{"id":1213,"date":"2015-07-31T23:41:15","date_gmt":"2015-07-31T14:41:15","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1213"},"modified":"2015-08-01T22:03:54","modified_gmt":"2015-08-01T13:03:54","slug":"htb201403","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201403\/","title":{"rendered":"\u4e00\u6a4b\u59272014\uff1a\u7b2c3\u554f"},"content":{"rendered":"\u5186 \\(C : \\ x^2 +y^2 = 1\\) \u4e0a\u306e\u70b9P\u306b\u304a\u3051\u308b\u63a5\u7dda\u3092 \\(l\\) \u3068\u3059\u308b. \u70b9 \\(( 1 , 0 )\\) \u3092\u901a\u308a, \\(l\\) \u3068\u5e73\u884c\u306a\u76f4\u7dda\u3092 \\(m\\) \u3068\u3059\u308b. \u76f4\u7dda \\(m\\) \u3068\u5186 \\(C\\) \u306e \\(( 1 , 0 )\\) \u4ee5\u5916\u306e\u5171\u6709\u70b9\u3092P'\u3068\u3059\u308b. \u305f\u3060\u3057, \\(m\\) \u304c\u76f4\u7dda \\(x = 1\\) \u306e\u3068\u304d\u306fP'\u3092 \\(( 1 , 0 )\\) \u3068\u3059\u308b. \r\n\u5186 \\(C\\) \u4e0a\u306e\u70b9 \\(( s , t )\\) \u304b\u3089\u70b9P' \\(( s' , t' )\\) \u3092\u5f97\u308b\u4e0a\u8a18\u306e\u64cd\u4f5c\u3092T\u3068\u547c\u3076. \r\n
    \r\n
  1. (1)<\/strong>\u3000\\(s' , t'\\) \u3092\u305d\u308c\u305e\u308c \\(s\\) \u3068 \\(t\\) \u306e\u591a\u9805\u5f0f\u3068\u3057\u3066\u8868\u305b. <\/li>\r\n
  2. (2)<\/strong>\u3000\u70b9P\u306b\u64cd\u4f5cT\u3092 \\(n\\) \u56de\u7e70\u308a\u8fd4\u3057\u3066\u5f97\u3089\u308c\u308b\u70b9\u3092 \\(\\text{P} _ n\\) \u3068\u304a\u304f. P\u304c \\(\\left( \\dfrac{\\sqrt{3}}{2} , \\dfrac{1}{2} \\right)\\) \u306e\u3068\u304d, \\(\\text{P} _ 1 , \\text{P} _ 2 , \\text{P} _ 3\\) \u3092\u56f3\u793a\u305b\u3088. <\/li>\r\n
  3. (3)<\/strong>\u3000\u6b63\u306e\u6574\u6570 \\(n\\) \u306b\u3064\u3044\u3066, \\(\\text{P} _ n = \\text{P}\\) \u3068\u306a\u308b\u3088\u3046\u306a\u70b9P\u306e\u500b\u6570\u3092\u6c42\u3081\u3088. <\/li>\r\n<\/ol>\r\n
    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n\r\n(1)<\/strong>\r\n\r\nA \\(( 1 , 0 )\\) , \u7dda\u5206OP\u3068 \\(l\\) \u306e\u4ea4\u70b9\u3092H\u3068\u304a\u304f. \r\n\\(l \/ \\hspace{-0.2em} \/ m\\) \u306a\u306e\u3067, \\(\\angle \\text{OHA} = \\angle \\text{OHP'} = 90^{\\circ}\\) \u3060\u304b\u3089\r\n\\[\r\n\\triangle \\text{OHA} \\equiv \\triangle \\text{OHP'}\r\n\\]\r\n\u3086\u3048\u306b\r\n\\[\r\n\\angle \\text{AOP} = \\angle \\text{POP'} \\quad ... [1]\r\n\\]\r\n\\(s = \\cos \\theta , \\ t = \\sin \\theta \\ ( 0 \\leqq \\theta \\lt 2 \\pi )\\) ... [2] \u3068\u304a\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067, [1]\u3088\u308a\r\n\\[ \\begin{align}\r\ns' & = \\cos 2 \\theta = \\underline{2s^2 -1} \\\\\r\nt' & = \\sin 2 \\theta = \\underline{2st}\r\n\\end{align} \\]\r\n\r\n(2)<\/strong>\r\n\r\nP \\(\\left( \\cos \\dfrac{\\pi}{6} , \\sin \\dfrac{\\pi}{6} \\right)\\) \u306a\u306e\u3067\r\n\\[ \\begin{align}\r\n\\text{P} _ 1 & \\ \\left( \\cos \\dfrac{\\pi}{3} , \\sin \\dfrac{\\pi}{3} \\right) \\ \\text{\u3059\u306a\u308f\u3061} \\ \\left( \\dfrac{1}{2} , \\dfrac{\\sqrt{3}}{2} \\right) , \\\\\r\n\\text{P} _ 2 & \\ \\left( \\cos \\dfrac{2 \\pi}{3} , \\sin \\dfrac{2 \\pi}{3} \\right) \\ \\text{\u3059\u306a\u308f\u3061} \\ \\left( -\\dfrac{1}{2} , \\dfrac{\\sqrt{3}}{2} \\right) , \\\\\r\n\\text{P} _ 3 & \\ \\left( \\cos \\dfrac{4 \\pi}{3} , \\sin \\dfrac{4 \\pi}{3} \\right) \\ \\text{\u3059\u306a\u308f\u3061} \\ \\left( -\\dfrac{1}{2} , -\\dfrac{\\sqrt{3}}{2} \\right)\r\n\\end{align} \\]\r\n\u3088\u3063\u3066, \u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b. \r\n\r\n\"htb20140301\"\r\n\r\n(3)<\/strong>\r\n\r\n\\(\\text{P} _ n \\ \\left( \\cos 2^n \\theta , \\sin 2^n \\theta \\right)\\) \u306a\u306e\u3067, \\(\\text{P} _ n = \\text{P}\\) \u3068\u306a\u308b\u6761\u4ef6\u306f, \u6574\u6570 \\(k\\) \u3092\u7528\u3044\u3066\r\n\\[ \\begin{align}\r\n2^n \\theta & = 2 \\pi k +\\theta \\\\\r\n\\text{\u2234} \\quad \\theta & = \\dfrac{2 \\pi k}{2^n -1}\r\n\\end{align} \\]\r\n[2]\u3092\u7528\u3044\u308c\u3070\r\n\\[ \\begin{align}\r\n0 & \\leqq \\dfrac{2 \\pi k}{2^n -1} \\lt 2 \\pi \\\\\r\n0 & \\leqq \\dfrac{k}{2^n -1} \\lt 1 \\\\\r\n\\text{\u2234} \\quad 0 & \\leqq k \\lt 2^n -1\r\n\\end{align} \\]\r\n\u3053\u308c\u3092\u307f\u305f\u3059\u6574\u6570 \\(k\\) \u306e\u500b\u6570\u304c, \u6c42\u3081\u308b\u500b\u6570\u306a\u306e\u3067\r\n\\[\r\n\\underline{2^n -1} \\ \\text{\u500b}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5186 \\(C : \\ x^2 +y^2 = 1\\) \u4e0a\u306e\u70b9P\u306b\u304a\u3051\u308b\u63a5\u7dda\u3092 \\(l\\) \u3068\u3059\u308b. \u70b9 \\(( 1 , 0 )\\) \u3092\u901a\u308a, \\(l\\) \u3068\u5e73\u884c\u306a\u76f4\u7dda\u3092 \\(m\\) \u3068\u3059\u308b. \u76f4\u7dda \\(m\\) \u3068\u5186 \\(C\\ … \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":[124],"tags":[146,112],"class_list":["post-1213","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2014","tag-hitotsubashi","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1213","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=1213"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1213\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1213"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1213"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}