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楼主: TSC999

[讨论] 三角形的达布点对

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发表于 2022-1-16 20:58:56 | 显示全部楼层

  1. \!\(\*OverscriptBox["a", "_"]\) = 1/a;
  2. \!\(\*OverscriptBox["b", "_"]\) = 1/b;
  3. \!\(\*OverscriptBox["c", "_"]\) = 1/c;(*原点在外心上,并且是单位圆*)
  4. Chuizu[a_, b_, p_] := (
  5. \!\(\*OverscriptBox["a", "_"]\) b - a
  6. \!\(\*OverscriptBox["b", "_"]\) + p (
  7. \!\(\*OverscriptBox["a", "_"]\) -
  8. \!\(\*OverscriptBox["b", "_"]\)) +
  9. \!\(\*OverscriptBox["p", "_"]\) (a - b))/(2 (
  10. \!\(\*OverscriptBox["a", "_"]\) -
  11. \!\(\*OverscriptBox["b", "_"]\)));(*=(1/2)[p+(
  12. \!\(\*OverscriptBox["a", "_"]\)b-a
  13. \!\(\*OverscriptBox["b", "_"]\)+
  14. \!\(\*OverscriptBox["p", "_"]\)(a-b))/(
  15. \!\(\*OverscriptBox["a", "_"]\)-
  16. \!\(\*OverscriptBox["b", "_"]\))]P到直线AB的垂足*)

  17. \!\(\*OverscriptBox["Chuizu", "_"]\)[a_, b_, p_] := (a
  18. \!\(\*OverscriptBox["b", "_"]\) -
  19. \!\(\*OverscriptBox["a", "_"]\) b +
  20. \!\(\*OverscriptBox["p", "_"]\) (a - b) + p (
  21. \!\(\*OverscriptBox["a", "_"]\) -
  22. \!\(\*OverscriptBox["b", "_"]\)))/(2 (a - b));
  23. d = Chuizu[c, b, p];
  24. \!\(\*OverscriptBox["d", "_"]\) =
  25. \!\(\*OverscriptBox["Chuizu", "_"]\)[c, b, p]; e = Chuizu[a, c, p];
  26. \!\(\*OverscriptBox["e", "_"]\) =
  27. \!\(\*OverscriptBox["Chuizu", "_"]\)[a, c, p]; f = Chuizu[a, b, p];
  28. \!\(\*OverscriptBox["f", "_"]\) =
  29. \!\(\*OverscriptBox["Chuizu", "_"]\)[a, b, p];
  30. Simplify[{d,
  31. \!\(\*OverscriptBox["d", "_"]\), , e,
  32. \!\(\*OverscriptBox["e", "_"]\), , f,
  33. \!\(\*OverscriptBox[
  34. RowBox[{"f", "\[IndentingNewLine]"}], "_"]\)}]
  35. Simplify[{(a - f)/(b - f), (b - d)/(c - d), (c - e)/(a - e)}]
  36. Simplify[{(a - f)/(b - f) + (b - d)/(c - d) + (c - e)/(
  37.    a - e)}](*根据Ceva定理,和等于0*)
  38. Factor[{(a - f)/(b - f) + (b - d)/(c - d) + (c - e)/(a - e)}]


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达布曲线是三次方程。

达布三次曲线

达布三次曲线

点评

最后的方程是人工整理,对称好看。  发表于 2022-1-16 21:00
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2022-1-16 23:06:18 | 显示全部楼层
38,39行错误,正确语句和结果如下图:
达布三次曲线.gif
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2022-1-17 20:32:23 | 显示全部楼层
达布三次曲线.gif
这次才是对的
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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