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Dynamic Demonstration of Rhombus and Parabola

Dynamic Demonstration of Rhombus and Parabola
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2017-05-28 09:57
PolygonVectorFunction
This example demonstrates the dynamic relationship between a rhombus and a parabola. Key mathematical concepts include the properties of a rhombus, the definition of a parabola, and its combination with vectors. Using GeoGebra commands such as Ray, Point, Segment, Rotate, Intersect, etc., the dynamic transformation process of the rhombus is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Ray(A, B) → j
  2. Point(j) → D
  3. Segment(A, D) → r_1
  4. Line(A, B) → f
  5. Rotate(B, π / 3, A) → B'
  6. Angle(B, A, B') → α
  7. Rotate(B', π / 3, A) → B''
  8. Angle(B', A, B'') → β
  9. Ray(A, B'') → g
  10. Ray(A, B') → h
  11. Point(h) → C
  12. Mirror(B, A) → B'_1
  13. Segment(C, D) → i
  14. Ray(A, B'_1) → k
  15. Segment(A, D) → l
  16. Segment(A, C) → m
  17. Circle(A, (0.15 * r_1)) → c
  18. Intersect(c, k, 1) → E
  19. Intersect(c, g) → F,
  20. CircleSector(A, F, E) → d
  21. Rotate(d, If[0 < a ≤ 1, ((-a) * π / 3), ((-π)) / 3], A) → d'
  22. Rotate(d', If[2 < a ≤ 3, ((-(a - 2)) * π / 3), ((-π)) / 3], A) → d''
  23. Line(A, C) → n
  24. OrthogonalLine(D, n) → p
  25. Intersect(n, p) → J
  26. Line(A, D) → q
  27. OrthogonalLine(C, q) → r
  28. Intersect(r, q) → H
  29. Line(A, C) → n_1
  30. Circle(C, 1) → e_1
  31. Intersect(e_1, n_1, 2) → N
  32. Circle(A, 1) → p_1
  33. Intersect(p_1, n_1) → O, P
  34. Ray(A, D) → s_1
  35. Circle(D, 1) → t_1
  36. Intersect(t_1, s_1) → Q, R
  37. Line(A, C) → q_1
  38. Circle(A, D) → c_1
  39. Intersect(c_1, q_1) → U, V
  40. CircleArc(A, D, V) → e
  41. Point(e) → G
  42. Ray(D, B) → s
  43. Midpoint(A, D) → I
  44. Dilate(A, If[3 < a ≤ 4, 4 - a, 0], I) → A'
  45. Circle(V, 1) → t
  46. Midpoint(A, V) → K
  47. Midpoint(G, V) → L
  48. Midpoint(D, G) → S
  49. Distance(I, S) → distanceIS
  50. Distance(S, L) → distanceSL
  51. Distance(L, K) → distanceLK
  52. Distance(K, I) → distanceKI
  53. Intersect(t, q_1, 2) → T
  54. Ray(V, T) → b
  55. Dilate(A, If[3 < a ≤ 4, 4 - a, 0], K) → A'_1
  56. Segment(A, A') → f_1
  57. Segment(A, A'_1) → g_1
  58. Rotate(A, If[4 < a ≤ 5, ((-(a - 4)) * π), (-π)], I) → A'_2
  59. Rotate(A', If[4 < a ≤ 5, ((-(a - 4)) * π), (-π)], I) → A''
  60. Segment(A'_2, A'') → h_1
  61. Rotate(A, If[4 < a ≤ 5, ((-(a - 4)) * π), (-π)], K) → A'_3
  62. Rotate(A'_1, If[4 < a ≤ 5, ((-(a - 4)) * π), (-π)], K) → W
  63. Segment(A'_3, W) → i_1
  64. Dilate(G, If[5 < a ≤ 6, 6 - a, 0], S) → G'
  65. Dilate(G, If[5 < a ≤ 6, 6 - a, 0], L) → G'_1
  66. Segment(G, G') → a_1
  67. Segment(G, G'_1) → b_1
  68. Dilate(L, If[6 < a ≤ 7, 7 - a, 0], V) → L'
  69. Dilate(S, If[6 < a ≤ 7, 7 - a, 0], D) → S'
  70. Segment(L, L') → d_1
  71. Segment(S, S') → f_2
  72. Rotate(G, If[7 < a ≤ 8, ((a - 7) * π), π], S) → G'_2
  73. Rotate(G', If[7 < a ≤ 8, ((a - 7) * π), π], S) → G''
  74. Segment(G'_2, G'') → j_1
  75. Rotate(G, If[7 < a ≤ 8, ((a - 7) * π), π], L) → G'_3
  76. Rotate(G'_1, If[7 < a ≤ 8, ((a - 7) * π), π], L) → Z
  77. Segment(G'_3, Z) → k_1
  78. Dilate(I, If[8 < a ≤ 9, 9 - a, 0], S) → I'
  79. Segment(I, I') → l_1
  80. Angle(S, I, K) → γ
  81. Rotate(I, If[9 < a ≤ 10, ((a - 9) * γ), γ], I) → I'_1
  82. Rotate(I', If[9 < a ≤ 10, ((a - 9) * γ), γ], I) → I''
  83. Segment(I'_1, I'') → m_1
  84. Dilate(I, If[10 < a ≤ 11, 11 - a, 0], K) → I'_2
  85. Vector(I, I'_2) → u
  86. Translate(I, u) → I'_3
  87. Translate(I', u) → I''_1
  88. Segment(I'_3, I''_1) → g_2
  89. Dilate(K, If[11 < a ≤ 12, 12 - a, 0], L) → K'
  90. Vector(K, K') → v
  91. Translate(I'_1, v) → M
  92. Translate(I'', v) → I'''
  93. Segment(M, I''') → h_2
  94. CircleSector(A, D, V) → c_2
  95. Polygon(I, S, L, K) → poly1, i_2, s_2, l_2, k_2