{"id":1969,"date":"2021-11-16T08:12:55","date_gmt":"2021-11-15T23:12:55","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1969"},"modified":"2021-11-16T08:12:55","modified_gmt":"2021-11-15T23:12:55","slug":"kyr202101","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr202101\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2021\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\n<p>\u6b21\u306e\u5404\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>\u554f 1<\/strong>\u3000\\(xyz\\) \u7a7a\u9593\u306e \\(3\\) \u70b9 A \\(( 1 , 0 , 0 )\\) , B \\(( 0 , -1 , 0 )\\) , C \\(( 0 , 0 , 2 )\\) , \u3092\u901a\u308b\u5e73\u9762 \\(\\alpha\\) \u306b\u95a2\u3057\u3066\u70b9 P \\(( 1, 1, 1 )\\) \u3068\u5bfe\u79f0\u306a\u70b9 Q \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.\r\n\u305f\u3060\u3057, \u70b9 Q \u304c\u5e73\u9762 \\(\\alpha\\) \u306b\u95a2\u3057\u3066 P \u3068\u5bfe\u79f0\u3067\u3042\u308b\u3068\u306f, \u7dda\u5206 PQ \u306e\u4e2d\u70b9 M \u304c\u5e73\u9762 \\(\\alpha\\) \u4e0a\u306b\u3042\u308a, \u76f4\u7dda PM \u304c P \u304b\u3089\u5e73\u9762 \\(\\alpha\\) \u306b\u4e0b\u308d\u3057\u305f\u5782\u7dda\u3068\u306a\u308b\u3053\u3068\u3067\u3042\u308b.<\/p><\/li>\r\n<li><p><strong>\u554f 2<\/strong>\u3000\u8d64\u7389, \u767d\u7389, \u9752\u7389, \u9ec4\u7389\u304c \\(1\\) \u500b\u305a\u3064\u5165\u3063\u305f\u888b\u304c\u3042\u308b.\r\n\u3088\u304f\u304b\u304d\u307e\u305c\u305f\u5f8c\u306b\u888b\u304b\u3089\u7389\u3092 \\(1\\) \u500b\u53d6\u308a\u51fa\u3057, \u305d\u306e\u7389\u306e\u8272\u3092\u8a18\u9332\u3057\u3066\u304b\u3089\u888b\u306b\u623b\u3059.\r\n\u3053\u306e\u8a66\u884c\u3092\u7e70\u308a\u8fd4\u3059\u3068\u304d, \\(n\\) \u56de\u76ee\u306e\u8a66\u884c\u3067\u521d\u3081\u3066\u8d64\u7389\u304c\u53d6\u308a\u51fa\u3055\u308c\u3066 \\(4\\) \u7a2e\u985e\u5168\u3066\u306e\u8272\u304c\u8a18\u9332\u6e08\u307f\u3068\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.\r\n\u305f\u3060\u3057, \\(n\\) \u306f \\(4\\) \u4ee5\u4e0a\u306e\u6574\u6570\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>\u554f 1<\/strong><\/p>\r\n<p>Q \\(( X , Y , Z )\\) \u3068\u304a\u304f.<br \/>\r\n\u5e73\u9762 \\(\\alpha\\) \u306e\u5f0f\u306f \\(x -y +\\dfrac{z}{2} = 1\\) \u3067, PQ \u306e\u4e2d\u70b9 M \\(\\left( \\dfrac{X+1}{2} , \\dfrac{Y+1}{2} , \\dfrac{Z+1}{2} \\right)\\)\u306f \\(\\alpha\\) \u4e0a\u306b\u3042\u308b\u306e\u3067\r\n\\[\\begin{align}\r\n\\dfrac{X+1}{2} -\\dfrac{Y+1}{2} +\\dfrac{Z+1}{4} & = 1 \\\\\r\n2x +2 -2y -2 +z +1 & = 4 \\\\\r\n\\text{\u2234} \\quad 2x -2y +z & = 3 \\quad ... [1]\r\n\\end{align}\\]\r\n\\(\\text{PQ} \\perp \\alpha\\) \u306a\u306e\u3067, \\(\\overrightarrow{\\text{PQ}} \\perp \\overrightarrow{\\text{AB}}\\) , \\(\\overrightarrow{\\text{PQ}} \\perp \\overrightarrow{\\text{AC}}\\) \u3067\u3042\u308b\u304b\u3089\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{PQ}} \\cdot \\overrightarrow{\\text{AB}} & = \\left( \\begin{array}{c} X-1 \\\\ Y-1\\\\ Z-1 \\end{array} \\right) \\cdot \\left( \\begin{array}{c} -1 \\\\ -1\\\\ 0 \\end{array} \\right) \\\\\r\n& = -x +1 -y +1 = 0 \\\\\r\n& \\text{\u2234} \\quad x +y = 2 \\quad ... [2] \\ , \\\\\r\n\\overrightarrow{\\text{PQ}} \\cdot \\overrightarrow{\\text{AC}} & = \\left( \\begin{array}{c} X-1 \\\\ Y-1\\\\ Z-1 \\end{array} \\right) \\cdot \\left( \\begin{array}{c} -1 \\\\ 0 \\\\ 2 \\end{array} \\right) \\\\\r\n& = -X +1 +2Z -2 = 0 \\\\\r\n& \\text{\u2234} \\quad X -2Z = -1 \\quad ... [3]\r\n\\end{align}\\]\r\n[2] [3] \u3088\u308a, \\(Y = 2-X\\) , \\(Z = \\dfrac{X+1}{2}\\) \u3067, [1] \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\\begin{align}\r\n2X -4 +2X +\\dfrac{X+1}{2} & = 3 \\\\\r\n9X & = 13 \\\\\r\n\\text{\u2234} \\quad X & = \\dfrac{13}{9}\r\n\\end{align}\\]\r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\nY & = 2 -\\dfrac{13}{9} = \\dfrac{5}{9} \\\\\r\nZ & = \\dfrac{1}{2} \\left( \\dfrac{13}{9} +1 \\right) = \\dfrac{11}{9}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, Q \u306e\u5ea7\u6a19\u306f\r\n\\[\r\n\\underline{\\left( \\dfrac{13}{9} , \\dfrac{5}{9} , \\dfrac{11}{9} \\right)}\r\n\\]\r\n<p><strong>\u554f 2<\/strong><\/p>\r\n<p>\\(n\\) \u56de\u76ee\u307e\u3067\u306e\u7389\u306e\u53d6\u308a\u51fa\u3057\u65b9\u306f, \\(4^n\\) \u901a\u308a.<br \/>\r\n\\(n-1\\) \u56de\u76ee\u307e\u3067\u306f, \u4ed6\u306e \\(3\\) \u8272\u306e\u7389\u304c\u3059\u3079\u3066\u51fa\u3066, \\(n\\) \u56de\u76ee\u306b\u521d\u3081\u3066\u8d64\u7389\u304c\u51fa\u308b\u5834\u5408\u306e\u6570\u3092\u8003\u3048\u308b.<br \/>\r\n\\(n-1\\) \u56de\u76ee\u307e\u3067\u306e\u7389\u306e\u53d6\u308a\u51fa\u3057\u65b9\u306b\u3064\u3044\u3066<\/p>\r\n<ul>\r\n<li><p>\\(1\\) \u8272\u3060\u3051\u51fa\u308b\u5834\u5408<br \/>\r\n\u8272\u306e\u9078\u3073\u65b9\u3060\u3051\u3092\u8003\u3048\u3066\r\n\\[\r\n3 \\ \\text{\u901a\u308a}\r\n\\]<\/li>\r\n<li><p>\\(2\\) \u8272\u3060\u3051\u51fa\u308b\u5834\u5408<br \/>\r\n\u8272\u306e\u9078\u3073\u65b9\u304c \\({} _ {3} \\text{C}{} _ {2} = 3\\) \u901a\u308a, \u7389\u306e\u51fa\u65b9\u304c \\(2^{n-1}\\) \u901a\u308a\u3042\u308a, \u3053\u308c\u306b\u306f \\(1\\) \u8272\u3060\u3051\u51fa\u308b\u5834\u5408\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u306e\u3067\r\n\\[\r\n3 \\left( 2^{n-1} -2 \\right) = 3 \\cdot 2^{n-1} -6 \\ \\text{\u901a\u308a}\r\n\\]<\/li>\r\n<li><p>\\(3\\) \u8272\u51fa\u308b\u3068\u3082\u5834\u5408<br \/>\r\n\u7389\u306e\u51fa\u65b9\u304c \\(3^{n-1}\\) \u901a\u308a\u3042\u308a, \u3053\u308c\u306b\u306f \\(2\\) \u8272\u3060\u3051\u304c\u51fa\u308b\u5834\u5408, \\(1\\) \u8272\u3060\u3051\u304c\u51fa\u308b\u5834\u5408\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u306e\u3067\r\n\\[\r\n3^{n-1} -\\left( 3 \\cdot 2^{n-1} -6 \\right) -3 = 3^{n-1} -3 \\cdot 2^{n-1} +3 \\ \\text{\u901a\u308a}\r\n\\]<\/li>\r\n<\/ul>\r\n<p>\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\\begin{align}\r\n\\underline{\\dfrac{3^{n-1} -3 \\cdot 2^{n-1} +3}{4^n}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u6b21\u306e\u5404\u554f\u306b\u7b54\u3048\u3088. \u554f 1\u3000\\(xyz\\) \u7a7a\u9593\u306e \\(3\\) \u70b9 A \\(( 1 , 0 , 0 )\\) , B \\(( 0 , -1 , 0 )\\) , C \\(( 0 , 0 , 2 )\\) , \u3092\u901a\u308b\u5e73\u9762 \\(\\ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr202101\/\">\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":[171],"tags":[140,165],"class_list":["post-1969","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2021","tag-kyoto_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1969","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=1969"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1969\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1969"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1969"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}