{"id":150,"date":"2011-12-01T17:43:28","date_gmt":"2011-12-01T08:43:28","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=150"},"modified":"2021-10-29T08:41:51","modified_gmt":"2021-10-28T23:41:51","slug":"wsr201002","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201002\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52010\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\\(xy\\) \u5e73\u9762\u4e0a\u306e\u70b9 \\(( x _ 1 , y _ 1 )\\) \u306b\u5bfe\u3057\u3066, \u70b9 \\(( x _ 2 , y _ 2 ) , ( x _ 3 , y _ 3 ) , \\cdots\\) \u3092\u6b21\u306e\u5f0f\u3067\u9806\u306b\u5b9a\u3081\u308b.\r\n\\[\r\n\\left( \\begin{array}{c} x _ {n+1} \\\\ y _ {n+1} \\end{array} \\right) = \\left\\{ \\begin{array}{ll} \\left( \\begin{array}{cc} 0 & -1 \\\\ 1 & 0 \\end{array} \\right) \\left( \\begin{array}{c} x _ n \\\\ y _ n \\end{array} \\right) & ( \\ y _ n \\geqq 0 \\text{\u306e\u3068\u304d} ) \\\\ \\left( \\begin{array}{cc} -1 & 0 \\\\ 0 & -1 \\end{array} \\right) \\left( \\begin{array}{c} x _ n \\\\ y _ n \\end{array} \\right) & ( \\ y _ n \\lt 0 \\text{\u306e\u3068\u304d} ) \\end{array} \\right.\r\n\\]\r\n\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(( x _ 1 , y _ 1 ) = ( -1 , 2 )\\) \u306e\u3068\u304d, \\(( x _ 3 , y _ 3 )\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(( x _ 1 , y _ 1 ) = ( 1 , 0 )\\) \u306e\u3068\u304d, \\(( x _ 5 , y _ 5 )\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(x _ 1 \\gt 0\\) \u304b\u3064 \\(y _ 1 \\gt 0\\) \u306e\u3068\u304d, \\(( x _ 4 , y _ 4 ) = ( x _ 1 , y _ 1 )\\) \u3068\u306a\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  4. (4)<\/strong>\u3000\\(( x _ n , y _ n ) = ( x _ 1 , y _ 1 )\\) \u3068\u306a\u308b \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570 \\(n\\) \u304c\u5b58\u5728\u3057\u306a\u3044\u3068\u304d, \u70b9 \\(( x _ 1 , y _ 1 )\\) \u306f\u3069\u306e\u3088\u3046\u306a\u7bc4\u56f2\u306b\u3042\u308b\u304b\u3092\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\[\\begin{align}\r\n\\left( \\begin{array}{c} x _ {n+1} \\\\ y _ {n+1} \\end{array} \\right) & = \\left\\{ \\begin{array}{l} \\left( \\begin{array}{cc} 0 & -1 \\\\ 1 & 0 \\end{array} \\right) \\left( \\begin{array}{c} x _ n \\\\ y _ n \\end{array} \\right) \\\\ \\left( \\begin{array}{cc} -1 & 0 \\\\ 0 & -1 \\end{array} \\right) \\left( \\begin{array}{c} x _ n \\\\ y _ n \\end{array} \\right) \\end{array} \\right. \\\\\r\n& = \\left\\{ \\begin{array}{ll} \\left( \\begin{array}{c} -y _ n \\\\ x _ n \\end{array} \\right) & ( \\ y _ n \\geqq 0 \\text{\u306e\u3068\u304d} ) \\\\ \\left( \\begin{array}{c} -x _ n \\\\ -y _ n \\end{array} \\right) & ( \\ y _ n \\lt 0 \\text{\u306e\u3068\u304d} ) \\end{array} \\right.\r\n\\end{align}\\]\r\n\u3053\u308c\u3092\u7528\u3044\u3066\u8a08\u7b97\u3059\u308c\u3070\u3088\u3044.
    \r\n\\(y _ 1 \\geqq 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 2 , y _ 2 ) = ( -y _ 1 , x _ 1 ) = ( -2 , -1 )\r\n\\]\r\n\\(y _ 2 \\lt 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 3 , y _ 3 ) = ( -x _ 2 , -y _ 2 ) = \\underline{( 2 , 1 )}\r\n\\]\r\n

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

    \\(y _ 1 \\geqq 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 2 , y _ 2 ) = ( -y _ 1 , x _ 1 ) = ( 0 , 1 )\r\n\\]\r\n\\(y _ 2 \\geqq 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 3 , y _ 3 ) = ( -y _ 2 , x _ 2 ) = ( -1 , 0 )\r\n\\]\r\n\\(y _ 3 \\lt 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 4 , y _ 4 ) = ( -x _ 3 , -y _ 3 ) = ( 0 , -1 )\r\n\\]\r\n\\(y _ 4 \\lt 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 5 , y _ 5 ) = ( -x _ 4 , -y _ 4 ) = \\underline{( 0 , 1 )}\r\n\\]\r\n

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

    \\(y _ 1 \\geqq 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 2 , y _ 2 ) = ( -y _ 1 , x _ 1 )\r\n\\]\r\n\\(y _ 2 \\geqq 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 3 , y _ 3 ) = ( -y _ 2 , x _ 2 ) = ( -x _ 1 , -y _ 1 )\r\n\\]\r\n\\(y _ 3 \\lt 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 4 , y _ 4 ) = ( -x _ 3 , -y _ 3 ) = \\underline{( x _ 1 , y _ 1 )}\r\n\\]\r\n

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

      \r\n

    1. 1*<\/strong>\u3000\\(x _ 1 \\gt 0\\) \u304b\u3064 \\(y _ 1 \\gt 0\\) \u306e\u3068\u304d
      \r\n(3)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \\(n = 3k+1 \\ ( k = 1 , 2 , \\cdots )\\) \u304c\u5b58\u5728\u3059\u308b.
      \r\n\u3055\u3089\u306b, \u3053\u306e\u3068\u304d \\(( x _ 2 , y _ 2 )\\) , \\(( x _ 3 , y _ 3 )\\) \u306b\u3042\u305f\u308b\u70b9\u304c, \\(( x _ 1 , y _ 1 )\\) \u3068\u306a\u3063\u305f\u5834\u5408\u3082\u540c\u69d8\u306e\u3053\u3068\u304c\u751f\u3058\u308b.
      \r\n\u3057\u305f\u304c\u3063\u3066, \u300c \\(x _ 1 \\lt 0\\) \u304b\u3064 \\(y _ 1 \\gt 0\\) \u300d , \u300c \\(x _ 1 \\lt 0\\) \u304b\u3064 \\(y _ 1 \\lt 0\\) \u300d \u306e\u3068\u304d\u3082, \\(n = 3k+1 \\ ( k = 1 , 2 , \\cdots )\\) \u304c\u5b58\u5728\u3059\u308b.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(x _ 1 \\gt 0\\) \u304b\u3064 \\(y _ 1 \\lt 0\\) \u306e\u3068\u304d
      \r\n\\(y _ 1 \\lt 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 2 , y _ 2 ) = ( -x _ 1 , -y _ 1 )\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066 \\(x _ 2 \\lt 0\\) \u304b\u3064 \\(y _ 2 \\lt 0\\) \u3068\u306a\u308b\u305f\u3081\r\n\\[\\begin{gather}\r\n( x _ {3k+2} , y _ {3k+2} ) = ( x _ 2 , y _ 2 ) , \\ ( x _ {3k+3} , y _ {3k+3} ) = ( x _ 3 , y _ 3 ) , \\\\\r\n( x _ {3k+4} , y _ {3k+4} ) = ( x _ 4 , y _ 4 ) \\quad ( k = 1 , 2 , \\cdots )\r\n\\end{gather}\\]\r\n\u3068\u306a\u308a, \u6761\u4ef6\u3092\u307f\u305f\u3059 \\(n\\) \u306f\u5b58\u5728\u3057\u306a\u3044.<\/p><\/li>\r\n

    3. 3*<\/strong>\u3000\\(x _ 1 = 0\\) \u304b\u3064 \\(y _ 1 \\gt 0\\) \u306e\u3068\u304d
      \r\n\\(y _ 1 \\geqq 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 2 , y _ 2 ) = ( -y _ 1 , 0 )\r\n\\]\r\n\\(y _ 2 \\geqq 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 3 , y _ 3 ) = ( -y _ 2 , x _ 2 ) = ( 0 , -y _ 1 )\r\n\\]\r\n\\(y _ 3 \\lt 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 4 , y _ 4 ) = ( -x _ 3 , -y _ 3 ) = ( 0 , y _ 1 ) = ( x _ 1 , y _ 1 )\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(n\\) \u304c\u5b58\u5728\u3059\u308b.
      \r\n\u3055\u3089\u306b, \u3053\u306e\u3068\u304d \\(( x _ 2 , y _ 2 )\\) , \\(( x _ 3 , y _ 3 )\\) \u306b\u3042\u305f\u308b\u70b9\u304c, \\(( x _ 1 , y _ 1 )\\) \u3068\u306a\u3063\u305f\u5834\u5408\u3082\u540c\u69d8\u306e\u3053\u3068\u304c\u751f\u3058\u308b.
      \r\n\u3086\u3048\u306b, \u300c \\(x _ 1 \\lt 0\\) \u304b\u3064 \\(y _ 1 = 0\\) \u300d , \u300c \\(x _ 1 = 0\\) \u304b\u3064 \\(y _ 1 \\lt 0\\) \u300d \u306e\u3068\u304d\u3082, \\(n = 3k+1 \\ ( k = 1 , 2 , \\cdots )\\) \u304c\u5b58\u5728\u3059\u308b.<\/p><\/li>\r\n

    4. 4*<\/strong>\u3000\\(x _ 1 \\gt 0\\) \u304b\u3064 \\(y _ 1 = 0\\) \u306e\u3068\u304d
      \r\n\\(y _ 1 \\geqq 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 2 , y _ 2 ) = ( 0 , x _ 1 )\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066 \\(x _ 2 = 0\\) \u304b\u3064 \\(y _ 2 \\gt 0\\) \u3068\u306a\u308b\u305f\u3081\r\n\\[\\begin{gather}\r\n( x _ {3k+2} , y _ {3k+2} ) = ( x _ 2 , y _ 2 ) , \\ ( x _ {3k+3} , y _ {3k+3} ) = ( x _ 3 , y _ 3 ) , \\\\\r\n( x _ {3k+4} , y _ {3k+4} ) = ( x _ 4 , y _ 4 ) \\quad ( k = 1 , 2 , \\cdots )\r\n\\end{gather}\\]\r\n\u3068\u306a\u308a, \u6761\u4ef6\u3092\u307f\u305f\u3059 \\(n\\) \u306f\u5b58\u5728\u3057\u306a\u3044.<\/p><\/li>\r\n

    5. 5*<\/strong>\u3000\\(x _ 1 = y _ 1 = 0\\) \u306e\u3068\u304d
      \r\n\\(y _ 1 \\geqq 0\\) \u306a\u306e\u3067\r\n\\[\r\n( x _ 2 , y _ 2 ) = ( 0 , 0 ) = ( x _ 1 , y _ 1 )\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(n\\) \u304c\u5b58\u5728\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a, 1*<\/strong> \uff5e 5*<\/strong> \u3088\u308a, \u6c42\u3081\u308b\u7bc4\u56f2\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u70b9\u7dda\u5883\u754c, \u25cb\u306f\u542b\u307e\u306a\u3044\uff09.<\/p>\r\n\"waseda2010_02_01\"\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u306e\u70b9 \\(( x _ 1 , y _ 1 )\\) \u306b\u5bfe\u3057\u3066, \u70b9 \\(( x _ 2 , y _ 2 ) , ( x _ 3 , y _ 3 ) , \\cdots\\) \u3092\u6b21\u306e\u5f0f\u3067\u9806\u306b\u5b9a\u3081\u308b. \\[ \\ … \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":[37],"tags":[147,14],"class_list":["post-150","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2010","tag-waseda_r","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/150","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=150"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/150\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}