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几何变换与函数图像 by Juan Carlos Ponce Campuzano

几何变换与函数图像 by Juan Carlos Ponce Campuzano
几何画板及绘图内容加载中，请稍等……
2019-01-10 10:59
函数三角函数变换
所属专题 GeoGebraScript for Making Constructions and Animations
该范例演示了如何使用GeoGebra进行几何变换，包括平移、缩放等操作，并展示了函数图像的绘制方法。核心数学概念包括函数、三角函数和变换。通过构造摘要中的命令，如Sequence、Polygon、Dilate等，可以了解该范例的具体实现。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Sequence(((t * cos(((k * 2) * π / 3) + π / 2)), (t * sin(((k * 2) * π / 3) + π / 2))), k, 0, 2) → Points
  2. Sequence(((((-t) + 1.5) * cos(((k * 2) * π / 3) + (3 * π / 2))), (((-t) + 1.5) * sin(((k * 2) * π / 3) + (3 * π / 2)))), k, 0, 2) → Points1
  3. Polygon(A1, B2, A3, B1, A2, B3) → triangle, a1, b2, a3, b1, a2, b3
  4. Dilate(A1, 1 / 10, (0, 0)) → A1'
  5. Dilate(B2, 1 / 10, (0, 0)) → B2'
  6. Dilate(A3, 1 / 10, (0, 0)) → A3'
  7. Dilate(B1, 1 / 10, (0, 0)) → B1'
  8. Dilate(A2, 1 / 10, (0, 0)) → A2'
  9. Dilate(B3, 1 / 10, (0, 0)) → B3'
  10. Polygon(Dilate[A1, 1 / 10, (0, 0)], Dilate[B2, 1 / 10, (0, 0)], Dilate[A3, 1 / 10, (0, 0)], Dilate[B1, 1 / 10, (0, 0)], Dilate[A2, 1 / 10, (0, 0)], Dilate[B3, 1 / 10, (0, 0)]) → C1, f, g, h, i, j, k
  11. Dilate(A1, 2 / 10, (0, 0)) → A1'_1
  12. Dilate(B2, 2 / 10, (0, 0)) → B2'_1
  13. Dilate(A3, 2 / 10, (0, 0)) → A3'_1
  14. Dilate(B1, 2 / 10, (0, 0)) → B1'_1
  15. Dilate(A2, 2 / 10, (0, 0)) → A2'_1
  16. Dilate(B3, 2 / 10, (0, 0)) → B3'_1
  17. Polygon(Dilate[A1, 2 / 10, (0, 0)], Dilate[B2, 2 / 10, (0, 0)], Dilate[A3, 2 / 10, (0, 0)], Dilate[B1, 2 / 10, (0, 0)], Dilate[A2, 2 / 10, (0, 0)], Dilate[B3, 2 / 10, (0, 0)]) → C2, l, m, n, p, q, r
  18. Dilate(A1, 3 / 10, (0, 0)) → A1'_2
  19. Dilate(B2, 3 / 10, (0, 0)) → B2'_2
  20. Dilate(A3, 3 / 10, (0, 0)) → A3'_2
  21. Dilate(B1, 3 / 10, (0, 0)) → B1'_2
  22. Dilate(A2, 3 / 10, (0, 0)) → A2'_2
  23. Dilate(B3, 3 / 10, (0, 0)) → B3'_2
  24. Polygon(Dilate[A1, 3 / 10, (0, 0)], Dilate[B2, 3 / 10, (0, 0)], Dilate[A3, 3 / 10, (0, 0)], Dilate[B1, 3 / 10, (0, 0)], Dilate[A2, 3 / 10, (0, 0)], Dilate[B3, 3 / 10, (0, 0)]) → C3, s, a, b, c, d, e
  25. Dilate(A1, 4 / 10, (0, 0)) → A1'_3
  26. Dilate(B2, 4 / 10, (0, 0)) → B2'_3
  27. Dilate(A3, 4 / 10, (0, 0)) → A3'_3
  28. Dilate(B1, 4 / 10, (0, 0)) → B1'_3
  29. Dilate(A2, 4 / 10, (0, 0)) → A2'_3
  30. Dilate(B3, 4 / 10, (0, 0)) → B3'_3
  31. Polygon(Dilate[A1, 4 / 10, (0, 0)], Dilate[B2, 4 / 10, (0, 0)], Dilate[A3, 4 / 10, (0, 0)], Dilate[B1, 4 / 10, (0, 0)], Dilate[A2, 4 / 10, (0, 0)], Dilate[B3, 4 / 10, (0, 0)]) → C4, f_1, g_1, h_1, i_1, j_1, k_1
  32. Dilate(A1, 5 / 10, (0, 0)) → A1'_4
  33. Dilate(B2, 5 / 10, (0, 0)) → B2'_4
  34. Dilate(A3, 5 / 10, (0, 0)) → A3'_4
  35. Dilate(B1, 5 / 10, (0, 0)) → B1'_4
  36. Dilate(A2, 5 / 10, (0, 0)) → A2'_4
  37. Dilate(B3, 5 / 10, (0, 0)) → B3'_4
  38. Polygon(Dilate[A1, 5 / 10, (0, 0)], Dilate[B2, 5 / 10, (0, 0)], Dilate[A3, 5 / 10, (0, 0)], Dilate[B1, 5 / 10, (0, 0)], Dilate[A2, 5 / 10, (0, 0)], Dilate[B3, 5 / 10, (0, 0)]) → C5, l_1, m_1, n_1, p_1, q_1, r_1
  39. Dilate(A1, 6 / 10, (0, 0)) → A1'_5
  40. Dilate(B2, 6 / 10, (0, 0)) → B2'_5
  41. Dilate(A3, 6 / 10, (0, 0)) → A3'_5
  42. Dilate(B1, 6 / 10, (0, 0)) → B1'_5
  43. Dilate(A2, 6 / 10, (0, 0)) → A2'_5
  44. Dilate(B3, 6 / 10, (0, 0)) → B3'_5
  45. Polygon(Dilate[A1, 6 / 10, (0, 0)], Dilate[B2, 6 / 10, (0, 0)], Dilate[A3, 6 / 10, (0, 0)], Dilate[B1, 6 / 10, (0, 0)], Dilate[A2, 6 / 10, (0, 0)], Dilate[B3, 6 / 10, (0, 0)]) → C6, s_1, t_1, a_1, b_1, c_1, d_1
  46. Dilate(A1, 7 / 10, (0, 0)) → A1'_6
  47. Dilate(B2, 7 / 10, (0, 0)) → B2'_6
  48. Dilate(A3, 7 / 10, (0, 0)) → A3'_6
  49. Dilate(B1, 7 / 10, (0, 0)) → B1'_6
  50. Dilate(A2, 7 / 10, (0, 0)) → A2'_6
  51. Dilate(B3, 7 / 10, (0, 0)) → B3'_6
  52. Polygon(Dilate[A1, 7 / 10, (0, 0)], Dilate[B2, 7 / 10, (0, 0)], Dilate[A3, 7 / 10, (0, 0)], Dilate[B1, 7 / 10, (0, 0)], Dilate[A2, 7 / 10, (0, 0)], Dilate[B3, 7 / 10, (0, 0)]) → C7, e_1, f_2, g_2, h_2, i_2, j_2
  53. Dilate(A1, 8 / 10, (0, 0)) → A1'_7
  54. Dilate(B2, 8 / 10, (0, 0)) → B2'_7
  55. Dilate(A3, 8 / 10, (0, 0)) → A3'_7
  56. Dilate(B1, 8 / 10, (0, 0)) → B1'_7
  57. Dilate(A2, 8 / 10, (0, 0)) → A2'_7
  58. Dilate(B3, 8 / 10, (0, 0)) → B3'_7
  59. Polygon(Dilate[A1, 8 / 10, (0, 0)], Dilate[B2, 8 / 10, (0, 0)], Dilate[A3, 8 / 10, (0, 0)], Dilate[B1, 8 / 10, (0, 0)], Dilate[A2, 8 / 10, (0, 0)], Dilate[B3, 8 / 10, (0, 0)]) → C8, k_2, l_2, m_2, n_2, p_2, q_2
  60. Dilate(A1, 9 / 10, (0, 0)) → A1'_8
  61. Dilate(B2, 9 / 10, (0, 0)) → B2'_8
  62. Dilate(A3, 9 / 10, (0, 0)) → A3'_8
  63. Dilate(B1, 9 / 10, (0, 0)) → B1'_8
  64. Dilate(A2, 9 / 10, (0, 0)) → A2'_8
  65. Dilate(B3, 9 / 10, (0, 0)) → B3'_8
  66. Polygon(Dilate[A1, 9 / 10, (0, 0)], Dilate[B2, 9 / 10, (0, 0)], Dilate[A3, 9 / 10, (0, 0)], Dilate[B1, 9 / 10, (0, 0)], Dilate[A2, 9 / 10, (0, 0)], Dilate[B3, 9 / 10, (0, 0)]) → C9, r_2, s_2, t_2, a_2, b_2, c_2
  67. Dilate(A1, 10 / 10, (0, 0)) → A1'_9
  68. Dilate(B2, 10 / 10, (0, 0)) → B2'_9
  69. Dilate(A3, 10 / 10, (0, 0)) → A3'_9
  70. Dilate(B1, 10 / 10, (0, 0)) → B1'_9
  71. Dilate(A2, 10 / 10, (0, 0)) → A2'_9
  72. Dilate(B3, 10 / 10, (0, 0)) → B3'_9
  73. Polygon(Dilate[A1, 10 / 10, (0, 0)], Dilate[B2, 10 / 10, (0, 0)], Dilate[A3, 10 / 10, (0, 0)], Dilate[B1, 10 / 10, (0, 0)], Dilate[A2, 10 / 10, (0, 0)], Dilate[B3, 10 / 10, (0, 0)]) → C10, d_2, e_2, f_3, g_3, h_3, i_3