{"id":1283,"date":"2015-09-22T22:41:29","date_gmt":"2015-09-22T13:41:29","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1283"},"modified":"2021-09-16T09:43:18","modified_gmt":"2021-09-16T00:43:18","slug":"thr201501","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201501\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2015\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(xy\\) \u5e73\u9762\u306b\u304a\u3044\u3066, \u6b21\u306e\u5f0f\u304c\u8868\u3059\u66f2\u7dda\u3092 \\(C\\) \u3068\u3059\u308b.\r\n\\[\r\nx^2 +4y^2 = 1 , \\ x \\gt 0 , \\ y \\gt 0\r\n\\]\r\nP \u3092 \\(C\\) \u4e0a\u306e\u70b9\u3068\u3059\u308b. P \u3067 \\(C\\) \u306b\u63a5\u3059\u308b\u76f4\u7dda\u3092 \\(l\\) \u3068\u3057, P \u3092\u901a\u308a \\(l\\) \u3068\u5782\u76f4\u306a\u76f4\u7dda\u3092 \\(m\\) \u3068\u3057\u3066, \\(x\\) \u8ef8\u3068 \\(y\\) \u8ef8\u3068 \\(m\\) \u3067\u56f2\u307e\u308c\u3066\u3067\u304d\u308b\u4e09\u89d2\u5f62\u306e\u9762\u7a4d\u3092 \\(S\\) \u3068\u3059\u308b.\r\nP \u304c \\(C\\) \u4e0a\u306e\u70b9\u5168\u4f53\u3092\u52d5\u304f\u3068\u304d, \\(S\\) \u306e\u6700\u5927\u5024\u3068\u305d\u306e\u3068\u304d\u306e P \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p>P \\(\\left( \\cos \\theta , \\dfrac{1}{2} \\sin \\theta \\right) \\ \\left( 0 \\lt \\theta \\lt \\dfrac{\\pi}{2} \\right)\\) \u3068\u8868\u305b\u308b.<br \/>\r\n\\(\\ell\\) \u306f P \u306b\u304a\u3051\u308b \\(C\\) \u306e\u63a5\u7dda\u306a\u306e\u3067, \\(\\ell\\) \u306e\u5f0f\u306f\r\n\\[\r\nx \\cos \\theta +2y \\sin \\theta = 1 \\ .\r\n\\]\r\n\\(m\\) \u306f \\(\\ell\\) \u3068\u5782\u76f4\u3067, P \u3092\u901a\u308b\u306e\u3067, \\(m\\) \u306e\u5f0f\u306f\r\n\\[\\begin{gather}\r\n2 ( x -\\cos \\theta ) \\sin \\theta -\\left( y -\\dfrac{1}{2} \\sin \\theta \\right) \\cos \\theta = 0 \\\\\r\n\\text{\u2234} \\quad 2x \\sin \\theta -y \\cos \\theta = \\dfrac{3}{2} \\cos \\theta \\sin \\theta \\ .\r\n\\end{gather}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(m\\) \u306e \\(x\\) \u5207\u7247, \\(y\\) \u5207\u7247\u306f\u305d\u308c\u305e\u308c\r\n\\[\r\n\\dfrac{3}{4} \\sin \\theta , \\quad -\\dfrac{3}{2} \\cos \\theta \\ .\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nS & = \\dfrac{1}{2} \\cdot \\dfrac{3}{4} \\sin \\theta \\cdot \\dfrac{3}{2} \\cos \\theta \\\\\r\n& = \\dfrac{9}{16} \\sin 2 \\theta \\leqq \\dfrac{9}{16} \\ .\r\n\\end{align}\\]\r\n\u7b49\u53f7\u6210\u7acb\u306f, \\(2 \\theta = \\dfrac{\\pi}{2}\\) \u3059\u306a\u308f\u3061 \\(\\theta = \\dfrac{\\pi}{4}\\) \u306e\u3068\u304d.<br \/>\r\n\u3088\u3063\u3066, \\(S\\) \u306f P \u304c \\(\\underline{\\left( \\dfrac{1}{\\sqrt{2}} , \\dfrac{\\sqrt{2}}{4} \\right)}\\) \u306e\u3068\u304d, \u6700\u5927\u5024 \\(\\underline{\\dfrac{9}{16}}\\) \u3092\u3068\u308b.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u306b\u304a\u3044\u3066, \u6b21\u306e\u5f0f\u304c\u8868\u3059\u66f2\u7dda\u3092 \\(C\\) \u3068\u3059\u308b. \\[ x^2 +4y^2 = 1 , \\ x \\gt 0 , \\ y \\gt 0 \\] P \u3092 \\(C\\) \u4e0a\u306e\u70b9\u3068\u3059\u308b. P \u3067 \\(C\\) \u306b\u63a5 &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/thr201501\/\">\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":[131],"tags":[148,137],"class_list":["post-1283","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2015","tag-tohoku_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1283","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=1283"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1283\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1283"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1283"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1283"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}