{"id":1403,"date":"2017-03-10T21:46:11","date_gmt":"2017-03-10T12:46:11","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1403"},"modified":"2021-09-23T22:43:10","modified_gmt":"2021-09-23T13:43:10","slug":"tok201603","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok201603\/","title":{"rendered":"\u6771\u5de5\u59272016\uff1a\u7b2c3\u554f"},"content":{"rendered":"

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\u6c34\u5e73\u306a\u5e73\u9762 \$\\alpha\$ \u306e\u4e0a\u306b\u534a\u5f84 \$r _ 1\$ \u306e\u7403 \$S _ 1\$ \u3068\u534a\u5f84 \$r _ 2\$ \u306e\u7403 \$S _ 2\$ \u304c\u4e57\u3063\u3066\u304a\u308a, \$S _ 1\$ \u3068 \$S _ 2\$ \u306f\u5916\u63a5\u3057\u3066\u3044\u308b.<\/p>\r\n

(1)<\/strong>\u3000\$S _ 1 , S _ 2\$ \u304c \$\\alpha\$ \u3068\u63a5\u3059\u308b\u70b9\u3092\u305d\u308c\u305e\u308c \$\\text{P} _ 1 , \\text{P} _ 2\$ \u3068\u3059\u308b. \u7dda\u5206 \$\\text{P} _ 1 \\text{P} _ 2\$ \u306e\u9577\u3055\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n
(2)<\/strong>\u3000\$\\alpha\$ \u306e\u4e0a\u306b\u4e57\u3063\u3066\u304a\u308a, \$S _ 1\$ \u3068 \$S _ 2\$ \u306e\u4e21\u65b9\u306b\u5916\u63a5\u3057\u3066\u3044\u308b\u7403\u3059\u3079\u3066\u3092\u8003\u3048\u308b. \u305d\u308c\u3089\u306e\u7403\u3068 \$\\alpha\$ \u306e\u63a5\u70b9\u306f, \$1\$ \u3064\u306e\u5186\u306e\u4e0a\u307e\u305f\u306f \$1\$ \u3064\u306e\u76f4\u7dda\u4e0a\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n
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\r\n \u89e3\u7b54\u306f\u3053\u3061\u3089 »<\/a>\r\n <\/p>\r\n <\/div>\r\n
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\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n
(1)<\/strong><\/p>\r\n $\"\"$ \r\n
\$r _ 1 \\neq r _ 2\$ \u306e\u3068\u304d, \$S _ 1 , S _ 2\$ \u306e\u4e2d\u5fc3\u3092\u7d50\u3076\u7dda\u5206\u3092\u659c\u8fba\u3068\u3059\u308b\u76f4\u89d2\u4e09\u89d2\u5f62\u306b\u7740\u76ee\u3057\u3066\r\n\\[\\begin{align}\r\n\\text{P} _ 1 \\text{P} _ 2 & = \\sqrt{( r _ 1 +r _ 2 )^2 -| r _ 1 -r _ 2 |^2} \\\\\r\n& = 2 \\sqrt{r _ 1 r _ 2} \\quad ... [1]\r\n\\end{align}\\]\r\n\$r _ 1 = r _ 2\$ \u306e\u3068\u304d, \$\\text{P} _ 1 \\text{P} _ 2 = 2 r _ 1\$ \u3067\u3042\u308a, [1] \u3067\u6e80\u305f\u3055\u308c\u3066\u3044\u308b.
\r\n\u3088\u3063\u3066\r\n\\[\r\n\\text{P} _ 1 \\text{P} _ 2 = \\underline{2 \\sqrt{r _ 1 r _ 2}}\r\n\\]\r\n
(2)<\/strong><\/p>\r\n
\$S _ 1 , S _ 2\$ \u4e21\u65b9\u306b\u5916\u63a5\u3059\u308b\u5186\u3092 \$S _ 3\$ \u3068\u3057, \$S _ 3\$ \u306e\u534a\u5f84\u3092 \$r _ 3\$ , \$\\alpha\$ \u3068\u306e\u63a5\u70b9\u3092 \$\\text{P} _ 3\$ \u3068\u304a\u304f.
\r\n(1)<\/strong> \u306e\u7d50\u679c\u304b\u3089\r\n\\[\r\n\\text{P} _ 1 \\text{P} _ 3 = 2 \\sqrt{r _ 1 r _ 3} , \\ \\text{P} _ 2 \\text{P} _ 3 = 2 \\sqrt{r _ 2 r _ 3} \\quad ... [2]\r\n\\]\r\n\$\\text{P} _ 1 \\ ( 0, 0 )\$ , \$\\text{P} _ 2 \\ ( 2 \\sqrt{ r _ 1 r _ 2 }, 0 )\$ \u3068\u306a\u308b\u3088\u3046\u306b, \$xy\$ \u5ea7\u6a19\u3092\u5b9a\u3081, \$\\text{P} _ 3 \\ ( X, Y )\$ \u3068\u304a\u304f\u3068, [2] \u3088\u308a\r\n\\[\\begin{align}\r\nX^2 +Y^2 & = 4 r _ 1 r _ 3 \\quad ... [3] \\\\\r\n( X -2 \\sqrt{ r _ 1 r _ 2 } )^2 +Y^2 & = 4 r _ 2 r _ 3 \\quad ... [4]\r\n\\end{align}\\]\r\n
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1*<\/strong>\u3000\$r _ 1 = r _ 2\$ \u306e\u3068\u304d
\r\n\$[3] -[4]\$ \u3088\u308a\r\n\\[\\begin{align}\r\n4 r _ 1 X -4 {r _ 1}^2 & = 0 \\\\\r\n\\text{\u2234} \\quad X & = r _ 1\r\n\\end{align}\\]\r\n\u3053\u308c\u306f, \u76f4\u7dda\u3092\u8868\u3059.<\/p><\/li>\r\n
2*<\/strong>\u3000\$r _ 1 \\neq r _ 2\$ \u306e\u3068\u304d
\r\n\$[3] \\times r _ 2 -[4] \\times r _ 1\$ \u3088\u308a\r\n\\[\\begin{align}\r\nr _ 2 X^2 +r _ 2 Y^2 & = r _ 1 ( X -2 \\sqrt{ r _ 1 r _ 2 } )^2 +r _ 1 Y^2 \\\\\r\n( r _ 2 -r _ 1 ) X^2 +4 r _ 1 \\sqrt{ r _ 1 r _ 2 } X & +( r _ 2 -r _ 1 ) Y^2 = 4 {r _ 1}^2 r _ 2 \\\\\r\n\\left( X +\\dfrac{2 r _ 1 \\sqrt{ r _ 1 r _ 2 }}{r _ 2 -r _ 1} \\right)^2 +Y^2 & = \\dfrac{4 {r _ 1}^2 r _ 2}{r _ 2 -r _ 1} +\\left( \\dfrac{2 r _ 1 \\sqrt{ r _ 1 r _ 2 }}{r _ 2 -r _ 1} \\right)^2 \\\\\r\n\\text{\u2234} \\quad \\left( X +\\dfrac{2 r _ 1 \\sqrt{ r _ 1 r _ 2 }}{r _ 2 -r _ 1} \\right)^2 +Y^2 & = \\left( \\dfrac{2 r _ 1 r _ 2}{r _ 2 -r _ 1} \\right)^2\r\n\\end{align}\\]\r\n\u3053\u308c\u306f, \u5186\u3092\u8868\u3059.<\/p><\/li>\r\n<\/ol>\r\n
\u4ee5\u4e0a\u3088\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n\r\n
\r\n « \u89e3\u7b54\u3092\u96a0\u3059 <\/a>\r\n <\/p>\r\n <\/div>","protected":false},"excerpt":{"rendered":"\u6c34\u5e73\u306a\u5e73\u9762 \$\\alpha\$ \u306e\u4e0a\u306b\u534a\u5f84 \$r _ 1\$ \u306e\u7403 \$S _ 1\$ \u3068\u534a\u5f84 \$r _ 2\$ \u306e\u7403 \$S _ 2\$ \u304c\u4e57\u3063\u3066\u304a\u308a, \$S _ 1\$ \u3068 \$S _ 2\$ \u306f\u5916\u63a5\u3057\u3066\u3044\u308b […]","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":[153],"tags":[141,162],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1403"}],"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=1403"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1403\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1403"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}