{"id":133,"date":"2011-11-30T01:14:55","date_gmt":"2011-11-29T16:14:55","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=133"},"modified":"2021-09-14T12:44:43","modified_gmt":"2021-09-14T03:44:43","slug":"iks201002","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/iks201002\/","title":{"rendered":"\u533b\u79d1\u6b6f\u79d1\u59272010\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u5ea7\u6a19\u7a7a\u9593\u306b\u304a\u3044\u3066, \\(8\\) \u70b9 O \\(( 0, 0, 0 )\\) , A \\(( 1, 0, 0 )\\) , B \\(( 0, 1, 0 )\\) , C \\(( 0, 0, 1 )\\) , D \\(( 0, 1, 1 )\\) , E \\(( 1, 0, 1 )\\) , F \\(( 1, 1, 0 )\\) , G \\(( 1, 1, 1 )\\) \u3092\u3068\u308a, \u3053\u306e \\(8\\) \u70b9\u3092\u9802\u70b9\u3068\u3059\u308b\u7acb\u65b9\u4f53\u3092 \\(Q\\) \u3068\u3059\u308b.\r\n\u307e\u305f\u70b9 P \\(( x , y , z )\\) \u3068\u6b63\u306e\u5b9f\u6570 \\(t\\) \u306b\u5bfe\u3057, \\(6\\) \u70b9 \\(( x+t , y , z )\\) , \\(( x-t , y , z )\\) , \\(( x , y+t , z )\\) , \\(( x , y-t , z )\\) , \\(( x , y , z+t )\\) , \\(( x , y , z-t )\\) \u3092\u9802\u70b9\u3068\u3059\u308b\u6b63\u516b\u9762\u4f53\u3092 \\(\\alpha _ t ( \\text{P} )\\) , \u305d\u306e\u5916\u90e8\u306e\u9818\u57df\u3092 \\(\\beta _ t ( \\text{P} )\\) \u3067\u8868\u3059. \u305f\u3060\u3057, \u7acb\u65b9\u4f53\u304a\u3088\u3073\u6b63\u516b\u9762\u4f53\u306f\u5185\u90e8\u306e\u9818\u57df\u3082\u542b\u3080\u3082\u306e\u3068\u3059\u308b. \u3053\u306e\u3068\u304d\u4ee5\u4e0b\u306e\u5404\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(0 \\lt t \\leqq 1\\) \u306e\u3068\u304d, \\(Q \\cap \\beta _ t ( \\text{O} ) \\cap \\beta _ t ( \\text{D} ) \\cap \\beta _ t ( \\text{E} ) \\cap \\beta _ t ( \\text{F} )\\) \u306e\u4f53\u7a4d, \u3059\u306a\u308f\u3061 \\(5\\) \u500b\u306e\u9818\u57df \\(Q\\) , \\(\\beta _ t ( \\text{O} ) , \\beta _ t ( \\text{D} ) , \\beta _ t ( \\text{E} ) , \\beta _ t ( \\text{F} )\\) \u306e\u5171\u901a\u90e8\u5206\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(Q \\cap \\alpha _ 1 ( \\text{O} ) \\cap \\beta _ 1 ( \\text{A} ) \\cap \\beta _ 1 ( \\text{B} ) \\cap \\beta _ 1 ( \\text{C} )\\) \u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(0 \\lt t \\leqq 1\\) \u306e\u3068\u304d\r\n\\[\r\nQ \\cap \\beta _ t ( \\text{O} ) \\cap \\beta _ t ( \\text{A} ) \\cap \\beta _ t ( \\text{B} ) \\cap \\beta _ t ( \\text{C} ) \\cap \\beta _ t ( \\text{D} ) \\cap \\beta _ t ( \\text{E} ) \\cap \\beta _ t ( \\text{F} ) \\cap \\beta _ t ( \\text{G} )\r\n\\]\r\n\u306e\u4f53\u7a4d\u3092 \\(t\\) \u3067\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u4e0e\u3048\u3089\u308c\u305f\u9818\u57df\u306f\u7acb\u65b9\u4f53\u304b\u3089\u4e0b\u56f3\u306e\u56db\u9762\u4f53 \\(R _ t\\) \u3092 \\(4\\) \u3064\u9664\u3044\u305f\u7acb\u4f53\u306a\u306e\u3067, \u6c42\u3081\u308b\u4f53\u7a4d\u306f<\/p>\r\n\"\"\r\n

    \\[\r\n1^3 -4 \\cdot \\dfrac{1}{3} \\left( \\dfrac{1}{2} t^2 \\right) t = \\underline{1 -\\dfrac{2}{3} t^3}\n\\]\r\n

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

    \\(\\alpha _ 1 ( \\text{O} ) \\cap \\alpha _ 1 ( \\text{A} )\\) \u306e\u9818\u57df\u3092 \\(T _ 1\\) \u3068\u3059\u308b.
    \r\n\u3053\u308c\u306f \\(R _ 1\\) \u306b\u5bfe\u3057\u3066\u76f8\u4f3c\u6bd4 \\(\\dfrac{1}{2}\\) \u306e\u7acb\u4f53\u3092 \\(2\\) \u3064\u3064\u306a\u3052\u305f\u7acb\u4f53\u3067\u3042\u308b.<\/p>\r\n\"\"\r\n

    \u3057\u305f\u304c\u3063\u3066\u305d\u306e\u4f53\u7a4d\u306f\r\n\\[\r\n2 \\left( \\dfrac{1}{2} \\right)^3 \\dfrac{1}{6} \\cdot 1^3 = \\dfrac{1}{24}\n\\]\r\n\u4e0e\u3048\u3089\u308c\u305f\u9818\u57df\u306f, \\(R _ 1\\) \u304b\u3089 \\(T _ 1\\) \u3092 \\(3\\) \u3064\u9664\u3044\u305f\u7acb\u4f53\u306a\u306e\u3067, \u6c42\u3081\u308b\u4f53\u7a4d\u306f\r\n\\[\r\n\\dfrac{1}{6} -3 \\cdot \\dfrac{1}{24} = \\underline{\\dfrac{1}{24}}\n\\]\r\n

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

      \r\n

    1. 1*<\/strong>\u3000\\(0 \\lt t \\leqq \\dfrac{1}{2}\\) \u306e\u3068\u304d
      \r\n\u4e0e\u3048\u3089\u308c\u305f\u9818\u57df\u306f\u7acb\u65b9\u4f53\u304b\u3089 \\(R _ t\\) \u3092 \\(8\\) \u3064\u9664\u3044\u305f\u7acb\u4f53\u306a\u306e\u3067, \u6c42\u3081\u308b\u4f53\u7a4d\u306f\r\n\\[\r\n1^3 -8 \\cdot \\dfrac{1}{3} \\left( \\dfrac{1}{2} t^2 \\right) t = 1 -\\dfrac{4}{3} t^3\n\\]<\/li>\r\n

    2. 2*<\/strong>\u3000\\(\\dfrac{1}{2} \\lt t \\leqq 1\\) \u306e\u3068\u304d
      \r\n\\(\\alpha _ t ( \\text{O} ) \\cap \\alpha _ t ( \\text{A} )\\) \u306e\u9818\u57df\u3092 \\(T _ t\\) \u3068\u3059\u308b.
      \r\n\u3053\u308c\u306f \\(T _ 1\\) \u306b\u5bfe\u3057\u3066\u76f8\u4f3c\u6bd4 \\(2t -1\\) \u306e\u7acb\u4f53\u3067\u3042\u308b.
      \r\n\u3057\u305f\u304c\u3063\u3066, \u305d\u306e\u4f53\u7a4d\u306f\r\n\\[\r\n\\dfrac{1}{24} (2t-1)^3\n\\]\r\n\u4e0e\u3048\u3089\u308c\u305f\u9818\u57df\u306f\u7acb\u65b9\u4f53\u304b\u3089 \\(R _ t\\) \u3092 \\(8\\) \u3064\u9664\u304d, \u91cd\u8907\u3057\u3066\u9664\u3044\u305f\u90e8\u5206, \u3059\u306a\u308f\u3061 \\(T _ t\\) \u3092 \\(12\\) \u500b\u3092\u52a0\u3048\u305f\u7acb\u4f53\u306a\u306e\u3067, \u6c42\u3081\u308b\u4f53\u7a4d\u306f\r\n\\[\\begin{align}\r\n1^3 & -8 \\cdot \\dfrac{1}{3} \\left( \\dfrac{1}{2} t^2 \\right) t +12 \\cdot \\dfrac{1}{24} (2t-1)^3 \\\\\r\n& = 1 -\\dfrac{4}{3} t^3 +\\dfrac{1}{2} (2t-1)^3\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n

      1*<\/strong> 2*<\/strong> \u3088\u308a\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} 1 -\\dfrac{4}{3} t^3 & \\left( \\ 0 \\lt t \\leqq \\dfrac{1}{2} \\text{\u306e\u3068\u304d} \\right) \\\\ 1 -\\dfrac{4}{3} t^3 +\\dfrac{1}{2} (2t-1)^3 & \\left( \\ \\dfrac{1}{2} \\lt t \\leqq 1 \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right. }\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u7a7a\u9593\u306b\u304a\u3044\u3066, \\(8\\) \u70b9 O \\(( 0, 0, 0 )\\) , A \\(( 1, 0, 0 )\\) , B \\(( 0, 1, 0 )\\) , C \\(( 0, 0, 1 )\\) , D \\(( 0, 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":[28],"tags":[145,14],"class_list":["post-133","post","type-post","status-publish","format-standard","hentry","category-ikashika_2010","tag-ikashika","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/133","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=133"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/133\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}