{"id":292,"date":"2012-02-05T20:56:00","date_gmt":"2012-02-05T11:56:00","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=292"},"modified":"2021-09-14T15:49:56","modified_gmt":"2021-09-14T06:49:56","slug":"iks200801","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/iks200801\/","title":{"rendered":"\u533b\u79d1\u6b6f\u79d1\u59272008\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u5ea7\u6a19\u7a7a\u9593\u5185\u306b \\(5\\) \u70b9\r\n\\[\r\n\\text{P} \\ (0,0,h) , \\quad \\text{Q} \\ (t,0,0) , \\quad \\text{R} \\ (0,t,0) , \\quad \\text{S} \\ (-t,0,0) , \\quad \\text{T} \\ (0,-t,0)\n\\]\r\n\u3092\u3068\u308b. \u3053\u3053\u3067 \\(t , h\\) \u306f \\(0 \\lt t \\lt 1 , \\ h \\gt 0\\) \u3092\u6e80\u305f\u3059\u5b9f\u6570\u3067\u3042\u308b. \u307e\u305f\u70b9 A \\((1,1,0)\\) \u3068\u70b9 Q \u3092\u7d50\u3076\u7dda\u5206\u306e\u9577\u3055\u306f\u7dda\u5206 PQ \u306e\u9577\u3055\u3068\u7b49\u3057\u3044\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\u56db\u89d2\u9318 PQRST \u306e\u8868\u9762\u7a4d\u3092 \\(t\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(h\\) \u3092 \\(t\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(t\\) \u304c \\(0 \\lt t \\lt 1\\) \u306e\u7bc4\u56f2\u3067\u5909\u5316\u3059\u308b\u3068\u304d, \u56db\u89d2\u9318 PQRST \u306e\u4f53\u7a4d\u306e\u6700\u5927\u5024\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

    \\(\\text{AQ} = \\text{PQ} = \\text{PR} = \\text{PS} = \\text{PT}\\) \u306a\u306e\u3067, \u56db\u89d2\u9318 PQRST \u306e\u5c55\u958b\u56f3\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n\"\"\r\n

    \u3088\u3063\u3066, \u6c42\u3081\u308b\u8868\u9762\u7a4d \\(S\\) \u306f\r\n\\[\r\nS = 2^2 -4 \\cdot \\dfrac{1}{2} (1-t) \\cdot 2 = \\underline{4t}\n\\]\r\n

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

    \\(\\text{AQ} = \\text{PQ}\\) \u3088\u308a\r\n\\[\\begin{align}\r\n(1-t)^2 +1^2 = t^2 +h^2 \\\\\r\n\\text{\u2234} \\quad h = \\underline{\\sqrt{2(1-t)}}\n\\end{align}\\]\r\n

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

    \u56db\u89d2\u9318\u306e\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\r\nV = \\dfrac{1}{3} \\cdot \\dfrac{1}{2} \\cdot (2t)^2 \\cdot \\sqrt{2(1-t)} = \\dfrac{2\\sqrt{2}}{3} \\sqrt{t^4 -t^5}\n\\]\r\n\\(f(t) = t^4-t^5\\) \u3068\u304a\u3051\u3070\r\n\\[\r\nf'(t) = 4t^3 -5t^4 =t^3 (4 -5t)\n\\]\r\n\\(0 \\lt t \\lt 1\\) \u306b\u304a\u3044\u3066 \\(f'(t) = 0\\) \u3092\u89e3\u304f\u3068\r\n\\[\r\nt = \\dfrac{4}{5}\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(t)\\) \u306e\u5897\u6e1b\u8868\u306f\u4e0b\u306e\u3068\u304a\u308a.\r\n\\[\r\n\\begin{array}{c|ccccc} t & (0) & \\cdots & \\dfrac{4}{5} & \\cdots & (1) \\\\ \\hline f'(t) & & + & 0 & - & \\\\ \\hline f(t) & & \\nearrow & \\text{\u6700\u5927} & \\searrow & \\end{array}\n\\]\r\n\u306a\u306e\u3067, \\(f(t)\\) \u306e\u6700\u5927\u5024\u306f\r\n\\[\r\nf \\left( \\dfrac{4}{5} \\right) = \\dfrac{4^4}{5^4} \\left( 1 -\\dfrac{4}{5} \\right) = \\dfrac{4^4}{5^5}\n\\]\r\n\u3088\u3063\u3066, \\(V\\) \u306e\u6700\u5927\u5024\u306f\r\n\\[\\begin{align}\r\n\\dfrac{2 \\sqrt{2}}{3} \\sqrt{f \\left( \\dfrac{4}{5} \\right)} & = \\dfrac{2 \\sqrt{2}}{3} \\cdot \\dfrac{4^2}{5^2 \\sqrt{5}} \\\\\r\n& = \\underline{\\dfrac{32 \\sqrt{10}}{375}}\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u7a7a\u9593\u5185\u306b \\(5\\) \u70b9 \\[ \\text{P} \\ (0,0,h) , \\quad \\text{Q} \\ (t,0,0) , \\quad \\text{R} \\ (0,t,0) , \\quad \\text{S} \\ … \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":[52],"tags":[145,16],"class_list":["post-292","post","type-post","status-publish","format-standard","hentry","category-ikashika_2008","tag-ikashika","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/292","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=292"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/292\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}