{"id":420,"date":"2012-06-04T23:42:08","date_gmt":"2012-06-04T14:42:08","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=420"},"modified":"2021-11-04T09:12:04","modified_gmt":"2021-11-04T00:12:04","slug":"htb201204","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201204\/","title":{"rendered":"\u4e00\u6a4b\u59272012\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(xyz\\) \u7a7a\u9593\u5185\u306e\u5e73\u9762 \\(z = 2\\) \u4e0a\u306b\u70b9 P \u304c\u3042\u308a, \u5e73\u9762 \\(z = 1\\) \u4e0a\u306b\u70b9 Q \u304c\u3042\u308b.\r\n\u76f4\u7dda PQ \u3068 \\(xy\\) \u5e73\u9762\u306e\u4ea4\u70b9\u3092 R \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000P \\((0,0,2)\\) \u3068\u3059\u308b. \u70b9 Q \u304c\u5e73\u9762 \\(z = 1\\) \u4e0a\u3067\u70b9 \\((0,0,1)\\) \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 \\(1\\) \u306e\u5186\u5468\u4e0a\u3092\u52d5\u304f\u3068\u304d, \u70b9 R \u306e\u8ecc\u8de1\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u5e73\u9762 \\(z = 1\\) \u4e0a\u306b \\(4\\) \u70b9 A \\((1,1,1)\\) , B \\((1,-1,1)\\) , C \\((-1,-1,1)\\) , D \\((-1,1,1)\\) \u3092\u3068\u308b. \u70b9 P \u304c\u5e73\u9762 \\(z = 2\\) \u4e0a\u3067\u70b9 \\((0,0,2)\\) \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 \\(1\\) \u306e\u5186\u5468\u4e0a\u3092\u52d5\u304d, \u70b9 Q \u304c\u6b63\u65b9\u5f62 ABCD \u306e\u5468\u4e0a\u3092\u52d5\u304f\u3068\u304d, \u70b9 R \u304c\u52d5\u304d\u3046\u308b\u9818\u57df\u3092 \\(xy\\) \u5e73\u9762\u4e0a\u306b\u56f3\u793a\u3057, \u305d\u306e\u9762\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    Q \\(( \\cos \\theta , \\sin \\theta , 1 )\\) \u3068\u304a\u3051\u308b\u306e\u3067\r\n\\[\r\n\\overrightarrow{\\text{PQ}} = ( \\cos \\theta , \\sin \\theta , -1 )\r\n\\]\r\nR \u306f \\(xy\\) \u5e73\u9762\u4e0a\u306b\u3042\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{OR}} & = \\overrightarrow{\\text{OP}} +2 \\overrightarrow{\\text{PQ}} \\\\\r\n& = ( 2 \\cos \\theta , 2 \\sin \\theta , 0 )\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u65b9\u7a0b\u5f0f\u306f\r\n\\[\r\n\\underline{x^2 +y^2 =4}\r\n\\]\r\n

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

    Q \\((a,b,1)\\) \u306b\u56fa\u5b9a\u3057\u3066\u8003\u3048\u308b.
    \r\nP \\(( \\cos \\theta , \\sin \\theta , 2 )\\) \u3068\u304a\u3051\u308b\u306e\u3067\r\n\\[\r\n\\overrightarrow{\\text{PQ}} = ( a -\\cos \\theta , b -\\sin \\theta , -1 )\r\n\\]\r\nR \u306f \\(xy\\) \u5e73\u9762\u4e0a\u306b\u3042\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{OR}} & = \\overrightarrow{\\text{OP}} +2 \\overrightarrow{\\text{PQ}} \\\\\r\n& = ( 2a -\\cos \\theta , 2b -\\sin \\theta , 0 )\r\n\\end{align}\\]\r\n\u3053\u3053\u3067 Q \u3092\u52d5\u304b\u305b\u3070, R \u306f \\(xy\\) \u5e73\u9762\u4e0a\u306e\u70b9 \\(( 2a , 2b )\\) , \u3064\u307e\u308a, \\(4\\) \u70b9 \\((2,2) , (-2,2) , (-2,-2) , (2,-2)\\) \u3092\u9802\u70b9\u3068\u3059\u308b\u6b63\u65b9\u5f62\u4e0a\u306e\u70b9\u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 \\(1\\) \u306e\u5186\u5468\u4e0a\u3092\u52d5\u304f.
    \r\n\u3088\u3063\u3066, R \u306e\u52d5\u304d\u3046\u308b\u9818\u57df\u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09.<\/p>\r\n\"hitotsubashi_2012_04_01\"\r\n

    \u307e\u305f, \u3053\u306e\u9762\u7a4d \\(S\\) \u306f\r\n\\[\r\nS = 3^2 \\pi -4 \\cdot 1^1 +1^2 \\pi = \\underline{28 +\\pi}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xyz\\) \u7a7a\u9593\u5185\u306e\u5e73\u9762 \\(z = 2\\) \u4e0a\u306b\u70b9 P \u304c\u3042\u308a, \u5e73\u9762 \\(z = 1\\) \u4e0a\u306b\u70b9 Q \u304c\u3042\u308b. \u76f4\u7dda PQ \u3068 \\(xy\\) \u5e73\u9762\u306e\u4ea4\u70b9\u3092 R \u3068\u3059\u308b. (1)\u3000P \\((0,0,2)\\) \u3068\u3059\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":[67],"tags":[146,68],"class_list":["post-420","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2012","tag-hitotsubashi","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/420","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=420"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/420\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}