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佐尔科夫菱形

佐尔科夫菱形
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2016-09-19 03:59
多边形三角函数变换
这个范例演示了佐尔科夫菱形的构造。涉及的核心数学概念包括菱形的性质、角度和三角函数。通过使用GeoGebra命令如Polygon、Angle、Rotate等，可以动态地展示菱形的变换和性质。适合初中及以上学生学习几何变换和菱形的性质。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(C, B, A) → α
  3. Angle(A, C, B) → β
  4. Angle(B, A, C) → γ
  5. Line(A, B) → f
  6. Line(C, f) → g
  7. Point(g) → D
  8. Line(D, a) → h
  9. Line(D, b) → i
  10. Intersect(i, f) → E
  11. Intersect(h, f) → F
  12. Polygon(D, E, F) → poly2, f_1, d, e
  13. Line(G, H) → j
  14. Line(I, j) → k
  15. Line(H, I) → l
  16. Line(G, l) → m
  17. Intersect(m, k) → J
  18. Polygon(I, J, G, H) → poly3, i_1, j_1, g_1, h_1
  19. Polygon(L, K, N, M) → poly4, l_1, k_1, n, m_1
  20. Segment(K, M) → p
  21. Line(O, P) → q
  22. Rotate(O, 90°, P) → O'
  23. Angle(O, P, O') → δ
  24. Line(O', q) → r
  25. Line(P, O') → s
  26. Line(O, s) → t
  27. Intersect(t, r) → Q
  28. Polygon(P, O, Q, O') → poly5, p_1, o, q_1, o'
  29. Line(C_1, D_1) → e_1
  30. Line(E_1, e_1) → f_2
  31. Point(f_2) → F_1
  32. Line(C_1, F_1) → g_2
  33. Line(D_1, E_1) → h_2
  34. Polygon(D_1, C_1, F_1, E_1) → poly8, d_2, c_2, f_3, e_2
  35. Line(G_1, H_1) → i_2
  36. Line(G_1, I_1) → j_2
  37. OrthogonalLine(H_1, j_2) → k_2
  38. Line(I_1, i_2) → l_2
  39. Line(H_1, I_1) → m_2
  40. Line(G_1, m_2) → n_2
  41. Intersect(n_2, l_2) → J_1
  42. Intersect(k_2, l_2) → K_1
  43. Segment(L_1, M_1) → p_2
  44. Line(M_1, N_1) → q_2
  45. Line(L_1, N_1) → r_2
  46. OrthogonalLine(M_1, r_2) → g_3
  47. Line(N_1, p_2) → h_3
  48. Line(L_1, q_2) → i_3
  49. Intersect(g_3, i_3) → P_1
  50. Intersect(g_3, h_3) → O_1
  51. Intersect(i_3, g_3) → Q_1
  52. Polygon(M_1, O_1, N_1) → poly6, n_3, m_3, o_1
  53. Line(S, T) → n_1
  54. Point(Circle[T, Distance[S, T]]) → U
  55. Segment(T, U) → r_1
  56. Line(U, n_1) → s_1
  57. Line(S, r_1) → t_1
  58. Intersect(t_1, s_1) → V
  59. Polygon(S, T, U, V) → poly9, s_2, t_2, u, v