{"id":1215,"date":"2015-07-31T23:45:49","date_gmt":"2015-07-31T14:45:49","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1215"},"modified":"2015-07-31T23:45:49","modified_gmt":"2015-07-31T14:45:49","slug":"htb201404","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201404\/","title":{"rendered":"\u4e00\u6a4b\u59272014\uff1a\u7b2c4\u554f"},"content":{"rendered":"\u534a\u5f84 \\(1\\) \u306e\u7403\u304c\u76f4\u5186\u9310\u306b\u5185\u63a5\u3057\u3066\u3044\u308b. \u3053\u306e\u76f4\u5186\u9310\u306e\u5e95\u9762\u306e\u534a\u5f84\u3092 \\(r\\) \u3068\u3057, \u8868\u9762\u7a4d\u3092 \\(S\\) \u3068\u3059\u308b. \r\n<ol>\r\n<li><strong>(1)<\/strong>\u3000\\(S\\) \u3092 \\(r\\) \u3092\u7528\u3044\u3066\u8868\u305b. <\/li>\r\n<li><strong>(2)<\/strong>\u3000\\(S\\) \u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u3088. <\/li>\r\n<\/ol>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n\r\n<strong>(1)<\/strong>\r\n\r\n\u76f4\u5186\u9310\u306e\u6bcd\u7dda\u306e\u9577\u3055\u3092 \\(m\\) \u3068\u304a\u304d, \u9802\u70b9\u3092A, \u5e95\u9762\u306e\u4e2d\u5fc3\u3092C, \u7403\u306e\u4e2d\u5fc3\u3092D\u3068\u3059\u308b.   \r\n\r\n<img decoding=\"async\" src=\"\/nyushi\/wp-content\/uploads\/htb20140401.svg\" alt=\"htb20140401\" class=\"aligncenter size-full wp-image-1216\" \/>\r\n\r\n\u4e0a\u56f3\u306e\u3088\u3046\u306a\u76f4\u5186\u9310\u306e\u8ef8\u3092\u542b\u3080\u5207\u308a\u53e3\u3092\u8003\u3048\u308c\u3070\r\n\\[ \\begin{align}\r\n\\text{AC} & = \\sqrt{m^2 -r^2} \\\\\r\n\\text{AE} & = m-r\r\n\\end{align} \\]\r\n\\(\\triangle \\text{ABC} \\sim \\triangle \\text{ADE}\\) \u306a\u306e\u3067\r\n\\[ \\begin{align}\r\n1 : (m-r) & = r : \\sqrt{m^2 -r^2} \\\\\r\nr^2 (m-r)^2 & = m^2 -r^2 \\\\\r\nr^2 (m-r) & = m+r \\quad ( \\ \\text{\u2235} \\ m \\gt r \\ ) \\\\\r\n( r^2 -1 ) m & = r ( r^2 +1 ) \\\\\r\n\\text{\u2234} \\quad m & = \\dfrac{r ( r^2 +1 )}{r^2 -1}\r\n\\end{align} \\]\r\n\u3088\u3063\u3066\r\n\\[ \\begin{align}\r\nS & = \\pi r^2 +\\pi r m \\\\\r\n& = \\pi r^2 \\left\\{ 1 +\\dfrac{r^2 +1}{r^2 -1} \\right\\} \\\\\r\n& = \\underline{\\dfrac{2 \\pi r^4}{r^2 -1}}\r\n\\end{align} \\]\r\n\r\n<strong>(2)<\/strong>\r\n\r\n\\(r \\gt 1\\) \u306a\u306e\u3067, \u76f8\u52a0\u76f8\u4e57\u5e73\u5747\u306e\u95a2\u4fc2\u3092\u7528\u3044\u308c\u3070\r\n\\[ \\begin{align}\r\nS & = 2 \\pi \\left( r^2 +1 +\\dfrac{1}{r^2 -1} \\right) \\\\\r\n& = 2 \\pi \\left( r^2 -1 +\\dfrac{1}{r^2 -1} +2 \\right) \\\\\r\n& \\geqq 2 \\pi \\left( 2 \\sqrt{( r^2 -1 ) \\cdot \\dfrac{1}{r^2 -1}} +2 \\right) \\\\\r\n& = 8 \\pi\r\n\\end{align} \\]\r\n\u7b49\u53f7\u6210\u7acb\u306f\r\n\\[ \\begin{align}\r\nr^2 -1 & = \\dfrac{1}{r^2 -1} \\\\\r\n\\text{\u2234} \\quad r & = \\sqrt{2}\r\n\\end{align} \\]\r\n\u306e\u3068\u304d.   \r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6700\u5927\u5024\u306f\r\n\\[\r\n\\underline{8 \\pi}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u534a\u5f84 \\(1\\) \u306e\u7403\u304c\u76f4\u5186\u9310\u306b\u5185\u63a5\u3057\u3066\u3044\u308b. \u3053\u306e\u76f4\u5186\u9310\u306e\u5e95\u9762\u306e\u534a\u5f84\u3092 \\(r\\) \u3068\u3057, \u8868\u9762\u7a4d\u3092 \\(S\\) \u3068\u3059\u308b. (1)\u3000\\(S\\) \u3092 \\(r\\) \u3092\u7528\u3044\u3066\u8868\u305b. (2)\u3000\\(S\\) \u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u3088.","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":[124],"tags":[146,112],"class_list":["post-1215","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2014","tag-hitotsubashi","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1215","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=1215"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1215\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1215"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1215"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1215"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}