[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/4911#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/4911","headline":"\u30c7\u30ab\u30eb\u30c8\u306e\u5186\u5b9a\u7406 – Wikipedia","name":"\u30c7\u30ab\u30eb\u30c8\u306e\u5186\u5b9a\u7406 – Wikipedia","description":"before-content-x4 \u5e7e\u4f55\u5b66\u306b\u304a\u3051\u308b\u30c7\u30ab\u30eb\u30c8\u306e\u5b9a\u7406\u3068\u306f\u3001\u4e92\u3044\u306b\u63a5\u3059\u308b4\u3064\u306e\u5186\u306e\u534a\u5f84\u306f\u3042\u308b\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3059\u3001\u3068\u3044\u3046\u4e3b\u5f35\u3067\u3042\u308b\u30021642\u5e74\u306b\u3053\u308c\u3092\u767a\u8868\u3057\u305f\u30eb\u30cd\u30fb\u30c7\u30ab\u30eb\u30c8\u306b\u56e0\u3080\u3002 after-content-x4 \u4e92\u3044\u306b\u63a5\u3059\u308b\u5186\u306e\u554f\u984c\u306b\u5bfe\u3059\u308b\u95a2\u5fc3\u306f\u53e4\u304f\u3001\u7d00\u5143\u524d\u4e09\u4e16\u7d00\u306e\u30ae\u30ea\u30b7\u30e3\u4eba\u3067\u3042\u308b\u30da\u30eb\u30ac\u306e\u30a2\u30dd\u30ed\u30cb\u30a6\u30b9\u304c\u591a\u304f\u306e\u8ad6\u8ff0\u3092\u6b8b\u3057\u3066\u3044\u308b\u3002 1643\u5e74\u3001\u30eb\u30cd\u30fb\u30c7\u30ab\u30eb\u30c8\u306f\u30d7\u30d5\u30a1\u30eb\u30c4\u516c\u5973\u30a8\u30ea\u30fc\u30b6\u30d9\u30c8\u3078\u306e\u624b\u7d19\u306e\u4e2d\u3067\u3053\u306e\u554f\u984c\u3092\u8a73\u7d30\u306b\u7814\u7a76\u3057\u3001\u5f8c\u8ff0\u3059\u308b\u5f0f(1)\u3068\u672c\u8cea\u7684\u306b\u540c\u3058\u7d50\u679c\u3092\u5f97\u305f\u3002 \u30d5\u30ec\u30c7\u30ea\u30c3\u30af\u30fb\u30bd\u30c7\u30a3\u304c1936\u5e74\u306b\u5f0f(1)\u3092\u518d\u767a\u898b\u3057 Nature \u306b\u767a\u8868\u3057\u305f[1]\u305f\u3081\u3001\u3053\u306e\u554f\u984c\u3067\u6271\u308f\u308c\u308b4\u3064\u306e\u5186\u306f\u30bd\u30c7\u30a3\u306e\u5186\uff08\u82f1: Soddy circles\uff09\u3068\u547c\u3070\u308c\u308b\u3002\u30d5\u30ec\u30c7\u30ea\u30c3\u30af\u30fb\u30bd\u30c7\u30a3\u306f\u3053\u306e\u554f\u984c\u3092\u7403\u3078\u3068\u62e1\u5f35\u3057\u3001\u3055\u3089\u306b\u30bd\u30ed\u30eb\u30c9\u30fb\u30b4\u30bb\u306f\u4efb\u610f\u306e\u6b21\u5143\u3078\u3068\u62e1\u5f35\u3057\u305f\u3002 after-content-x4 \u4e92\u3044\u306b\u63a5\u3059\u308b3\u3064\u306e\u5186\uff08\u9ed2\uff09\u306e\u5168\u3066\u306b\u63a5\u3059\u308b\u5186\u306f2\u3064\u5b58\u5728\u3059\u308b\uff08\u8d64\uff09 \u534a\u5f84 r \u306e\u5186\u306e\u66f2\u7387 k \u3092 k=\u00b11r{displaystyle k=pm {frac","datePublished":"2022-03-25","dateModified":"2022-03-25","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/8\/87\/Descartes_Circles.svg\/220px-Descartes_Circles.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/8\/87\/Descartes_Circles.svg\/220px-Descartes_Circles.svg.png","height":"220","width":"220"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki5\/archives\/4911","about":["Wiki"],"wordCount":4829,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u5e7e\u4f55\u5b66\u306b\u304a\u3051\u308b\u30c7\u30ab\u30eb\u30c8\u306e\u5b9a\u7406\u3068\u306f\u3001\u4e92\u3044\u306b\u63a5\u3059\u308b4\u3064\u306e\u5186\u306e\u534a\u5f84\u306f\u3042\u308b\u4e8c\u6b21\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3059\u3001\u3068\u3044\u3046\u4e3b\u5f35\u3067\u3042\u308b\u30021642\u5e74\u306b\u3053\u308c\u3092\u767a\u8868\u3057\u305f\u30eb\u30cd\u30fb\u30c7\u30ab\u30eb\u30c8\u306b\u56e0\u3080\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u4e92\u3044\u306b\u63a5\u3059\u308b\u5186\u306e\u554f\u984c\u306b\u5bfe\u3059\u308b\u95a2\u5fc3\u306f\u53e4\u304f\u3001\u7d00\u5143\u524d\u4e09\u4e16\u7d00\u306e\u30ae\u30ea\u30b7\u30e3\u4eba\u3067\u3042\u308b\u30da\u30eb\u30ac\u306e\u30a2\u30dd\u30ed\u30cb\u30a6\u30b9\u304c\u591a\u304f\u306e\u8ad6\u8ff0\u3092\u6b8b\u3057\u3066\u3044\u308b\u30021643\u5e74\u3001\u30eb\u30cd\u30fb\u30c7\u30ab\u30eb\u30c8\u306f\u30d7\u30d5\u30a1\u30eb\u30c4\u516c\u5973\u30a8\u30ea\u30fc\u30b6\u30d9\u30c8\u3078\u306e\u624b\u7d19\u306e\u4e2d\u3067\u3053\u306e\u554f\u984c\u3092\u8a73\u7d30\u306b\u7814\u7a76\u3057\u3001\u5f8c\u8ff0\u3059\u308b\u5f0f(1)\u3068\u672c\u8cea\u7684\u306b\u540c\u3058\u7d50\u679c\u3092\u5f97\u305f\u3002\u30d5\u30ec\u30c7\u30ea\u30c3\u30af\u30fb\u30bd\u30c7\u30a3\u304c1936\u5e74\u306b\u5f0f(1)\u3092\u518d\u767a\u898b\u3057 Nature \u306b\u767a\u8868\u3057\u305f[1]\u305f\u3081\u3001\u3053\u306e\u554f\u984c\u3067\u6271\u308f\u308c\u308b4\u3064\u306e\u5186\u306f\u30bd\u30c7\u30a3\u306e\u5186\uff08\u82f1: Soddy circles\uff09\u3068\u547c\u3070\u308c\u308b\u3002\u30d5\u30ec\u30c7\u30ea\u30c3\u30af\u30fb\u30bd\u30c7\u30a3\u306f\u3053\u306e\u554f\u984c\u3092\u7403\u3078\u3068\u62e1\u5f35\u3057\u3001\u3055\u3089\u306b\u30bd\u30ed\u30eb\u30c9\u30fb\u30b4\u30bb\u306f\u4efb\u610f\u306e\u6b21\u5143\u3078\u3068\u62e1\u5f35\u3057\u305f\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4  \u4e92\u3044\u306b\u63a5\u3059\u308b3\u3064\u306e\u5186\uff08\u9ed2\uff09\u306e\u5168\u3066\u306b\u63a5\u3059\u308b\u5186\u306f2\u3064\u5b58\u5728\u3059\u308b\uff08\u8d64\uff09\u534a\u5f84 r \u306e\u5186\u306e\u66f2\u7387 k \u3092 k=\u00b11r{displaystyle k=pm {frac {1}{r}}} \u3067\u5b9a\u7fa9\u3059\u308b\u3002\u5927\u304d\u306a\u5186\u307b\u3069\u66f2\u7387\u306e\u7d76\u5bfe\u5024\u306f\u5c0f\u3055\u3044\u3002k \u304c\u6b63\u306e\u3068\u304d\u3001\u305d\u306e\u5186\u306f\u4ed6\u306e\u5186\u3068\u5916\u63a5\u3059\u308b\u3082\u306e\u3068\u3059\u308b\uff08\u56f3\u4e2d\u306e\u9ed2\u3044\u5186\uff09\u3002\u540c\u3058\u304f\u8ca0\u3067\u3042\u308b\u3068\u304d\u3001\u305d\u306e\u5186\u306f\u4ed6\u306e\u5186\u3068\u5185\u63a5\uff08\u5185\u5305\uff09\u3059\u308b\u3082\u306e\u3068\u3059\u308b\uff08\u56f3\u4e2d\u306e\u5927\u304d\u306a\u8d64\u3044\u5186\uff09\u3002k \u304c 0 \u306e\u3068\u304d\u306f\u3001\u534a\u5f84\u304c\u7121\u9650\u306b\u5927\u304d\u306a\u5186\u3068\u307f\u306a\u3057\u3001\u76f4\u7dda\u3092\u8868\u3059\u3082\u306e\u3068\u3059\u308b\u3002       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u4e92\u3044\u306b\u63a5\u3059\u308b4\u3064\u306e\u5186\uff08\u3082\u3057\u304f\u306f3\u3064\u306e\u5186\u30681\u3064\u306e\u76f4\u7dda\uff09\u306e\u66f2\u7387\u3092 k1, k2, k3, k4 \u3068\u3059\u308b\u3002\u30c7\u30ab\u30eb\u30c8\u306e\u5b9a\u7406\u306f\u3001\u3053\u306e\u3068\u304d\u4ee5\u4e0b\u306e\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u4e3b\u5f35\u3059\u308b\u3002(k1+k2+k3+k4)2=2(k12+k22+k32+k42){displaystyle (k_{1}+k_{2}+k_{3}+k_{4})^{2}=2({k_{1}}^{2}+{k_{2}}^{2}+{k_{3}}^{2}+{k_{4}}^{2})}(1)\u5148\u306b3\u3064\u306e\u5186\uff08\u3082\u3057\u304f\u306f2\u3064\u306e\u5186\u30681\u3064\u306e\u76f4\u7dda\uff09\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u30014\u3064\u76ee\u306e\u5186\u306e\u66f2\u7387\u306f\u4e0a\u5f0f\u3092\u6574\u7406\u3057\u305f\u4ee5\u4e0b\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b\u3002k4=k1+k2+k3\u00b12k1k2+k2k3+k3k1{displaystyle k_{4}=k_{1}+k_{2}+k_{3}pm 2{sqrt {k_{1}k_{2}+k_{2}k_{3}+k_{3}k_{1}}}}(2)\u8907\u53f7\u306b\u3088\u308a\u89e3\u306f2\u3064\u4e0e\u3048\u3089\u308c\u308b\u3002\u76f4\u7dda\u3078\u306e\u9000\u5316\u3092\u7121\u8996\u3059\u308c\u3070\u3001\u4e00\u65b9\u306e\u89e3\u306f\u5e38\u306b\u6b63\u3067\u4ed6\u65b9\u306f\u6b63\u3082\u3057\u304f\u306f\u8ca0\u3067\u3042\u308b\u3002\u8ca0\u306e\u89e3\u306f\u5148\u8ff0\u3057\u305f\u3088\u3046\u306b3\u3064\u306e\u5186\u3092\u5185\u5305\u3059\u308b\u5186\u3092\u8868\u3059\u3002Table of Contents\u7279\u5225\u306a\u5834\u5408[\u7de8\u96c6]3\u3064\u306e\u5186\u304c\u540c\u3058\u70b9\u3067\u63a5\u3057\u3066\u3044\u308b\u5834\u5408[\u7de8\u96c6]\u76f4\u7dda\u304c\u5b58\u5728\u3059\u308b\u5834\u5408[\u7de8\u96c6]\u66f2\u7387\u304c\u5e73\u65b9\u6570\u306e\u5834\u5408[\u7de8\u96c6]\u8907\u7d20\u6570\u5b9a\u7406[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u7279\u5225\u306a\u5834\u5408[\u7de8\u96c6]3\u3064\u306e\u5186\u304c\u540c\u3058\u70b9\u3067\u63a5\u3057\u3066\u3044\u308b\u5834\u5408[\u7de8\u96c6]  \u4e00\u70b9\u3067\u63a5\u3059\u308b3\u3064\u306e\u51863\u3064\u306e\u5186\u304c\u540c\u3058\u70b9\u3067\u63a5\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u30c7\u30ab\u30eb\u30c8\u306e\u5b9a\u7406\u306f\u9069\u7528\u3067\u304d\u306a\u3044\u3002\u76f4\u7dda\u304c\u5b58\u5728\u3059\u308b\u5834\u5408[\u7de8\u96c6]  \u76f4\u7dda\u304c\u5b58\u5728\u3057\u3066\u3082\u30c7\u30ab\u30eb\u30c8\u306e\u5b9a\u7406\u306f\u9069\u7528\u53ef\u80fd\u3067\u3042\u308b\u5186\u306e1\u3064\u304c\u76f4\u7dda\u306e\u5834\u5408\u76f4\u7dda\u3067\u306f k = 0 \u3060\u304b\u3089\u3001\u5f0f(2)\u3088\u308a k4=k1+k2\u00b12k1k2{displaystyle k_{4}=k_{1}+k_{2}pm 2{sqrt {k_{1}k_{2}}}} \u3092\u5f97\u308b\u3002\u5186\u306e2\u3064\u304c\u76f4\u7dda\u306e\u5834\u5408\u540c\u69d8\u306b\u5f0f(2)\u3088\u308a\u81ea\u660e\u306a\u5f0f k4=k1{displaystyle k_{4}=k_{1}} \u3092\u5f97\u308b\u3002\u66f2\u7387\u304c\u5e73\u65b9\u6570\u306e\u5834\u5408[\u7de8\u96c6]\u66f2\u7387\u304c\u5168\u3066\u5e73\u65b9\u6570\u3060\u3063\u305f\u5834\u5408\u3092\u8003\u3048\u308b\u3002\u3053\u306e\u3068\u304d\u5f0f(2)\u306f(v2+x2+y2+z2)2=2(v4+x4+y4+z4){displaystyle (v^{2}+x^{2}+y^{2}+z^{2})^{2}=2(v^{4}+x^{4}+y^{4}+z^{4})}(3)\u3068\u8868\u305b\u308b\u3002\u30aa\u30a4\u30e9\u30fc\u306f v, x, y, z \u306e\u7d44\u307f\u5408\u308f\u305b\u304c\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u4e09\u3064\u7d44\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u305f\u3002(2vx)2+(2yz)2=(v2+x2\u2212y2\u2212z2)2{displaystyle (2vx)^{2}+(2yz)^{2}=(v^{2}+x^{2}-y^{2}-z^{2})^{2}}(2vy)2+(2xz)2=(v2\u2212x2+y2\u2212z2)2{displaystyle (2vy)^{2}+(2xz)^{2}=(v^{2}-x^{2}+y^{2}-z^{2})^{2}}(2vz)2+(2xy)2=(v2\u2212x2\u2212y2+z2)2{displaystyle (2vz)^{2}+(2xy)^{2}=(v^{2}-x^{2}-y^{2}+z^{2})^{2}}\u4eca k1 \u304c\u8ca0\u3067\u3042\u3063\u305f\u3068\u3059\u308b\u3068(\u2212v2+x2+y2+z2)2=2(v4+x4+y4+z4){displaystyle (-v^{2}+x^{2}+y^{2}+z^{2})^{2}=2(v^{4}+x^{4}+y^{4}+z^{4})}\u306e\u89e3\u306f\u5a92\u4ecb\u5909\u6570\u8868\u793a\u3067\u304d\u3066[v,x,y,z]=[2(ab\u2212cd)(ab+cd),(a2+b2+c2+d2)(a2\u2212b2+c2\u2212d2),2(ac\u2212bd)(a2+c2),2(ac\u2212bd)(b2+d2)]{displaystyle [v,x,y,z]=[2(ab-cd)(ab+cd),(a^{2}+b^{2}+c^{2}+d^{2})(a^{2}-b^{2}+c^{2}-d^{2}),2(ac-bd)(a^{2}+c^{2}),2(ac-bd)(b^{2}+d^{2})]}\u3068\u306a\u308b\u3002\u3053\u3053\u3067 a, b, c, d \u306f\u4ee5\u4e0b\u306e\u6052\u7b49\u5f0f\u3092\u6e80\u305f\u3059\u3082\u306e\u3067\u3042\u308b\u3002a4+b4=c4+d4{displaystyle a^{4}+b^{4}=c^{4}+d^{4}}\u7279\u306b v+x=y\u2227z\u22600{displaystyle v+x=yland zneq 0} \u306e\u3068\u304d\u5f0f(3)\u306f4(x2+vx+v2)=z2{displaystyle 4(x^{2}+vx+v^{2})=z^{2}}\u3068\u4e8c\u5143\u4e8c\u6b21\u4e0d\u5b9a\u65b9\u7a0b\u5f0f\u306e\u5f62\u306b\u306a\u308a\u3001\u3084\u306f\u308a\u89e3\u306e\u5f62\u3092\u66f8\u304d\u4e0b\u305b\u308b\u3002\u8907\u7d20\u6570\u5b9a\u7406[\u7de8\u96c6]\u4ee5\u4e0b\u3001\u5186\u306f\u8907\u7d20\u5e73\u9762\u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3082\u306e\u3068\u3059\u308b\u3002i \u756a\u76ee\u306e\u5186\u306e\u4e2d\u5fc3\u3092 zi \u3067\u8868\u3059\u3068\u3001\u5f0f(1)\u3068\u4f3c\u305f\u5f62\u306e\u5f0f(4)\u3067\u4e2d\u5fc3\u5ea7\u6a19\u304c\u8868\u305b\u308b\u3002\u3053\u308c\u3092 complex Descartes’ theorem \u3068\u547c\u3076\u3002(w1+w2+w3+w4)2=2(w12+w22+w32+w42){displaystyle (w_{1}+w_{2}+w_{3}+w_{4})^{2}=2(w_{1}^{2}+w_{2}^{2}+w_{3}^{2}+w_{4}^{2})}(4)z4=(w1+w2+w3\u00b12w1w2+w2w3+w3w1)k4{displaystyle z_{4}={frac {(w_{1}+w_{2}+w_{3}pm 2{sqrt {w_{1}w_{2}+w_{2}w_{3}+w_{3}w_{1}}})}{k_{4}}}}(5)where\u00a0wi=kizi{displaystyle where w_{i}=k_{i}z_{i}}\u8907\u53f7\u304a\u3088\u3073\u8907\u7d20\u6570\u306e\u5e73\u65b9\u6839\u306e\u591a\u4fa1\u6027\u306b\u3088\u308a1\u3064\u306e k4 \u306b\u5bfe\u30572\u3064\u306e\u89e3\u304c\u5f97\u3089\u308c\u3001\u305d\u306e\u3046\u3061\u306e\u4e00\u65b9\u304c\u6b63\u3057\u3044\u4e2d\u5fc3\u3092\u4e0e\u3048\u308b\u3002n\u6b21\u5143\u3078\u306e\u4e00\u822c\u5316\u306f\u30bd\u30c7\u30a3\u2013\u30b4\u30bb\u306e\u5b9a\u7406\u3068\u547c\u3070\u308c\u308b\u3002n\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u306b\u304a\u3044\u3066\u5168\u3066\u304c\u4e92\u3044\u306b\u63a5\u3059\u308b\u8d85\u7403\u306e\u6700\u5927\u6570\u306f n + 2 \u500b\u3067\u3042\u308a\u3001\u305d\u306e\u66f2\u7387\u306b\u3064\u3044\u3066(\u2211i=1n+2ki)2=n\u2211i=1n+2ki2{displaystyle left(textstyle sum limits _{i=1}^{n+2}k_{i}right)^{2}=ntextstyle sum limits _{i=1}^{n+2}{k_{i}}^{2}}\u304c\u6210\u308a\u7acb\u3064\u3002\u8d85\u7403\u306e\u4e2d\u5fc3\u306b\u3064\u3044\u3066\u306f\u884c\u5217\u306b\u3088\u308b\u8868\u793a\u304c\u77e5\u3089\u308c\u3066\u3044\u308b[2][3]\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]     (adsbygoogle = window.adsbygoogle || 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