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# [讨论] 三角形的达布点对

 \!\(\*OverscriptBox["a", "_"]\) = 1/a; \!\(\*OverscriptBox["b", "_"]\) = 1/b; \!\(\*OverscriptBox["c", "_"]\) = 1/c;(*原点在外心上，并且是单位圆*) Chuizu[a_, b_, p_] := ( \!\(\*OverscriptBox["a", "_"]\) b - a \!\(\*OverscriptBox["b", "_"]\) + p ( \!\(\*OverscriptBox["a", "_"]\) - \!\(\*OverscriptBox["b", "_"]\)) + \!\(\*OverscriptBox["p", "_"]\) (a - b))/(2 ( \!\(\*OverscriptBox["a", "_"]\) - \!\(\*OverscriptBox["b", "_"]\)));(*=(1/2)[p+( \!\(\*OverscriptBox["a", "_"]\)b-a \!\(\*OverscriptBox["b", "_"]\)+ \!\(\*OverscriptBox["p", "_"]\)(a-b))/( \!\(\*OverscriptBox["a", "_"]\)- \!\(\*OverscriptBox["b", "_"]\))]P到直线AB的垂足*) \!\(\*OverscriptBox["Chuizu", "_"]\)[a_, b_, p_] := (a \!\(\*OverscriptBox["b", "_"]\) - \!\(\*OverscriptBox["a", "_"]\) b + \!\(\*OverscriptBox["p", "_"]\) (a - b) + p ( \!\(\*OverscriptBox["a", "_"]\) - \!\(\*OverscriptBox["b", "_"]\)))/(2 (a - b)); d = Chuizu[c, b, p]; \!\(\*OverscriptBox["d", "_"]\) = \!\(\*OverscriptBox["Chuizu", "_"]\)[c, b, p]; e = Chuizu[a, c, p]; \!\(\*OverscriptBox["e", "_"]\) = \!\(\*OverscriptBox["Chuizu", "_"]\)[a, c, p]; f = Chuizu[a, b, p]; \!\(\*OverscriptBox["f", "_"]\) = \!\(\*OverscriptBox["Chuizu", "_"]\)[a, b, p]; Simplify[{d, \!\(\*OverscriptBox["d", "_"]\), , e, \!\(\*OverscriptBox["e", "_"]\), , f, \!\(\*OverscriptBox[ RowBox[{"f", "\[IndentingNewLine]"}], "_"]\)}] Simplify[{(a - f)/(b - f), (b - d)/(c - d), (c - e)/(a - e)}] Simplify[{(a - f)/(b - f) + (b - d)/(c - d) + (c - e)/(    a - e)}](*根据Ceva定理，和等于0*) Factor[{(a - f)/(b - f) + (b - d)/(c - d) + (c - e)/(a - e)}] 复制代码 达布曲线是三次方程。

### 点评

 38,39行错误，正确语句和结果如下图：

 这次才是对的

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