Thompson 三次曲线的几何构造与要点

GeoGebra 命令及参数

1. Line(A, B) → f
2. Line(B, C) → g
3. Line(C, A) → h
4. Polygon(A, B, C) → t1, c, a, b
5. TriangleCurve(A, B, C, (A * ((c^(2) * B^(2)) - (b^(2) * C^(2)))) + (B * ((a^(2) * C^(2)) - (c^(2) * A^(2)))) + (C * ((b^(2) * A^(2)) - (a^(2) * B^(2)))) = 0) → eq2
6. Circle(B, A, C) → d
7. Center(Incircle[A, B, C]) → I
8. Center(d) → O
9. Incircle(A, B, C) → e
10. Midpoint(B, A) → M_c
11. Midpoint(A, C) → M_b
12. Midpoint(C, B) → M_a
13. Centroid(t1) → G
14. AngularBisector(f, h) → i, j
15. AngularBisector(g, h) → k, l
16. Intersect(i, k) → I_B
17. Intersect(k, j) → I_A
18. Intersect(l, i) → I_C
19. Intersect(eq2, d, 3) → Q_1
20. Intersect(eq2, d, 6) → Q_2
21. Intersect(eq2, d, 2) → Q_3
22. OrthogonalLine(I_C, g) → m
23. OrthogonalLine(I_A, f) → n
24. OrthogonalLine(I_B, g) → p
25. Intersect(g, p) → D
26. Circle(I_B, D) → q
27. Intersect(g, m) → F
28. Circle(I_C, F) → s
29. Intersect(f, n) → E
30. Circle(I_A, E) → r
31. OrthogonalLine(A, g) → t
32. OrthogonalLine(B, h) → f_1
33. OrthogonalLine(C, f) → g_1
34. Intersect(f_1, t) → H
35. Mirror(M_a, G) → J
36. Mirror(M_b, G) → K
37. Conic(M_a, K, M_c, J, M_b) → c_1
38. Focus(c_1) → F_1, F_2