{"id":268,"date":"2012-01-21T23:06:25","date_gmt":"2012-01-21T14:06:25","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=268"},"modified":"2021-03-24T09:36:02","modified_gmt":"2021-03-24T00:36:02","slug":"kyr200805","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr200805\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb\u4e592008\uff1a\u7b2c5\u554f"},"content":{"rendered":"<hr \/>\n<p>\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b\u5e95\u9762\u306e\u534a\u5f84\u304c \\(2\\) , \u9ad8\u3055\u304c \\(1\\) \u306e\u5186\u67f1 \\(C\\) \u3092\u8003\u3048\u308b.\r\n\\[\r\nC = \\left\\{ (x,y,z) | x^2+y^2 \\leqq 4 , \\ 0 \\leqq z \\leqq 1 \\right\\}\r\n\\]\r\n\\(xy\\) \u5e73\u9762\u4e0a\u306e\u76f4\u7dda \\(y=1\\) \u3092\u542b\u307f, \\(xy\\) \u5e73\u9762\u3068 \\(45^{\\circ}\\) \u306e\u89d2\u3092\u306a\u3059\u5e73\u9762\u306e\u3046\u3061, \u70b9 \\((0, 2, 1)\\) \u3092\u901a\u308b\u3082\u306e\u3092 \\(H\\) \u3068\u3059\u308b.\r\n\u5186\u67f1 \\(C\\) \u3092\u5e73\u9762 \\(H\\) \u3067 \\(2\\) \u3064\u306b\u5206\u3051\u308b\u3068\u304d, \u70b9 \\((0, 2, 0)\\) \u3092\u542b\u3080\u65b9\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>\u4f53\u7a4d\u3092\u6c42\u3081\u308b\u7acb\u4f53 \\(D\\) \u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyoto_r1_2008_05_01.png\" alt=\"\" title=\"kyoto_r1_2008_05_01\" class=\"aligncenter size-full\" \/>\r\n<p>\\(D\\) \u306e, \u5e73\u9762 \\(x =t \\ \\left( -\\sqrt{3} \\lt t \\lt \\sqrt{3} \\right)\\) \u306b\u3088\u308b\u65ad\u9762\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyoto_r1_2008_05_02.png\" alt=\"\" title=\"kyoto_r1_2008_05_02\" class=\"aligncenter size-full\" \/>\r\n<p>\u3053\u306e\u9762\u7a4d\u3092 \\(S(t)\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nS(t) & = \\dfrac{1}{2} \\left( \\sqrt{4-t^2} -1 \\right)^2 \\\\\r\n& = \\dfrac{5 -t^2}{2} -\\sqrt{4-t^2}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6c42\u3081\u308b\u4f53\u7a4d \\(V\\) \u306f, \u5bfe\u79f0\u6027\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\nV & = 2 \\displaystyle\\int _ 0^{\\sqrt{3}} S(t) \\, dt \\\\\r\n& = \\underline{\\displaystyle\\int _ 0^{\\sqrt{3}} (5-t^2) \\, dt} _ {[1]} -2 \\underline{\\displaystyle\\int _ 0^{\\sqrt{3}} \\sqrt{4-t^2} \\, dt} _ {[2]}\r\n\\end{align}\\]\r\n\u3053\u3053\u3067\r\n\\[\r\n[1] = \\left[ 5t -\\dfrac{t^3}{3} \\right] _ 0^{\\sqrt{3}} =4 \\sqrt{3}\r\n\\]\r\n\u307e\u305f, [2] \u306f\u4e0b\u56f3\u659c\u7dda\u90e8\u306e\u9762\u7a4d\u3092\u8868\u3059\u306e\u3067<\/p>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/kyoto_r1_2008_05_03.png\" alt=\"\" title=\"kyoto_r1_2008_05_03\" class=\"aligncenter size-full\" \/>\r\n<p>\\[\\begin{align}\r\n[2] & = \\dfrac{1}{2} \\cdot \\sqrt{3} \\cdot 1 +\\dfrac{1}{2} \\cdot 2^2 \\cdot \\dfrac{\\pi}{3} \\\\\r\n& = \\dfrac{\\sqrt{3}}{2} +\\dfrac{2 \\pi}{3}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\nV & = 4 \\sqrt{3} -2 \\left( \\dfrac{\\sqrt{3}}{2} +\\dfrac{2 \\pi}{3} \\right) \\\\\r\n& =\\underline{3\\sqrt{3} -\\dfrac{4 \\pi}{3}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b\u5e95\u9762\u306e\u534a\u5f84\u304c \\(2\\) , \u9ad8\u3055\u304c \\(1\\) \u306e\u5186\u67f1 \\(C\\) \u3092\u8003\u3048\u308b. \\[ C = \\left\\{ (x,y,z) | x^2+y^2 \\leqq 4 , \\ 0 \\leqq z \\leqq &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr200805\/\">\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":[49],"tags":[140,16],"class_list":["post-268","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2008","tag-kyoto_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/268","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=268"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/268\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=268"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}