拼图正方形与等边三角形——几何剖分探索

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Point(xAxis) → B
3. Polygon(A, B, 3) → poly1, a, a_1, b, C
4. Segment(A, B) → c
5. Segment(B, C) → d
6. Segment(C, A) → e
7. Midpoint(d) → D
8. Midpoint(e) → E
9. Circle(D, C) → f
10. Ray(A, D) → g
11. Intersect(f, g) → F_1, F
12. Midpoint(A, F) → G
13. Circle(G, F) → h
14. Ray(B, C) → i
15. Intersect(h, i) → H,
16. Circle(D, H) → k
17. Intersect(k, c, 1) → J
18. Circle(J, Segment[C, D]) → p
19. Intersect(p, c, 1) → K
20. Segment(J, D) → j
21. OrthogonalLine(E, j) → l
22. Intersect(l, j) → N
23. OrthogonalLine(K, j) → m
24. Intersect(m, j) → R
25. Segment(E, N) → n
26. Segment(K, R) → q
27. Polygon(C, D, N, E) → poly2, c_1, d_1, n_1, e_1
28. Polygon(D, B, K, R) → poly3, d_2, b_1, k_1, r
29. Polygon(J, K, R) → poly4, r_1, j_1, k_2
30. Polygon(A, J, N, E) → poly5, a_2, j_2, n_2, e_2
31. Rotate(C, (-α), D) → C'_1
32. Rotate(D, (-α), D) → D'
33. Rotate(N, (-α), D) → N'_1
34. Rotate(E, (-α), D) → E'_1
35. Polygon(C'_1, D', N'_1, E'_1) → poly2', c', d', n', e'_1
36. Rotate(J, α, K) → J'_1
37. Rotate(K, α, K) → K'
38. Rotate(R, α, K) → R'
39. Polygon(J'_1, K', R') → poly4', r', j', k'
40. Rotate(A, α, K') → A'
41. Rotate(J, α, K') → J'
42. Rotate(N, α, K') → N'
43. Rotate(E, α, K') → E'
44. Polygon(A', J', N', E') → poly5', a', j'_1, n'_1, e'
45. Intersect(b, e) → I
46. Intersect(a_1, d) → L
47. Intersect(b, e) → M
48. Intersect(a_1, d) → O
49. Point(poly1) → P
50. Line(N, R) → s
51. Circle(D', N') → t
52. Line(N, D') → f_1
53. Circle(D', N) → g_1
54. Intersect(g_1, f_1, 2) → Q
55. Polygon(Q, R, 4) → poly6, q_1, r_2, h_1, i_1, S, T
56. Circle(Q, D') → p_1
57. Point(poly6) → U
58. Polygon(D', Q, U, B) → poly7, d'_1, q_2, u, b_2
59. Circle(K', J) → s_1
60. Point(poly6) → V
61. Polygon(K', V, S) → poly8, s_2, k'_1, v
62. Polygon(B, U, T, V) → poly9, b_3, u_1, t_1, v_1
63. Rotate(B, α - 360°, V) → B'
64. Rotate(U, α - 360°, V) → U'
65. Rotate(T, α - 360°, V) → T'
66. Rotate(V, α - 360°, V) → V'
67. Polygon(B', U', T', V') → poly9', b', u', t', v'