{"id":915,"date":"2013-08-31T21:56:59","date_gmt":"2013-08-31T12:56:59","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=915"},"modified":"2021-09-30T00:04:01","modified_gmt":"2021-09-29T15:04:01","slug":"kbr201303","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr201303\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2013\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\\(xyz\\) \u7a7a\u9593\u306b\u304a\u3044\u3066, \u70b9 \\(A (1,0,0)\\) , \\(B (0,1,0)\\) , \\(C (0,0,1)\\) \u3092\u901a\u308b\u5e73\u9762\u4e0a\u306b\u3042\u308a, \u6b63\u4e09\u89d2\u5f62 \\(ABC\\) \u306b\u5185\u63a5\u3059\u308b\u5186\u677f \\(D\\) \u3068\u3059\u308b.\r\n\u5186\u677f \\(D\\) \u306e\u4e2d\u5fc3\u3092 \\(P\\) , \u5186\u677f \\(D\\) \u3068\u8fba \\(AB\\) \u306e\u63a5\u70b9\u3092 \\(Q\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u70b9 \\(P\\) \u3068\u70b9 \\(Q\\) \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u5186\u677f \\(D\\) \u304c\u5e73\u9762 \\(z = t\\) \u3068\u5171\u6709\u70b9\u3092\u3082\u3064 \\(t\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u5186\u677f \\(D\\) \u3068\u5e73\u9762 \\(z = t\\) \u306e\u5171\u901a\u90e8\u5206\u304c\u7dda\u5206\u3067\u3042\u308b\u3068\u304d, \u305d\u306e\u7dda\u5206\u306e\u9577\u3055\u3092 \\(t\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  4. (4)<\/strong>\u3000\u5186\u677f \\(D\\) \u3092 \\(z\\) \u8ef8\u306e\u307e\u308f\u308a\u306b\u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u7acb\u4f53\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n\"tsukuba_r_2013_03_01\"\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

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

    \\(\\triangle ABC \\) \u306f\u6b63\u4e09\u89d2\u5f62\u306a\u306e\u3067, \u5185\u5fc3\u306f\u91cd\u5fc3\u306b\u4e00\u81f4\u3059\u308b\u306e\u3067\r\n\\[\r\nP \\ \\underline{\\left( \\dfrac{1}{3} , \\dfrac{1}{3} , \\dfrac{1}{3} \\right)}\r\n\\]\r\n\u540c\u3058\u7406\u7531\u3088\u308a, \\(Q\\) \u306f \\(AB\\) \u306e\u4e2d\u70b9\u3060\u304b\u3089\r\n\\[\r\nQ \\ \\underline{\\left( \\dfrac{1}{2} , \\dfrac{1}{2} , 0 \\right)}\r\n\\]\r\n

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

    \\(D\\) \u306b\u542b\u307e\u308c\u308b\u70b9\u306e \\(z\\) \u5ea7\u6a19\u306e\u3068\u308b\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.<\/p>\r\n\"tsukuba_r_2013_03_02\"\r\n

    \u4e0a\u56f3\u306e\u3088\u3046\u306b, \\(CQ\\) \u3068 \\(D\\) \u306e\u5171\u6709\u70b9\u3092 \\(R\\) \u3068\u304a\u304f\u3068, \u70b9 \\(R\\) \u3067 \\(z\\) \u5ea7\u6a19\u304c\u6700\u5927\u3068\u306a\u308b.
    \r\n(1)<\/strong> \u306e\u7d50\u679c\u3082\u7528\u3044\u308c\u3070\r\n\\[\r\n\\overrightarrow{PR} = -\\overrightarrow{PQ} = \\left( -\\dfrac{1}{6} , -\\dfrac{1}{6} , \\dfrac{1}{3} \\right) \\quad ... [1]\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\nR \\ \\left( \\dfrac{1}{6} , \\dfrac{1}{6} , \\dfrac{2}{3} \\right)\r\n\\]\r\n\u307e\u305f, \\(z\\) \u5ea7\u6a19\u304c\u6700\u5c0f\u306b\u306a\u308b\u306e\u306f, \u70b9 \\(Q\\) \u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u5024\u306e\u7bc4\u56f2\u306f\r\n\\[\r\n\\underline{0 \\leqq t \\leqq \\dfrac{2}{3}}\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n\"tsukuba_r_2013_03_03\"\r\n

    \u4e0a\u56f3\u306e\u3088\u3046\u306b, \u5e73\u9762 \\(z = t\\) \u3068 \\(D\\) \u3068\u306e\u4ea4\u7dda\u4e0a\u306e\u70b9\u3092 \\(S , T , T'\\) \u3068\u304a\u304f.
    \r\n[1] \u3088\u308a, \\(D\\) \u306e\u534a\u5f84 \\(r\\) \u306f\r\n\\[\r\nr = \\dfrac{1}{6} \\sqrt{1^2+1^2+2^2} = \\dfrac{\\sqrt{6}}{6}\r\n\\]\r\n\\(S , P\\) \u306f\u3068\u3082\u306b, \\(QC\\) \u4e0a\u306e\u70b9\u306a\u306e\u3067 \\(z\\) \u5ea7\u6a19\u306b\u7740\u76ee\u3059\u308c\u3070\r\n\\[\r\nPS = \\dfrac{\\left| \\frac{1}{3} -t \\right|}{\\frac{1}{3}} PQ = | 1-3t | r\r\n\\]\r\n\u3086\u3048\u306b\r\n\\[\\begin{align}\r\nST & = \\sqrt{\\text{PT}^2 -\\text{PS}^2} \\\\\r\n& = r \\sqrt{1 -( 1-3t )^2} \\\\\r\n& = \\dfrac{\\sqrt{2t(2-3t)}}{2}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u7dda\u5206\u306e\u9577\u3055\u306f\r\n\\[\r\nTT' = 2 ST = \\underline{\\sqrt{2t(2-3t)}}\r\n\\]\r\n

    (4)<\/strong><\/p>\r\n\"tsukuba_r_2013_03_04\"\r\n

    \\(O' \\ ( 0 , 0 , t )\\) \u3068\u304a\u304f\u3068, \\(\\triangle O'ST\\) \u306f\u76f4\u89d2\u4e09\u89d2\u5f62\u3067\u3042\u308b.
    \r\n\u306a\u306e\u3067, \u56de\u8ee2\u4f53\u306e\u5e73\u9762 \\(z = t \\ \\left( 0 \\leqq t \\leqq \\dfrac{2}{3} \\right)\\) \u306b\u3088\u308b\u65ad\u9762\u306e\u9762\u7a4d \\(S(t)\\) \u306f, \u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u7528\u3044\u3066\r\n\\[\\begin{align}\r\nS(t) & = \\pi \\left( O'T^2 -O'S^2 \\right) \\\\\r\n& = \\pi ST^2 = \\dfrac{\\pi t(2-3t)}{2}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u56de\u8ee2\u4f53\u306e\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\\begin{align}\r\nV & = \\displaystyle\\int _ {0}^{\\frac{2}{3}} S(t) \\, dt \\\\\r\n& = \\dfrac{1}{2} \\pi \\left[ t^2 -t^3 \\right] _ {0}^{\\frac{2}{3}} \\\\\r\n& = \\underline{\\dfrac{2 \\pi}{27}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xyz\\) \u7a7a\u9593\u306b\u304a\u3044\u3066, \u70b9 \\(A (1,0,0)\\) , \\(B (0,1,0)\\) , \\(C (0,0,1)\\) \u3092\u901a\u308b\u5e73\u9762\u4e0a\u306b\u3042\u308a, \u6b63\u4e09\u89d2\u5f62 \\(ABC\\) \u306b\u5185\u63a5\u3059\u308b\u5186\u677f \\(D\\) \u3068\u3059\u308b. \u5186\u677f … \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":[102],"tags":[144,111],"class_list":["post-915","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2013","tag-tsukuba_r","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/915","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=915"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/915\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=915"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}