三角形的达布点对

dlsh

1. 
   
2. \!\(\*OverscriptBox["a", "_"]\) = 1/a;
   
3. \!\(\*OverscriptBox["b", "_"]\) = 1/b;
   
4. \!\(\*OverscriptBox["c", "_"]\) = 1/c;(*原点在外心上，并且是单位圆*)
   
5. Chuizu[a_, b_, p_] := (
   
6. \!\(\*OverscriptBox["a", "_"]\) b - a
   
7. \!\(\*OverscriptBox["b", "_"]\) + p (
   
8. \!\(\*OverscriptBox["a", "_"]\) -
   
9. \!\(\*OverscriptBox["b", "_"]\)) +
   
10. \!\(\*OverscriptBox["p", "_"]\) (a - b))/(2 (
    
11. \!\(\*OverscriptBox["a", "_"]\) -
    
12. \!\(\*OverscriptBox["b", "_"]\)));(*=(1/2)[p+(
    
13. \!\(\*OverscriptBox["a", "_"]\)b-a
    
14. \!\(\*OverscriptBox["b", "_"]\)+
    
15. \!\(\*OverscriptBox["p", "_"]\)(a-b))/(
    
16. \!\(\*OverscriptBox["a", "_"]\)-
    
17. \!\(\*OverscriptBox["b", "_"]\))]P到直线AB的垂足*)
    
18. 
    
19. \!\(\*OverscriptBox["Chuizu", "_"]\)[a_, b_, p_] := (a
    
20. \!\(\*OverscriptBox["b", "_"]\) -
    
21. \!\(\*OverscriptBox["a", "_"]\) b +
    
22. \!\(\*OverscriptBox["p", "_"]\) (a - b) + p (
    
23. \!\(\*OverscriptBox["a", "_"]\) -
    
24. \!\(\*OverscriptBox["b", "_"]\)))/(2 (a - b));
    
25. d = Chuizu[c, b, p];
    
26. \!\(\*OverscriptBox["d", "_"]\) =
    
27. \!\(\*OverscriptBox["Chuizu", "_"]\)[c, b, p]; e = Chuizu[a, c, p];
    
28. \!\(\*OverscriptBox["e", "_"]\) =
    
29. \!\(\*OverscriptBox["Chuizu", "_"]\)[a, c, p]; f = Chuizu[a, b, p];
    
30. \!\(\*OverscriptBox["f", "_"]\) =
    
31. \!\(\*OverscriptBox["Chuizu", "_"]\)[a, b, p];
    
32. Simplify[{d,
    
33. \!\(\*OverscriptBox["d", "_"]\), , e,
    
34. \!\(\*OverscriptBox["e", "_"]\), , f,
    
35. \!\(\*OverscriptBox[
    
36. RowBox[{"f", "\[IndentingNewLine]"}], "_"]\)}]
    
37. Simplify[{(a - f)/(b - f), (b - d)/(c - d), (c - e)/(a - e)}]
    
38. Simplify[{(a - f)/(b - f) + (b - d)/(c - d) + (c - e)/(
    
39.    a - e)}](*根据Ceva定理，和等于0*)
    
40. Factor[{(a - f)/(b - f) + (b - d)/(c - d) + (c - e)/(a - e)}]
    
41. 
    
42. 
    

复制代码

达布曲线是三次方程。

dlsh

38,39行错误，正确语句和结果如下图：

dlsh

这次才是对的