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Huygens Reflection

Huygens Reflection
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2016-02-11 01:35
AngleVectorTransformation
This example illustrates Huygens' principle of reflection. Key mathematical concepts include reflection, angles, and vectors. Using commands such as Rotate, Angle, Line, Circle, Intersect, OrthogonalLine, Mirror, etc., complex geometric shapes can be constructed. Suitable for high school students and teachers for geometric construction and transformation lessons.

GeoGebra Commands & Parameters

  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