304c \\(x \\lt 0 , \\ y \\lt 0\\) \u306e\u9818\u57df\u306b\u5165\u308b\u306e\u306f, \\(n= 6 \\ell -3 \\ ( \\ell =1, 2, \\cdots )\\) \u306e\u3068\u304d\u3067\u3042\u308b.
\r\n\u3053\u308c\u3089\u306e\u70b9 \\(\\text{P} _ {6 \\ell -3}\\) \u306f\u3059\u3079\u3066 \\(y = \\dfrac{x}{\\sqrt{3}} \\ ... [1]\\) \u4e0a\u306b\u3042\u308b.
\r\n\\(\\sqrt{3}x+y +2^{-k} =0\\) \u3068 [1] \u306f\u5782\u76f4\u3067, \u539f\u70b9\u3068\u306e\u8ddd\u96e2\u306f\r\n\\[\r\n\\dfrac{\\left| 2^{-k} \\right|}{\\sqrt{3+1}} = 2^{-k-1}\n\\]\r\n\u3086\u3048\u306b, \u70b9 \\(\\text{P} _ {6 \\ell -3}\\) \u304c \\(D _ k\\) \u306b\u542b\u307e\u308c\u308b\u6761\u4ef6\u306f\r\n\\[\\begin{align}\r\n2^{-k-1} & \\leqq 2^{-(6 \\ell -3)+5} \\\\\r\n\\text{\u2234} \\quad -k-1 & \\leqq -6 \\ell +8 \\\\\r\n\\text{\u2234} \\quad \\ell & \\leqq \\dfrac{k+9}{6}\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u500b\u6570\u306f\r\n\\[\r\n\\underline{\\left[ \\dfrac{k+9}{6} \\right]} \\quad \\left( [ \\ ] \\text{\u306f\u30ac\u30a6\u30b9\u8a18\u53f7} \\right)\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u884c\u5217 \\(A = \\left( \\begin{array}{cc} \\cos \\dfrac{\\pi}{3} & -\\sin \\dfrac{\\pi}{3} \\\\ \\sin \\dfrac{\\pi}{3} & \\cos \\df … \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":[30],"tags":[142,15],"class_list":["post-192","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2009","tag-osaka_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/192","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=192"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/192\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=192"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=192"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=192"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}