\u600e\u6837\u7528\u4e00\u652f\u65e0\u523b\u5ea6\u7684\u76f4\u5c3a\u548c\u4e00\u4e2a\u5706\u89c4\u6765\u753b\u4e00\u4e2a\u5df2\u7ed9\u51fa\u7684\u89d2

\u5443\uff0c\u662f\u4e0d\u662f\u9898\u76ee\u4e2d\u753b\u7740\u4e00\u4e2a\u89d2\uff0c\u4f60\u60f3\u590d\u5236\u90a3\u4e2a\u89d2\uff1f\u8fd8\u662f\u9898\u76ee\u7ed9\u4f60\u4e00\u4e2a\u5ea6\u6570\u8ba9\u4f60\u53bb\u753b\uff1f
\u5982\u679c\u662f\u524d\u8005\uff0c\u90a3\u5148\u7528\u5706\u89c4\u5728\u7ed9\u51fa\u7684\u89d2\u8ba9\u4ee5\u89d2\u7684\u9876\u70b9\u4e3a\u5706\u5fc3\u753b\u5f27\uff0c\u4ea4\u4e24\u8fb9\u5206\u522b\u4e8e\u70b9a\u70b9b\u3002
\u7136\u540e\u4fdd\u6301\u5706\u89c4\u7684\u6837\u5b50\u653e\u5728\u4e00\u8fb9\uff0c\u7528\u76f4\u5c3a\u753b\u4e00\u6761\u7ebf\uff0c\u4ee5\u7ebf\u7684\u4e00\u7aef\u4e3a\u5706\u5fc3\uff0c\u7528\u5706\u89c4\u753b\u5f27\uff0c\u4ea4\u4e8e\u4e00\u70b9A\u3002
\u73b0\u5728\u4ee5a\u70b9\u4e3a\u5706\u5fc3\uff0c\u5c06\u5706\u89c4\u8c03\u5236\u521a\u597dab\u4e24\u70b9\u95f4\u7684\u8ddd\u79bb\uff0c\u7136\u540e\u4ee5A\u4e3a\u5706\u5fc3\u753b\u5f27\uff0c\u540c\u4e0a\u9762\u90a3\u4e00\u6b65\u9aa4\u4e2d\u7684\u5f27\u4ea4\u4e8e\u4e00\u70b9B\u3002
\u7528\u76f4\u5c3a\u753b\u7ebf\uff0c\u8fde\u7ed3\u7aef\u70b9\u548cB\u70b9\u3002\u753b\u5b8c\u4e86\u3002\u4e0d\u77e5\u9053\u4f60\u770b\u61c2\u6ca1\u3002

\u9ad8\u65af\u7528\u4ee3\u6570\u7684\u65b9\u6cd5\u89e3\u51b3\u7684\uff0c\u4ed6\u4e5f\u89c6\u6b64\u4e3a\u751f\u5e73\u5f97\u610f\u4e4b\u4f5c\uff0c\u8fd8\u4ea4\u5f85\u8981\u628a\u6b63\u5341\u4e03\u8fb9\u5f62\u523b\u5728\u4ed6\u7684\u5893\u7891\u4e0a\uff0c\u4f46\u540e\u6765\u4ed6\u7684\u5893\u7891\u4e0a\u5e76\u6ca1\u6709\u523b\u4e0a\u5341\u4e03\u8fb9\u5f62\uff0c\u800c\u662f\u5341\u4e03\u89d2\u661f\uff0c\u56e0\u4e3a\u8d1f\u8d23\u523b\u7891\u7684\u96d5\u523b\u5bb6\u8ba4\u4e3a\uff0c\u6b63\u5341\u4e03\u8fb9\u5f62\u548c\u5706\u592a\u50cf\u4e86\uff0c\u5927\u5bb6\u4e00\u5b9a\u5206\u8fa8\u4e0d\u51fa\u6765\u3002

\u5173\u4e8e\u6b63\u5341\u4e03\u8fb9\u5f62\u7684\u753b\u6cd5\uff08\u9ad8\u65af\u7684\u601d\u8def\uff0c\u672c\u4eba\u5e76\u975e\u6709\u610f\u527d\u7a83^_^\uff09\uff1a
\u6709\u4e00\u4e2a\u5b9a\u7406\u5728\u8fd9\u91cc\u8981\u7528\u5230\u7684\uff1a
\u82e5\u957f\u4e3a|a|,|b|\u7684\u7ebf\u6bb5\u53ef\u4ee5\u7528\u51e0\u4f55\u65b9\u6cd5\u505a\u51fa\u6765\uff0c\u90a3\u4e48\u957f\u4e3a|c|\u7684\u7ebf\u6bb5\u4e5f\u80fd\u7528\u51e0\u4f55\u65b9\u6cd5\u505a\u51fa\u7684\uff0c
\u5176\u4e2dc\u662f\u65b9\u7a0bx^2+ax+b=0\u7684\u5b9e\u6839\u3002
\u4e0a\u9762\u7684\u5b9a\u7406\u5b9e\u9645\u4e0a\u5c31\u662f\u5728\u6709\u7ebf\u6bb5\u957f\u5ea6|a|\u548c|b|\u7684\u65f6\u5019\uff0c\u505a\u51fa\u957f\u4e3asqrt(a^2-4b)\u7684\u7ebf\u6bb5\u3002
\uff08\u8fd9\u4e00\u6b65\uff0c\u5927\u5bb6\u4f1a\u753b\u5427\uff1f\uff09
\u800c\u8981\u5728\u4e00\u4e2a\u5355\u4f4d\u5706\u4e2d\u505a\u51fa\u6b63\u5341\u4e03\u8fb9\u5f62\uff0c\u4e3b\u8981\u5c31\u662f\u505a\u51fa\u957f\u5ea6\u662fcos(2pai/17)\u7684\u7ebf\u6bb5\u3002
\u4e0b\u9762\u6211\u628a\u5f53\u5e74\u9ad8\u65af\u8bc1\u660e\u53ef\u4ee5\u505a\u51facos(2pai/17)\u7684\u8bc1\u660e\u7ed9\u51fa\uff0c\u540c\u65f6\u4e5f\u5c31\u7ed9\u51fa\u4e86\u5177\u4f53\u7684\u505a\u6cd5\u3002
\u8bbea=2[cos(2pai/17)+cos(4pai/17)+cos(8pai/17)+cos(16pai/17)]>0
a1=2[cos(6pai/17)+cos(10pai/17)+cos(12pai/17)+cos(14pai/17)]<0
\u5219\u6709a+a1=-1,a*a1=-4,\u5373a,a1\u662f\u65b9\u7a0bx^2+x-4=0\u7684\u6839\uff0c\u6240\u4ee5\u957f\u4e3a|a|\u548c|a1|\u7684\u7ebf\u6bb5\u53ef\u4ee5\u505a\u51fa\u3002
\u4ee4b=2[cos(2pai/17)+cos(8pai/17)]>0 b1=2[cos(4pai/17)+cos(16pai/17)]<0
c=2[cos(6pai/17)+cos(10pai/17)]>0 c1=2[cos(12pai/17)+cos(14pai/17)]<0
\u5219\u6709b+b1=a b*b1=-1 c+c1=a1 c*c1=-1
\u540c\u6837\u9053\u7406\uff0c\u957f\u5ea6\u662f|b|,|b1|,|c|,|c1|\u7684\u7ebf\u6bb5\u90fd\u53ef\u4ee5\u505a\u51fa\u6765\u7684\u3002
\u518d\u67092cos(2pai/17)+2cos(8pai/17)\uff1db [2cos(2pai/17)]*[2cos(8pai/17)]=c
\u8fd9\u6837\uff0c2cos(2pai/17\uff09\u662f\u65b9\u7a0bx^2-bx+c=0\u8f83\u5927\u7684\u5b9e\u6839,
\u663e\u7136\u4e5f\u53ef\u4ee5\u505a\u51fa\u6765\uff0c\u5e76\u4e14\u4f5c\u56fe\u7684\u65b9\u6cd5\u4e0a\u9762\u5df2\u7ecf\u7ed9\u51fa\u6765\u4e86

\u53c2\u8003\u8d44\u6599\u6709\u4f5c\u56fe\u65b9\u6cd5\uff0c\u4e0d\u8fc7\u662f\u7e41\u4f53\u7684\uff0c\u8981\u5230\u67e5\u770b\uff0d\u7f16\u7801\uff0d\u7e41\u4f53\u4e2d\u6587\u7684\u6a21\u5f0f\u4e0b\u624d\u80fd\u770b\u5230\u6c49\u5b57
\u53c2\u8003\u8d44\u6599\uff1ahttp://www.vtsh.tc.edu.tw/~jck/dynamic/heptadecagon.htm