{"id":3230,"date":"2025-09-22T00:51:27","date_gmt":"2025-09-21T15:51:27","guid":{"rendered":"https:\/\/math-friend.com\/?p=3230"},"modified":"2025-09-22T12:53:52","modified_gmt":"2025-09-22T03:53:52","slug":"%e3%80%90%e6%9d%b1%e4%ba%ac%e5%a4%a7%e5%ad%a6%e5%85%a5%e8%a9%a6%e3%80%912%e3%81%a4%e3%81%ae%e5%86%86%e3%81%ab%e5%86%85%e6%8e%a5%e3%83%bb%e5%a4%96%e6%8e%a5%e3%81%99%e3%82%8b%e5%86%86%e3%81%ae%e4%b8%ad","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=3230","title":{"rendered":"\u3010\u6771\u4eac\u5927\u5b66\u5165\u8a66\u30112\u3064\u306e\u5186\u306b\u5185\u63a5\u30fb\u5916\u63a5\u3059\u308b\u5186\u306e\u4e2d\u5fc3\u3068\u6700\u5927\u306e\u9ad8\u3055(2009)"},"content":{"rendered":"\n

\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n

\u5ea7\u6a19\u5e73\u9762\u306b\u304a\u3044\u3066\u539f\u70b9\u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84\\(2\\)\u306e\u5186\u3092\\(C_1\\), \u70b9\\((1,0)\\)\u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84\\(1\\)\u306e\u5186\u3092\\(C_2\\)\u3068\u3059\u308b. \u307e\u305f, \u70b9\\((a,b)\\)\u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84\\(t\\)\u306e\u5186\\(C_3\\)\u304c, \\(C_1\\)\u306b\u5185\u63a5\u3057, \u304b\u3064\\(C_2\\)\u306b\u5916\u63a5\u3057\u3066\u3044\u308b. \u305f\u3060\u3057, \\(b\\)\u306f\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b.
(1) \\(a\\), \\(b\\)\u3092\\(t\\)\u3092\u7528\u3044\u3066\u8868\u305b. \u307e\u305f, \\(t\\)\u304c\u3068\u308a\u5f97\u308b\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.
(2) \\(t\\)\u304c(1)\u3067\u6c42\u3081\u305f\u7bc4\u56f2\u3092\u52d5\u304f\u3068\u304d, \\(b\\)\u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.
(2009 \u6771\u4eac\u5927\u5b66 \u6587\u7cfb [1])<\/span><\/p>\n\n\n\n

\u305d\u308c\u3067\u306f\u89e3\u3044\u3066\u3044\u304d\u307e\u3057\u3087\u3046.<\/p>\n\n\n\n

\n

\u5186\\(C_1\\), \\(C_2\\), \\(C_3\\)\u306e\u4e2d\u5fc3\u3092\u305d\u308c\u305e\u308c\\(\\mathrm{O}(0,0)\\), \\(\\mathrm{O_2}(1,0)\\), \\(\\mathrm{O_3}(a,b)\\)\u3068\u304a\u304f\u3068, \\(C_3\\)\u3068\\(C_1\\)\u306b\u5185\u63a5\u3059\u308b\u3053\u3068\u304b\u3089,$$
\\begin{align}
&\\mathrm{OO_3}+t=2\\\\[1.5ex]
\\iff & \\sqrt{a^2+b^2}=2-t
\\end{align}
$$\u3067\u3042\u308a, \\(C_2\\)\u3068\\(C_3\\)\u304c\u5916\u63a5\u3059\u308b\u3053\u3068\u304b\u3089,$$
\\begin{align}
&\\mathrm{O_2O_3}=1+t\\\\[1.5ex]
\\iff & \\sqrt{(a-1)^2+b^2}=1+t
\\end{align}
$$\u3067\u3042\u308b.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\\(b\\)\u306f\u6b63\u306e\u5b9f\u6570\u3067\u3042\u308b\u304b\u3089, \\(2-t=\\sqrt{a^2+b^2}>0\\), \\(1+t=\\sqrt{(a-1)^2+b^2}>0\\)\u3067\u3042\u308b\u304b\u3089, \u300c\\(2-t>0\\)\u304b\u3064, \\(1+t>0\\)\u300d\u3064\u307e\u308a, \u300c\\(-1<t<2\\)\u300d\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a, \u3053\u306e\u7bc4\u56f2\u3067\u306f\\(2\\)\u5f0f\u3067\u4e21\u8fba\u3092\u5e73\u65b9\u3057\u3066\u3082\u540c\u5024\u95a2\u4fc2\u306f\u5d29\u308c\u306a\u3044.$$
\\begin{align}
& \\sqrt{a^2+b^2}=2-t\\\\[1.5ex]
\\iff & a^2+b^2=(2-t)^2\\\\[1.5ex]
& \\sqrt{(a-1)^2+b^2}=1+t\\\\[1.5ex]
\\iff & (a-1)^2+b^2=(1+t)^2\\\\[1.5ex]
\\end{align}
$$\u5e73\u65b9\u3057\u305f\\(2\\)\u5f0f\u3067\u8fba\u3005\u3092\u5f15\u304f\u3068,$$
\\begin{align}
& a^2-(a-1)^2=(2-t)^2-(1+t)^2\\\\[1.5ex]
\\iff & 2a-1=-6t+3\\\\[1.5ex]
\\iff & a=-3t+2
\\end{align}
$$\u3067\u3042\u308a, \u3053\u308c\u3092\\(a^2+b^2=(2-t)^2\\)\u306b\u4ee3\u5165\u3057\u3066,$$
\\begin{align}
&(-3t+2)^2+b^2=(2-t)^2\\\\[1.5ex]
\\iff & b^2=8t-8t^2
\\end{align}
$$\u3068\u306a\u308b. \u3053\u3053\u3067, \\(b\\)\u306f\u6b63\u306e\u5b9f\u6570\u3088\u308a, \\(b^2>0\\)\u3067\u3042\u308b\u304b\u3089, \\(t\\)\u306f$$
\\begin{align}
& b^2=8t-8t^2>0\\\\[1.5ex]
\\iff & t(t-1)<0\\\\[1.5ex]
\\iff & 0<t<1
\\end{align}
$$\u3068\u306a\u308b\u5fc5\u8981\u304c\u3042\u308b. \u305d\u3057\u3066\u3053\u306e\u3068\u304d, \\(b\\)\u306f\u6b63\u3088\u308a$$
b=\\sqrt{8t-8t^2}
$$\u304c\u308f\u304b\u308b. \u3088\u3063\u3066,$$
\\begin{align}
a&=-3t+2\\\\[1.5ex]
b&=\\sqrt{8t-8t^2}
\\end{align}
$$\u3067\u3042\u308b. \u307e\u305f, \\(t\\)\u304c\u3068\u308a\u5f97\u308b\u5024\u306e\u7bc4\u56f2\u306f, \u5148\u306b\u6c42\u3081\u305f2\u3064\u306e\u5fc5\u8981\u6761\u4ef6\u300c\\(-1<t<2\\)\u300d,\u300c\\(0<t<2\\)\u300d\u3068, \\(t\\)\u306f\u5186\\(C_3\\)\u306e\u534a\u5f84\u3067\u3042\u308b\u304b\u3089\u300c\\(t>0\\)\u300d\u306e\u5171\u901a\u7bc4\u56f2\u3068\u3057\u3066, \\(0<t<1\\)\u3068\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a, \u9006\u306b\u3053\u306e\u7bc4\u56f2\u3067\u6761\u4ef6\u3092\u6e80\u305f\u3059\\(a\\), \\(b\\)\u304c\u6c42\u307e\u3063\u305f\u306e\u3067\u3053\u308c\u306f\u5341\u5206\u6761\u4ef6\u3067\u3082\u3042\u308b. \u3088\u3063\u3066\\(t\\)\u306e\u3068\u308a\u5f97\u308b\u5024\u306e\u7bc4\u56f2\u306f,$$
0<t<1
$$\u3067\u3042\u308b.<\/p>\n\n\n\n

(2) \\(b\\)\u306f\u6b63\u306e\u5b9f\u6570\u3067\u3042\u308b\u304b\u3089, \\(b^2\\)\u304c\u6700\u5927\u306e\u3068\u304d, \\(b\\)\u3082\u307e\u305f\u6700\u5927\u306b\u306a\u308b. $$
b^2=8t-8t^2=-8\\left(t-\\frac{1}{2}\\right)^2+2
$$\u3067\u3042\u308a, \\(0<t<1\\)\u3088\u308a\\(b^2\\)\u306f\\(\\displaystyle t=\\frac{1}{2}\\)\u306e\u3068\u304d\u6700\u5927\u5024\\(2\\)\u3092\u3068\u308b\u3053\u3068\u304c\u308f\u304b\u308b.

\u3088\u3063\u3066\\(b\\)\u306f\\(\\displaystyle t=\\frac{1}{2}\\)\u306e\u3068\u304d\u6700\u5927\u5024\\(\\sqrt{2}\\)\u3092\u3068\u308b.<\/p>\n<\/div><\/div>\n\n\n\n

youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n