{"id":1139,"date":"2015-07-02T10:14:21","date_gmt":"2015-07-02T01:14:21","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1139"},"modified":"2021-09-15T07:20:14","modified_gmt":"2021-09-14T22:20:14","slug":"ngr201401","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr201401\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2014\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u7a7a\u9593\u5185\u306b\u3042\u308b\u534a\u5f84 \\(1\\) \u306e\u7403\uff08\u5185\u90e8\u3092\u542b\u3080\uff09\u3092 \\(B\\) \u3068\u3059\u308b. \u76f4\u7dda \\(\\ell\\) \u3068 \\(B\\) \u304c\u4ea4\u308f\u3063\u3066\u304a\u308a, \u305d\u306e\u4ea4\u308f\u308a\u306f\u9577\u3055 \\(\\sqrt{3}\\) \u306e\u7dda\u5206\u3067\u3042\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(B\\) \u306e\u4e2d\u5fc3\u3068 \\(\\ell\\) \u3068\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\ell\\) \u306e\u307e\u308f\u308a\u306b \\(B\\) \u3092 \\(1\\) \u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u7acb\u4f53\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong><\/p>\r\n\"ngr20140101\"\r\n

    \\(B\\) \u306e\u4e2d\u5fc3\u3092 A, \\(\\ell\\) \u3068 \\(B\\) \u306e\u4ea4\u308f\u308a\u306e\u4e21\u7aef\u3092 P , Q , A \u304b\u3089 \\(\\ell\\) \u306b\u4e0b\u308d\u3057\u305f\u5782\u7dda\u306e\u8db3\u3092H\u3068\u304a\u304f.
    \r\nA , P , Q \u3092\u542b\u3080 \\(B\\) \u306e\u65ad\u9762 \\(C\\) \u3092\u8003\u3048\u308c\u3070, H \u306f PQ \u306e\u4e2d\u70b9\u306a\u306e\u3067, \u6c42\u3081\u308b\u8ddd\u96e2 \\(h\\) \u306f\r\n\\[\\begin{align}\r\nh & = \\sqrt{\\text{AP}^2 -\\text{PH}^2} \\\\\r\n& = \\sqrt{1^2 -\\left( \\dfrac{\\sqrt{3}}{2} \\right)^2} = \\underline{\\dfrac{1}{2}} \\ .\r\n\\end{align}\\]\r\n

    (2)<\/strong><\/p>\r\n\"ngr20140102\"\r\n

    \\(\\ell\\) \u3068\u5782\u76f4\u306a \\(B\\) \u306e\u65ad\u9762\u3092\u8003\u3048\u308b\u3068, \\(\\ell\\) \u3068\u306e\u8ddd\u96e2\u304c\u6700\u5927, \u307e\u305f\u306f\u6700\u5c0f\u3067\u3042\u308b\u70b9\u306f, \u3044\u305a\u308c\u3082 \\(\\ell\\) \u3068 \\(A\\) \u3092\u542b\u3080\u65ad\u9762 \\(C\\) \u4e0a\u306b\u5b58\u5728\u3059\u308b.
    \r\n\u3057\u305f\u304c\u3063\u3066, \\(C\\) \u3092 \\(\\ell\\) \u306e\u307e\u308f\u308a\u306b \\(1\\) \u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u7acb\u4f53\u306e\u4f53\u7a4d\u3092\u6c42\u3081\u308c\u3070\u3088\u3044.<\/p>\r\n

    \"ngr20140103\"<\/p>\r\n

    \\(\\ell\\) \u3092 \\(x\\) \u8ef8\u3068\u3057, A \\(\\left( 0 , \\dfrac{1}{2} \\right)\\) \u3068\u306a\u308b\u3088\u3046\u306b \\(xy\\) \u5ea7\u6a19\u3092\u304a\u304f\u3068, \\(C\\) \u306e\u5f0f\u306f\r\n\\[\\begin{gather}\r\nx^2 +\\left( y -\\dfrac{1}{2} \\right)^2 = 1 \\\\\r\n\\text{\u2234} \\quad y = \\dfrac{1}{2} \\pm \\sqrt{1 -x^2} \\ .\r\n\\end{gather}\\]\r\n\\(C\\) \u306e\u3046\u3061, \\(y \\geqq \\dfrac{1}{2}\\) , \\(y \\lt \\dfrac{1}{2}\\) \u306e\u90e8\u5206\u306e\u5f0f\u3092\u305d\u308c\u305e\u308c \\(y _ {+} , y _ {-}\\) \u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\ny _ {+} & = \\dfrac{1}{2} + \\sqrt{1 -x^2} , \\\\\r\ny _ {-} & = \\dfrac{1}{2} - \\sqrt{1 -x^2} \\ .\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u6c42\u3081\u308b\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\\begin{align}\r\nV & = 2 \\pi \\displaystyle\\int _ 0^1 {y _ {+}}^2 \\, dx -2 \\pi \\displaystyle\\int _ {\\frac{\\sqrt{3}}{2}}^1 {y _ {-}}^2 \\, dx \\\\\r\n& = 2 \\pi \\displaystyle\\int _ 0^1 \\left( \\dfrac{5}{4} -x^2 +\\sqrt{1 -x^2} \\right) \\, dx \\\\\r\n& \\qquad -2 \\pi \\displaystyle\\int _ {\\frac{\\sqrt{3}}{2}}^1 \\left( \\dfrac{5}{4} -x^2 -\\sqrt{1 -x^2} \\right) \\, dx \\\\\r\n& = 2 \\pi \\left[ \\dfrac{5x}{4} -\\dfrac{x^3}{3} \\right] _ 0^1 +2 \\pi \\underline{\\displaystyle\\int _ 0^1 \\sqrt{1 -x^2} \\, dx} _ {[1]} \\\\\r\n& \\qquad -2 \\pi \\left[ \\dfrac{5x}{4} +\\dfrac{x^3}{3} \\right] _ {\\frac{\\sqrt{3}}{2}}^1 +2 \\pi \\underline{\\displaystyle\\int _ {\\frac{\\sqrt{3}}{2}}^1 \\sqrt{1 -x^2} \\, dx} _ {[2]} \\ .\r\n\\end{align}\\]\r\n\u3053\u3053\u3067, [1] \u306f\u534a\u5f84 \\(1\\) \u306e\u56db\u5206\u5186, [2] \u306f\u4e0b\u56f3\u659c\u7dda\u90e8\u306e\u9762\u7a4d\u3092\u793a\u3059\u306e\u3067<\/p>\r\n\"ngr20140104\"\r\n

    \\[\\begin{align}\r\nV & = 2 \\pi \\left( \\dfrac{5 \\sqrt{3}}{8} -\\dfrac{\\sqrt{3}}{8} \\right) +2 \\pi \\cdot \\dfrac{\\pi}{4} \\\\\r\n& \\qquad +2 \\pi \\left( \\dfrac{1}{2} \\cdot 1^2 \\cdot \\dfrac{\\pi}{6} -\\dfrac{1}{2} \\cdot \\dfrac{\\sqrt{3}}{2} \\cdot \\dfrac{1}{2} \\right) \\\\\r\n& = \\sqrt{3} \\pi +\\dfrac{\\pi^2}{2} +\\dfrac{\\pi^2}{6} -\\dfrac{\\sqrt{3} \\pi}{4} \\\\\r\n& = \\underline{\\dfrac{2 \\pi^2}{3} +\\dfrac{3 \\sqrt{3} \\pi}{4}} \\ .\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u7a7a\u9593\u5185\u306b\u3042\u308b\u534a\u5f84 \\(1\\) \u306e\u7403\uff08\u5185\u90e8\u3092\u542b\u3080\uff09\u3092 \\(B\\) \u3068\u3059\u308b. \u76f4\u7dda \\(\\ell\\) \u3068 \\(B\\) \u304c\u4ea4\u308f\u3063\u3066\u304a\u308a, \u305d\u306e\u4ea4\u308f\u308a\u306f\u9577\u3055 \\(\\sqrt{3}\\) \u306e\u7dda\u5206\u3067\u3042\u308b. (1)\u3000\\(B\\) \u306e\u4e2d\u5fc3\u3068 … \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":[119],"tags":[143,112],"class_list":["post-1139","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2014","tag-nagoya_r","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1139","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=1139"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1139\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1139"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1139"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}