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Parabolic Antenna Mirror

Parabolic Antenna Mirror
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2016-01-31 02:26
VectorFunctionCoordinate Geometry
This example demonstrates the geometric construction of a parabolic antenna mirror. Key mathematical concepts include parabolas, vectors, and geometric transformations. Using GeoGebra commands such as Intersect, Point, Line, and Parabola, a model of the parabolic antenna mirror can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Line(A, B) → a
  4. Point(xAxis) → C
  5. Line(A, C) → b
  6. Point(b) → F
  7. Parabola(F, a) → c
  8. Point(c) → D
  9. Point(c) → E
  10. Point(c) → G
  11. Point(c) → H
  12. Point(c) → I
  13. Point(c) → J
  14. Point(c) → K
  15. Line(D, b) → d
  16. Line(E, b) → e
  17. Line(G, b) → f
  18. Line(H, b) → g
  19. Line(I, b) → h
  20. Line(J, b) → i
  21. Line(K, b) → j
  22. Circle(D, 0.1) → k
  23. Circle(E, 0.1) → p
  24. Circle(G, 0.1) → q
  25. Circle(H, 0.1) → r
  26. Circle(I, 0.1) → s
  27. Circle(J, 0.1) → t
  28. Circle(K, 0.1) → c_1
  29. Intersect(c, k, 2) → L
  30. Intersect(c, k, 1) → M
  31. Intersect(c, p, 2) → N
  32. Intersect(c, p, 1) → O
  33. Intersect(c, q, 2) → P
  34. Intersect(c, q, 1) → Q
  35. Intersect(c, r, 2) → R
  36. Intersect(c, r, 1) → S
  37. Intersect(c, s, 2) → T
  38. Intersect(c, s, 1) → U
  39. Intersect(c, t, 2) → V
  40. Intersect(c, t, 1) → W
  41. Intersect(c, c_1, 2) → Z
  42. Intersect(c, c_1, 1) → A_1
  43. Segment(L, M) → l
  44. Segment(N, O) → m
  45. Segment(P, Q) → n
  46. Segment(R, S) → a_1
  47. Segment(T, U) → b_1
  48. Segment(V, W) → d_1
  49. Segment(Z, A_1) → e_1
  50. OrthogonalLine(D, l) → f_1
  51. OrthogonalLine(E, m) → g_1
  52. OrthogonalLine(G, n) → h_1
  53. OrthogonalLine(H, a_1) → i_1
  54. OrthogonalLine(I, b_1) → j_1
  55. OrthogonalLine(J, d_1) → k_1
  56. OrthogonalLine(K, e_1) → l_1
  57. Point(d) → B_1
  58. Point(e) → C_1
  59. Point(f) → D_1
  60. Point(g) → E_1
  61. Point(h) → F_1
  62. Point(i) → G_1
  63. Point(j) → H_1
  64. Mirror(B_1, f_1) → I_1
  65. Mirror(C_1, g_1) → J_1
  66. Mirror(D_1, h_1) → K_1
  67. Mirror(E_1, i_1) → L_1
  68. Mirror(F_1, j_1) → M_1
  69. Mirror(G_1, k_1) → N_1
  70. Mirror(H_1, l_1) → O_1
  71. Vector(D, I_1) → u
  72. Vector(E, J_1) → v
  73. Vector(G, K_1) → w
  74. Vector(H, F) → u_1
  75. Vector(H, L_1) → v_1
  76. Vector(I, M_1) → w_1
  77. Vector(J, N_1) → m_1
  78. Vector(K, O_1) → n_1