{"id":249,"date":"2012-01-07T12:00:56","date_gmt":"2012-01-07T03:00:56","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=249"},"modified":"2021-03-16T17:04:23","modified_gmt":"2021-03-16T08:04:23","slug":"tkr200803","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr200803\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2008\uff1a\u7b2c3\u554f"},"content":{"rendered":"<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u6b63\u516b\u9762\u4f53\u306e\u3072\u3068\u3064\u306e\u9762\u3092\u4e0b\u306b\u3057\u3066\u6c34\u5e73\u306a\u53f0\u306e\u4e0a\u306b\u7f6e\u304f. \u3053\u306e\u516b\u9762\u4f53\u3092\u771f\u4e0a\u304b\u3089\u898b\u305f\u56f3\uff08\u5e73\u9762\u56f3\uff09\u3092\u63cf\u3051.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u6b63\u516b\u9762\u4f53\u306e\u4e92\u3044\u306b\u5e73\u884c\u306a \\(2\\) \u3064\u306e\u9762\u3092\u3068\u308a, \u305d\u308c\u305e\u308c\u306e\u9762\u306e\u91cd\u5fc3\u3092 \\(\\text{G} {} _ 1 , \\text{G} {} _ 2\\) \u3068\u3059\u308b.\r\n\\(\\text{G} {} _ 1 , \\text{G} {} _ 2\\) \u3092\u901a\u308b\u76f4\u7dda\u3092\u8ef8\u3068\u3057\u3066\u3053\u306e\u516b\u9762\u4f53\u3092 \\(1\\) \u56de\u8ee2\u3055\u305b\u3066\u3067\u304d\u308b\u7acb\u4f53\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.\r\n\u305f\u3060\u3057\u516b\u9762\u4f53\u306f\u5185\u90e8\u3082\u542b\u3080\u3082\u306e\u3068\u3057, \u5404\u8fba\u306e\u9577\u3055\u306f \\(1\\) \u3068\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tokyo_r_2008_03_01.png\" alt=\"\" title=\"tokyo_r_2008_03_01\" class=\"aligncenter size-full\" \/><\/p>\r\n<p><strong>(2)<\/strong>\r\n<p>\\(h\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3057\u3066, \\(\\text{G} _ 1 , \\text{G} _ 2\\) \u304c \\(z\\) \u8ef8\u4e0a\u306b\u306a\u308b\u3088\u3046\u306b, \u6b63\u516b\u9762\u4f53\u306e \\(6\\) \u3064\u306e\u9802\u70b9\u3092\r\n\\[\\begin{align}\r\n\\text{A} \\left( \\dfrac{\\sqrt{3}}{3} , 0 , h \\right) , & \\quad \\text{B} \\left( -\\dfrac{\\sqrt{3}}{6} , \\dfrac{1}{2} , h \\right) , \\quad \\text{C} \\left( -\\dfrac{\\sqrt{3}}{6} , -\\dfrac{1}{2} , h \\right) , \\\\\r\n\\text{D} \\left( -\\dfrac{\\sqrt{3}}{3} , 0 , -h \\right) , & \\quad \\text{E} \\left( \\dfrac{\\sqrt{3}}{6} , \\dfrac{1}{2} , -h \\right) , \\quad \\text{F} \\left( \\dfrac{\\sqrt{3}}{6} , -\\dfrac{1}{2} , -h \\right)\r\n\\end{align}\\]\r\n\u3068\u304a\u304f.\r\n\\(\\text{AE} =1\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\left( \\dfrac{\\sqrt{3}}{6} \\right)^2 + & \\left( \\dfrac{1}{2} \\right)^2 +(2h)^2 =1 \\\\\r\n4h^2 & =\\dfrac{2}{3} \\\\\r\n\\text{\u2234} \\quad h & =\\dfrac{\\sqrt{6}}{6}\r\n\\end{align}\\]\r\n\u5bfe\u79f0\u6027\u304b\u3089 \\(z \\geqq 0\\) \u306e\u9818\u57df\u306b\u3064\u3044\u3066\u8003\u3048\u308c\u3070\u3088\u3044.<br \/>\r\n\u5e73\u9762 \\(z = t \\quad ( 0 \\leqq t \\leqq h )\\) \u3068 AE \u306e\u4ea4\u70b9\u3092 P \u3068\u304a\u3051\u3070, P \u306f AE \u3092 \\((h-t) : (h+t)\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3067\u3042\u308b.<br \/>\r\n\u307e\u305f, AE \u306e\u4e2d\u70b9\u3092 M \u3068\u304a\u3044\u3066, \u5e73\u9762 \\(z=t\\) \u3067\u306e\u6b63\u516b\u9762\u4f53\u306e\u5207\u308a\u53e3\u3092 \\(z\\) \u8ef8\u65b9\u5411\u304b\u3089\u898b\u308b\u3068, \u4e0b\u56f3\u659c\u7dda\u90e8\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tokyo_r_2008_03_02.png\" alt=\"\" title=\"tokyo_r_2008_03_02\" class=\"aligncenter size-full\" \/>\r\n<p>\\[\\begin{align}\r\n\\text{AE} & = \\dfrac{\\sqrt{3}}{3} , \\quad \\text{OM} =\\dfrac{1}{2} , \\\\\r\n\\text{PM} & = \\dfrac{t}{2h} \\text{AE} = \\dfrac{\\sqrt{2} t}{2}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\n\\text{OP}^2 =\\left( \\dfrac{1}{2} \\right)^2 +\\left( \\dfrac{\\sqrt{2} t}{2} \\right)^2 =\\dfrac{2 t^2+1}{4}\r\n\\]\r\n\u3053\u306e\u56f3\u5f62\u3092 \\(z\\) \u8ef8\u3092\u4e2d\u5fc3\u306b\u56de\u8ee2\u3055\u305b\u3066\u3067\u304d\u308b\u5186\u306e\u9762\u7a4d \\(S(t)\\) \u3068\u3059\u308b\u3068\r\n\\[\r\nS(t) =\\pi \\text{OP}^2 =\\dfrac{\\pi ( 2t^2+1 )}{4}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\\begin{align}\r\nV & = 2 \\displaystyle\\int _ 0^{\\frac{\\sqrt{6}}{6}} S(t) dt \\\\\r\n& = \\dfrac{\\pi}{2} \\displaystyle\\int _ 0^{\\frac{\\sqrt{6}}{6}} \\, (2t^2+1) dt \\\\\r\n& = \\dfrac{\\pi}{2} \\left[ \\dfrac{2t^3}{3} +t \\right] _ 0^{\\frac{\\sqrt{6}}{6}} \\\\\r\n& =\\dfrac{\\pi}{2} \\left( \\dfrac{\\sqrt{6}}{54} +\\dfrac{\\sqrt{6}}{6} \\right) \\\\\r\n& = \\underline{\\dfrac{5 \\sqrt{6} \\pi}{54}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"(1)\u3000\u6b63\u516b\u9762\u4f53\u306e\u3072\u3068\u3064\u306e\u9762\u3092\u4e0b\u306b\u3057\u3066\u6c34\u5e73\u306a\u53f0\u306e\u4e0a\u306b\u7f6e\u304f. \u3053\u306e\u516b\u9762\u4f53\u3092\u771f\u4e0a\u304b\u3089\u898b\u305f\u56f3\uff08\u5e73\u9762\u56f3\uff09\u3092\u63cf\u3051. (2)\u3000\u6b63\u516b\u9762\u4f53\u306e\u4e92\u3044\u306b\u5e73\u884c\u306a \\(2\\) \u3064\u306e\u9762\u3092\u3068\u308a, \u305d\u308c\u305e\u308c\u306e\u9762\u306e\u91cd\u5fc3\u3092 \\(\\text{G} {} _  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkr200803\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[17],"tags":[139,16],"class_list":["post-249","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2008","tag-tokyo_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/249","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=249"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/249\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=249"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=249"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=249"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}