{"id":1804,"date":"2018-11-03T11:17:49","date_gmt":"2018-11-03T02:17:49","guid":{"rendered":"http:\/\/math.co.jp\/blog\/?p=1804"},"modified":"2019-02-25T16:38:34","modified_gmt":"2019-02-25T07:38:34","slug":"%e9%ab%98%e6%a0%a1%e6%95%b0%e5%ad%a6%e8%a7%a3%e8%aa%ac%e8%ac%9b%e5%ba%a7%e3%80%80%ef%bc%91","status":"publish","type":"post","link":"https:\/\/math.co.jp\/blog\/?p=1804","title":{"rendered":"\u9ad8\u6821\u6570\u5b66\u89e3\u8aac\u8b1b\u5ea7\u3000\uff11"},"content":{"rendered":"<p><br \/>\n<font size=\"+1\"><strong>1.\u3000\u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f\u306b\u3064\u3044\u3066<\/strong><\/font><\/p>\n<p>\u3000\u9ad8\u6821\u6570\u5b66\u3067\u5b66\u7fd2\u3059\u308b\u7d76\u5bfe\u4e0d\u7b49\u5f0f\u306e\u4e00\u3064\u306b<strong>\u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f<\/strong>\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f,<br \/>\n (1)\u3000\\((ax+by)^{2}\\leqq (a^{2}+b^{2})(x^{2}+y^{2})\\)<br \/>\n (2)\u3000\\((ax+by+cz)^{2}\\leqq (a^{2}+b^{2}+c^{2})(x^{2}+y^{2}+z^{2})\\)<br \/>\n (3)\u3000\\((ax+by+cz+dw)^{2}\\leqq (a^{2}+b^{2}+c^{2}+d^{2})(x^{2}+y^{2}+z^{2}+w^{2})\\)<br \/>\n $$\\vdots$$<br \/>\n\u306e\u3088\u3046\u306a\u4e0d\u7b49\u5f0f\u3067, \u4e00\u822c\u306b\u306f, \\(\\sum\\) \u8a18\u53f7\u3092\u7528\u3044\u3066,<br \/>\n$$\\left(\\sum_{k=1}^{n}a_{k}b_{k}\\right)^{2}\\leqq \\left( \\sum_{k=1}^{n}a_{k}^{\\,2}\\right)\\left( \\sum_{k=1}^{n}b_{k}^{\\,2}\\right)\u3000\u3000\\cdots\\cdots\\,(\u2605)$$<br \/>\n\u3068\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057, \u6587\u5b57\u306f\u3059\u3079\u3066<font color=\"magenta\">\u5b9f\u6570<\/font>\u3068\u3057\u307e\u3059\u3002<br \/>\n\u3000\u3068\u3053\u308d\u3067, \u4e0d\u7b49\u5f0f (\u2605) \u306e \\(n=3\\) \u306e\u5834\u5408\u306f,<br \/>\n$$(a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3})^{2}\\leqq (a_{1}^{\\,2}+a_{2}^{\\,2}+a_{3}^{\\,2})(b_{1}^{\\,2}+b_{2}^{\\,2}+b_{3}^{\\,2})$$<br \/>\n\u3067\u3059\u304c, \u3053\u308c\u306f,<br \/>\n$$\\vec{a}=\\left( \\begin{array}{c} a_{1} \\\\ a_{2} \\\\ a_{3} \\\\ \\end{array}\\right),\u3000\\vec{b}=\\left( \\begin{array}{c} b_{1} \\\\ b_{2} \\\\ b_{3} \\\\ \\end{array}\\right)$$<br \/>\n\u3068\u304a\u304f\u3068,<br \/>\n\u3000\u3000\\(\\vec{a}\\) \u3068 \\(\\vec{b}\\) \u306e\u5185\u7a4d\u306f,\u3000<br \/>\n$$\\vec{a}\\cdot \\vec{b}=a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}$$<br \/>\n\u3000\u3000\\(\\vec{a}\\) \u3068 \\(\\vec{b}\\) \u306e\u5927\u304d\u3055\u306f, \u305d\u308c\u305e\u308c,<br \/>\n$$|\\vec{a}|^{2}=a_{1}^{\\,2}+a_{2}^{\\,2}+a_{3}^{\\,2},\u3000|\\vec{b}|^{2}=b_{1}^{\\,2}+b_{2}^{\\,2}+b_{3}^{\\,2}$$<br \/>\n\u3067\u3059\u304b\u3089,<br \/>\n$$(\\vec{a}\\cdot \\vec{b})^{2}\\leqq |\\vec{a}|^{2}|\\vec{b}|^{2}$$<br \/>\n\u3068\u8868\u305b\u307e\u3059\u3002\u3053\u306e\u4e0d\u7b49\u5f0f\u306f\u9ad8\u6821\u6570\u5b66\u3067\u306e\u5185\u7a4d\u306e\u5b9a\u7fa9\u3092\u8003\u3048\u308c\u3070\u6210\u308a\u7acb\u3064\u3053\u3068\u306f\u660e\u3089\u304b\u3067\u3059\u3002\u306a\u305c\u306a\u3089,<br \/>\n$$\\vec{a}\\cdot \\vec{b}=|\\vec{a}||\\vec{b}|\\cos \\theta\u3000(\\theta \u306f \\vec{a} \u3068 \\vec{b} \u306e\u306a\u3059\u89d2)$$<br \/>\n\u304c\u5185\u7a4d\u306e\u5b9a\u7fa9\u3067\u3059\u304b\u3089,<br \/>\n$$(\\vec{a}\\cdot \\vec{b})^{2}=|\\vec{a}|^{2}|\\vec{b}|^{2}\\cos^{2}\\theta$$<br \/>\n\u3068\u306a\u308a, \\(\\cos^{2}\\theta \\leqq 1\\) \u3067\u3059\u304b\u3089, \u53f3\u8fba\u306f,<br \/>\n$$|\\vec{a}|^{2}|\\vec{b}|^{2}\\cos^{2}\\theta\\leqq |\\vec{a}|^{2}|\\vec{b}|^{2}$$<br \/>\n\u3068\u306a\u308b\u306e\u3067,<br \/>\n$$(\\vec{a}\\cdot \\vec{b})^{2}\\leqq |\\vec{a}|^{2}|\\vec{b}|^{2}$$<br \/>\n\u3068\u306a\u308b\u304b\u3089\u3067\u3059\u3002<br \/>\n\u3000\u3055\u3066, \\(n=3\\) \u306e\u5834\u5408\u306f\u4ee5\u4e0a\u306e\u3088\u3046\u306b\u8003\u3048\u3066\u8aac\u660e\u3059\u308b\u3053\u3068\u3082\u53ef\u80fd\u3067\u3059\u304c, \u4e00\u822c\u306e 2 \u4ee5\u4e0a\u306e\u81ea\u7136\u6570 \\(n\\) \u306b\u3064\u3044\u3066\u306f, \u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3068\u5185\u7a4d\u306e\u95a2\u4fc2\u3092\u7406\u7531\u306b\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002 4 \u6b21\u5143\u4ee5\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3068\u5185\u7a4d\u304c\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3089\u3067\u3059\u3002<br \/>\n(\u6ce8)<br \/>\n\u3082\u3061\u308d\u3093, \u9ad8\u6821\u6570\u5b66\u3092\u8d85\u3048\u308c\u3070, \u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3068\u5185\u7a4d\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3000\u3055\u3066, \u305d\u308c\u3067\u306f, \u4e00\u822c\u306e\u5834\u5408\u306b\u3064\u3044\u3066\u8a3c\u660e\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><font size=\"+1\"><strong>\u8a3c\u660e<\/strong><\/font><br \/>\n\u3000\u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f<br \/>\n$$\\left( \\sum_{k=1}^{n}a_{k}b_{k}\\right)^{2}\\leqq \\left( \\sum_{k=1}^{n}a_{k}^{\\,2}\\right)\\left( \\sum_{k=1}^{n}b_{k}^{\\,2}\\right)$$<br \/>\n\u3092\u793a\u3059\u305f\u3081\u306b, \u6b21\u306e\u3088\u3046\u306a\u95a2\u6570\u3092\u7528\u610f\u3057\u307e\u3059\u3002<br \/>\n$$f(t)=\\sum_{k=1}^{n}(a_{k}t-b_{k})^{2}$$<br \/>\n\u5c11\u3057\u308f\u304b\u308a\u306b\u304f\u3044\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c, \u4f8b\u3048\u3070 \\(n=3\\) \u306e\u5834\u5408\u3067\u3042\u308b<br \/>\n$$(a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3})^{2}\\leqq (a_{1}^{\\,2}+a_{2}^{\\,2}+a_{3}^{\\,2})(b_{1}^{\\,2}+b_{2}^{\\,2}+b_{3}^{\\,2})$$<br \/>\n\u3092\u793a\u3059\u5834\u5408\u3067\u3042\u308c\u3070,<br \/>\n$$f(t)=(a_{1}t-b_{1})^{2}+(a_{2}t-b_{2})^{2}+ (a_{3}t-b_{3})^{2}$$<br \/>\n\u3068\u304a\u304f\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<br \/>\n\u3000\u3055\u3066, \u8a71\u3092\u4e00\u822c\u306e\u5834\u5408\u306e \\(n\\) \u306e\u5834\u5408\u306b\u623b\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u3068\u304d \\(f(t)\\) \u306f\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<br \/>\n$$\\begin{eqnarray}<br \/>\nf(t)&#038;=&#038;\\sum_{k=1}^{n}(a_{k}t-b_{k})^{2}\\\\<br \/>\n&#038;=&#038;\\sum_{k=1}^{n}(a_{k}^{\\,2}t^{2}-2a_{k}b_{k}t+b_{k}^{\\,2})<br \/>\n\\end{eqnarray}$$<br \/>\n\u3053\u308c\u3092 \\(\\sum\\) \u8a18\u53f7\u3092\u7528\u3044\u305a\u306b\u66f8\u304f\u3068,<br \/>\n$$f(t)=(a_{1}^{\\,2}t^{2}-2a_{1}b_{1}t+b_{1}^{\\,2})+(a_{2}^{\\,2}t^{2}-2a_{2}b_{2}t+b_{2})+\\cdots +(a_{n}^{\\,2}t^{2}-2a_{n}b_{n}t+b_{n}^{\\,2})$$<br \/>\n\u306e\u3088\u3046\u306b\u306a\u308a, \u3053\u308c\u3092 \\(t\\) \u3067\u6574\u7406\u3059\u308b\u3068,<br \/>\n$$f(t)=(a_{1}^{\\,2}+a_{2}^{\\,2}+\\cdots +a_{n}^{\\,2})t^{2}-2(a_{1}b_{1}+a_{2}b_{2}+\\cdots +a_{n}b_{n})t +(b_{1}^{\\,2}+b_{2}^{\\,2}+\\cdots +b_{n}^{\\,2})$$<br \/>\n\u3068\u306a\u308b\u306e\u3067, \u7d50\u5c40 \\(\\sum\\) \u8a18\u53f7\u3092\u7528\u3044\u308c\u3070,<br \/>\n$$f(t)=\\left( \\sum_{k=1}^{n}a_{k}^{\\,2}\\right)\\, t^{2} -2\\left( \\sum_{k=1}^{n}a_{k}b_{k}\\right)\\,t+\\sum_{k=1}^{n}b_{k}^{\\,2}$$<br \/>\n\u3068\u8868\u305b\u307e\u3059\u3002\u3053\u3053\u3067,<br \/>\n$$\\begin{eqnarray}<br \/>\nA&#038;=&#038;a_{1}^{\\,2}+a_{2}^{\\,2}+\\cdots +a_{n}^{\\,2}\\\\<br \/>\nB&#038;=&#038;b_{1}^{\\,2}+b_{2}^{\\,2}+\\cdots +b_{n}^{\\,2}\\\\<br \/>\nC&#038;=&#038;a_{1}b_{1}+a_{2}b_{2}+\\cdots +a_{n}b_{n}\\\\<br \/>\n\\end{eqnarray}$$<br \/>\n\u3068\u304a\u304f\u3068, \\(f(t)\\) \u306f,<br \/>\n$$f(t)=At^{2}-2Ct+B$$<br \/>\n\u3068\u8868\u305b\u307e\u3059\u3002\u306a\u304a, \u4eca, \u793a\u3057\u305f\u3044\u5f0f\u3092 \\(A\\), \\(B\\), \\(C\\) \u3092\u7528\u3044\u3066\u8868\u3059\u3068, \\(C^{2}\\leqq AB\\) \u3068\u306a\u308a\u307e\u3059\u3002<br \/>\n\u3000\u3055\u3066, \u4e00\u822c\u306e \\(C^{2}\\leqq AB\\) \u306e\u8aac\u660e\u3092\u59cb\u3081\u308b\u524d\u306b, \u4f8b\u5916\u7684\u306a\u5834\u5408\u3067\u3042\u308b \\(A=0\\) \u306e\u5834\u5408, \u3059\u306a\u308f\u3061, \\(a_{1}=a_{2}=\\cdots =a_{n}=0\\) \u306e\u5834\u5408\u306b\u89e6\u308c\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u5834\u5408\u306f, \\(C=0\\) \u3067\u3082\u3042\u308b\u306e\u3067, \\(C^{2}\\leqq AB\\) \u306f\u7b49\u53f7\u3067\u6210\u7acb\u3057\u307e\u3059\u3002\\(A=0\\) \u306e\u5834\u5408\u306f, \u3053\u308c\u3067\u793a\u3055\u308c\u305f\u306e\u3067\u4ee5\u4e0b\u306f \\(A\\neq 0\\) \u306e\u5834\u5408\u3092\u8003\u3048\u308b\u3053\u3068\u306b\u3057\u307e\u3059\u3002<br \/>\n\u3000\u518d\u3073 \\(f(t)\\) \u306b\u3064\u3044\u3066\u3067\u3059\u304c\u3053\u308c\u306f,<br \/>\n$$f(t)=(a_{1}t-b_{1})^{2}+(a_{2}t-b_{2})^{2}+\\cdots +(a_{n}t-b_{n})^{2}$$<br \/>\n\u306e\u3088\u3046\u306b\u300c2 \u4e57\u306e\u548c\u300d\u306e\u5f62\u3067\u8868\u3055\u308c\u308b\u5f0f\u3067\u3057\u305f\u304b\u3089 \\(t\\) \u306b\u3069\u306e\u3088\u3046\u306a\u5b9f\u6570\u3092\u4ee3\u5165\u3057\u3066\u3082 \\(f(t)<0\\) \u3068\u306a\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066, \u3059\u3079\u3066\u306e\u5b9f\u6570 \\(t\\) \u306b\u5bfe\u3057\u3066 \\(f(t)\\geqq 0\\) \u3067\u3042\u308b\u306e\u3067, \\(f(t)\\) \u3092\u4eca\u4e00\u5ea6 \\(f(t)=At^{2}-2Ct+B\\) \u3068\u898b\u308b\u3068, 2 \u6b21\u65b9\u7a0b\u5f0f \\(At^{2}-2Ct+B=0\\) \u306e\u5224\u5225\u5f0f \\(D\\) \u306f \\(D\\leqq 0\\) \u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067, \n$$\\frac{D}{4}=C^{2}-AB$$\n\u3067\u3059\u304b\u3089, \\(D\\leqq 0\\) \u306f, \n$$C^{2}-AB\\leqq 0$$\n\u3059\u306a\u308f\u3061, \n$$C^{2}\\leqq AB$$\n\u304c\u6210\u7acb\u3057\u307e\u3059\u3002\u3053\u308c\u3067, \u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f\u306f\u793a\u3055\u308c\u307e\u3057\u305f\u3002<\/br><br \/>\n\u3000\u3068\u3053\u308d\u3067, \u3053\u306e\u4e0d\u7b49\u5f0f\u306e\u7b49\u53f7\u304c\u6210\u7acb\u3059\u308b\u5834\u5408\u3067\u3059\u304c, \u3053\u308c\u306f \\(C^{2}=AB\\) \u3068\u306a\u308b\u5834\u5408, \u3059\u306a\u308f\u3061, \u5224\u5225\u5f0f \\(D\\) \u304c \\(D=0\\) \u3068\u306a\u308b\u5834\u5408\u3067\u3059\u3002\u5143\u3005, \\(f(t)\\) \u306f,<br \/>\n$$f(t)=\\sum^{n}_{k=1} (a_{k}t-b_{k})^{2}$$<br \/>\n\u3068\u8868\u3055\u308c, \u6c7a\u3057\u3066\u8ca0\u306b\u306a\u308b\u3053\u3068\u306e\u306a\u3044 2 \u6b21\u5f0f\u3067\u3057\u305f\u306e\u3067, \\(D=0\\) \u3067\u3042\u308b\u3053\u3068\u306f, \u3053\u3053\u3067\u306f, \u300c\u3042\u308b \\(t\\) \u306b\u5bfe\u3057 \\(f(t)=0\\) \u3068\u306a\u308b\u300d\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u306f, \u3059\u3079\u3066\u306e \\(k=1,2,3,\\cdots ,n\\) \u306b\u5bfe\u3057\u3066 \\(a_{k}t-b_{k}=0\\) \u3068\u306a\u308b \\(t\\) \u306e\u5b58\u5728\u3059\u308b\u3053\u3068, \u3064\u307e\u308a,<br \/>\n$$a_{1}t-b_{1}=0, a_{2}t-b_{2}=0,\\cdots ,a_{n}t-b_{n}=0$$<br \/>\n\u304c\u3059\u3079\u3066\u540c\u3058\u89e3\u306b\u306a\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u306f,<br \/>\n$$\\frac{b_{1}}{a_{1}}=\\frac{b_{2}}{a_{2}}=\\cdots =\\frac{b_{n}}{a_{n}}$$<br \/>\n\u3068\u306a\u308b\u3053\u3068\u3067\u3059\u3002\u305f\u3060\u3057, \u5206\u6bcd\u304c 0 \u306e\u3068\u304d\u306f, \u5206\u5b50\u3082 0 \u3068\u3057\u307e\u3059\u3002<\/br><\/p>\n<p><font size=\"+1\"><strong>\u88dc\u8db3<\/strong><\/font><br \/>\n\u3000\u3053\u3053\u3067\u306f, \u4e00\u822c\u306e \\(n\\) \u306e\u5834\u5408\u306b\u3064\u3044\u3066\u8a3c\u660e\u3092\u3057\u307e\u3057\u305f\u304c, \\(n=2,3\\) \u306a\u3069\u306e\u5834\u5408\u306b\u306f\u6b21\u306e\u3088\u3046\u306a\u8a3c\u660e\u3082\u53ef\u80fd\u3067\u3059\u3002<\/p>\n<ul>\n<li><font color=\"magenta\">\\((ax+by)^{2}\\leqq (a^{2}+b^{2})(x^{2}+y^{2})\\) \u306b\u3064\u3044\u3066<\/font><br \/>\n\u3000\u3000\\((a^{2}+b^{2})(x^{2}+y^{2})-(ax+by)^{2}\\)<br \/>\n\u3000\u3000\u3000\\(=(a^{2}x^{2}+a^{2}y^{2}+b^{2}x^{2}+b^{2}y^{2})-(a^{2}x^{2}+2abxy+b^{2}y^{2})\\)<br \/>\n\u3000\u3000\u3000\\(=(ay)^{2}+(bx)^{2}-2ay\\cdot bx\\)<br \/>\n\u3000\u3000\u3000\\(=(ay-bx)^{2}\\)<br \/>\n\u3000\u3000\u3000\\(\\geqq 0\\)<br \/>\n\u3057\u305f\u304c\u3063\u3066<br \/>\n\u3000\u3000\\((ax+by)^{2}\\leqq (a^{2}+b^{2})(x^{2}+y^{2})\\)<\/li>\n<li><font color=\"magenta\">\\((ax+by+cz)^{2}\\leqq (a^{2}+b^{2}+c^{2})(x^{2}+y^{2}+z^{2})\\) \u306b\u3064\u3044\u3066<\/font><br \/>\n\u540c\u69d8\u306b\u6b21\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u307e\u3059\u3002<br \/>\n\u3000\u3000\\((a^{2}+b^{2}+c^{2})(x^{2}+y^{2}+z^{2})-(ax+by+cz)^{2}\\)<br \/>\n\u3000\u3000\u3000\\(=(ay-bx)^{2}+(bz-cy)^{2}+(cx-az)^{2}\\)<br \/>\n\u3000\u3000\u3000\\(\\geqq 0\\)<br \/>\n\u3057\u305f\u304c\u3063\u3066<br \/>\n\u3000\u3000\\((ax+by+cz)^{2}\\leqq (a^{2}+b^{2}+c^{2})(x^{2}+y^{2}+z^{2})\\)\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>1.\u3000\u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f\u306b\u3064\u3044\u3066 \u3000\u9ad8\u6821\u6570\u5b66\u3067\u5b66\u7fd2\u3059\u308b\u7d76\u5bfe\u4e0d\u7b49\u5f0f\u306e\u4e00\u3064\u306b\u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f, (1)\u3000\\((ax+by)^{2}\\leqq (a^{2}+b^{2})(x^ [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-1804","post","type-post","status-publish","format-standard","hentry","category-19"],"_links":{"self":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1804","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1804"}],"version-history":[{"count":38,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1804\/revisions"}],"predecessor-version":[{"id":1849,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1804\/revisions\/1849"}],"wp:attachment":[{"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1804"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1804"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.co.jp\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1804"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}