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Animation 279: Geometric Construction of Parallelograms and Trapezoids

Animation 279: Geometric Construction of Parallelograms and Trapezoids
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2017-06-04 09:56
CirclePolygonProbability & StatisticsTransformationGeometric Construction
①This GeoGebra example dynamically demonstrates the construction of parallelograms, trapezoids, and triangles, incorporating elements of binomial distribution to blend geometry with probability. ②Core mathematical concepts include properties of parallelograms and trapezoids, triangle construction, circle rotation and arcs, and binomial distribution, along with LCM and GCD relationships. ③Construction highlights: Based on the summary, commands such as Circle, Point, Rotate, CircleArc, Segment, Intersect, Ray, Polygon, Line, OrthogonalLine, Angle, Dilate, Vector, and Translate are used, creating multiple points, lines, circles, polygons, and vectors, with transformations like rotation, translation, and dilation to produce dynamic animations. ④Suitable for middle and high school mathematics, this example serves as a visual aid for geometric constructions, and can also be used to explore connections between geometry and probability, ideal for classroom demonstrations or student self-study of transformations and distributions.

GeoGebra Commands & Parameters

  1. Circle(A_1, B_1) → c
  2. Point(c) → C_1
  3. Rotate(C_1, 2°, A_1) → C'
  4. CircleArc(A_1, C', C_1) → d
  5. Point(d) → D
  6. CircleArc(A_1, D, C_1) → e
  7. Point(e) → C
  8. CircleArc(A_1, C, C_1) → f
  9. Point(f) → B
  10. CircleArc(A_1, B, C_1) → g
  11. Point(g) → A
  12. Segment(D, C) → b
  13. Segment(C, B) → h
  14. Segment(D, A) → a
  15. Segment(A, B) → i
  16. Circle(B, (0.2 * Distance[A_1, B_1])) → k
  17. Circle(C, (0.2 * Distance[A_1, B_1])) → p
  18. Circle(A, (0.2 * Distance[A_1, B_1])) → q
  19. Circle(D, (0.2 * Distance[A_1, B_1])) → r
  20. Intersect(k, i, 1) → H_1
  21. Intersect(k, h, 1) → I
  22. Intersect(p, h, 1) → J
  23. Intersect(p, b, 1) → K
  24. Intersect(r, a, 1) → L
  25. Intersect(r, b, 1) → M_1
  26. Intersect(q, a, 1) → N_1
  27. Intersect(q, i, 1) → O
  28. Circle(A_1, B_1) → e_1
  29. Ray(D, A) → l
  30. Point(l) → P
  31. Ray(A, P) → m
  32. Ray(A, D) → n
  33. Point(n) → Q
  34. Ray(D, Q) → a_1
  35. Polygon(A, D, C, B) → poly1, g_2, d_2, e_2, f_2
  36. Line(A, D) → s
  37. Line(C, B) → t
  38. Line(C, D) → f_1
  39. Line(B, A) → h_1
  40. OrthogonalLine(C, s) → g_1
  41. OrthogonalLine(B, m) → i_1
  42. OrthogonalLine(D, h_1) → j_1
  43. Intersect(g_1, s) → G
  44. Intersect(i_1, s) → F
  45. OrthogonalLine(A, f_1) → k_1
  46. Intersect(f_1, k_1) → E
  47. Intersect(h_1, j_1) → H
  48. Intersect(i_1, j_1) → N
  49. Intersect(k_1, g_1) → M
  50. Line(N, M) → l_1
  51. Angle(B, F, A) → γ
  52. Angle(D, G, C) → δ
  53. Angle(C, E, A) → ε
  54. Angle(D, H, B) → ζ
  55. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], N) → B'
  56. Segment(B, B') → m_1
  57. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], M) → C'_1
  58. Segment(C, C'_1) → n_1
  59. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], N) → D'
  60. Dilate(N, If[3 < o ≤ 4, 4 - o, 0], H) → N'
  61. Segment(N, N') → p_1
  62. Dilate(N, If[1 < o ≤ 2, 2 - o, 0], F) → N'_1
  63. Segment(N, N'_1) → q_1
  64. Dilate(M, If[1 < o ≤ 2, 2 - o, 0], G) → M'
  65. Segment(M, M') → r_1
  66. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], M) → A'
  67. Segment(A, A') → s_1
  68. Dilate(M, If[5 < o ≤ 6, 6 - o, 0], E) → M'_1
  69. Segment(M, M'_1) → t_1
  70. Dilate(N, If[6 < o ≤ 7, 7 - o, 0], M) → N'_2
  71. Segment(N, N'_2) → b_1
  72. Segment(N, B) → c_1
  73. Line(N, M) → h_2
  74. Dilate(N, If[7 < o ≤ 8, 8 - o, 0], B) → N'_3
  75. Segment(N, N'_3) → d_1
  76. Dilate(N, If[8 < o ≤ 9, 9 - o, 0], B) → N'_4
  77. Vector(N, N'_4) → u
  78. Translate(N, u) → N'_5
  79. Translate(N'_2, u) → R
  80. Segment(N'_5, R) → i_2
  81. Dilate(N, If[9 < o ≤ 10, 10 - o, 0], M) → N'_6
  82. Vector(N, N'_6) → v
  83. Translate(N, v) → N'_7
  84. Translate(N'_3, v) → S
  85. Segment(N'_7, S) → j_2
  86. Polygon(N, M, C, B) → poly2, n_2, m_2, c_2, b_2
  87. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], N) → D'_1
  88. Segment(D, D'_1) → j