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惠更斯反射

惠更斯反射
几何画板及绘图内容加载中，请稍等……
2016-02-11 01:35
角向量变换
该范例演示了惠更斯反射原理。涉及的核心数学概念包括反射、角度和向量。通过使用旋转、角度、线、圆、交点、正交线、镜像等 GeoGebra 命令，可以构建出复杂的几何图形。适合高中学生和教师用于几何作图和变换教学。

GeoGebra 命令及参数

  1. Rotate(A, i, B) → A'
  2. Angle(A, B, A') → α
  3. Line(A', B) → a
  4. Circle(B, 5 - t) → c
  5. Intersect(c, a, 1) → C
  6. OrthogonalLine(C, a) → b
  7. Mirror(b, xAxis) → b'
  8. Point(xAxis) → D
  9. Point(xAxis) → E
  10. Point(xAxis) → F
  11. Point(xAxis) → G
  12. Point(xAxis) → H
  13. OrthogonalLine(D, b') → d
  14. OrthogonalLine(E, b') → e
  15. OrthogonalLine(F, b') → f
  16. OrthogonalLine(G, b') → g
  17. OrthogonalLine(H, b') → h
  18. Intersect(b', d) → I
  19. Circle(D, I) → k
  20. Intersect(b', e) → J
  21. Circle(E, J) → p
  22. Intersect(b', f) → K
  23. Circle(F, K) → q
  24. Intersect(b', g) → L
  25. Circle(G, L) → r
  26. Intersect(b', h) → M
  27. Circle(H, M) → s
  28. Intersect(k, xAxis, 1) → N
  29. Intersect(k, xAxis, 2) → O
  30. Semicircle(N, O) → c_1
  31. Intersect(b, b') → P
  32. Segment(B, P) → j
  33. Intersect(p, j, 2) → Q
  34. Intersect(p, j, 1) → R
  35. Intersect(q, j, 2) → S
  36. Intersect(q, j, 1) → T
  37. Intersect(p, xAxis, 1) → U
  38. Intersect(p, xAxis, 2) → V
  39. Semicircle(U, V) → d_1
  40. Intersect(q, xAxis, 1) → W
  41. Intersect(q, xAxis, 2) → Z
  42. Semicircle(W, Z) → e_1
  43. Intersect(r, xAxis, 1) → A_1
  44. Intersect(r, xAxis, 2) → B_1
  45. Semicircle(A_1, B_1) → f_1
  46. Intersect(s, xAxis, 1) → C_1
  47. Intersect(s, xAxis, 2) → D_1
  48. Semicircle(C_1, D_1) → g_1
  49. Line(E_1, a) → l
  50. Mirror(a, yAxis) → a'
  51. Line(E_1, a') → m
  52. Intersect(b, l) → F_1
  53. Intersect(c, a, 1) → G_1
  54. Segment(F_1, G_1) → n
  55. Intersect(c_1, b', 1) → H_1
  56. Point(j) → I_1
  57. Segment(H_1, I_1) → a_1
  58. Point(l) → J_1
  59. Vector(J_1, E_1) → u
  60. Point(m) → K_1
  61. Vector(E_1, K_1) → v
  62. Point(a) → L_1
  63. Intersect(α, a, 1) → M_1
  64. Intersect(a, a') → N_1
  65. Vector(L_1, N_1) → w
  66. Point(a') → O_1
  67. Vector(N_1, O_1) → u_1
  68. Segment(G_1, I_1) → b_1