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Dynamic Equilateral Triangle and Rectangle Area Problem

Dynamic Equilateral Triangle and Rectangle Area Problem
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2016-12-15 04:11
TrianglePolygonGeometric Construction
This example demonstrates a dynamic illustration of an equilateral triangle inside a rectangle, focusing on area calculations. Key math concepts include area computation, coordinate geometry, and geometric transformations. It utilizes GeoGebra commands like Line, Segment, Circle, Intersect, Rotate, and Polygon. Suitable for high school mathematics education, this tool helps students understand the relationships between areas of special shapes and the properties of transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → i
  2. Segment(A, B) → l
  3. OrthogonalLine(B, i) → f
  4. Circle(B, l / 2) → d
  5. Intersect(d, f, 2) → C
  6. OrthogonalLine(A, l) → q
  7. Circle(B, 1) → c
  8. Intersect(c, f, 2) → D
  9. Ray(B, D) → g
  10. Rotate(B, α, A) → B'
  11. Angle(B, A, B') → β
  12. Ray(A, B') → h
  13. Intersect(g, h) → E
  14. Polygon(A, E, 3) → poly1, m, n, p, F
  15. Polygon(E, B, A) → poly3, a_1, e, b
  16. OrthogonalLine(F, q) → r
  17. Intersect(q, r) → G
  18. Intersect(r, g) → H
  19. Polygon(A, F, G) → poly2, g_1, a, f_1
  20. Polygon(E, H, F) → poly4, f_2, e_1, h_1
  21. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], E) → A'
  22. Segment(A, A') → s
  23. Dilate(E, If[1 < o ≤ 2, 2 - o, 0], F) → E'
  24. Rotate(A, If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → A'_1
  25. Rotate(A', If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → A''
  26. Segment(A'_1, A'') → s'
  27. Rotate(A'_1, If[2 < o ≤ 3, ((o - 2) * π / 3), π / 3], F) → I
  28. Rotate(A'', If[2 < o ≤ 3, ((o - 2) * π / 3), π / 3], F) → A'''
  29. Segment(I, A''') → s''
  30. Angle(A, G, H) → γ
  31. Angle(G, H, B) → δ
  32. Angle(H, B, A) → ε
  33. Segment(G, F) → t
  34. Segment(G, A) → i_1
  35. Segment(F, H) → j_1
  36. Segment(H, B) → k_1
  37. Segment(B, A) → l_1
  38. Circle(A, (0.2 * l_1)) → c_1
  39. Intersect(c_1, l_1) → J,
  40. Intersect(c_1, s) → K,
  41. CircleSector(A, J, K) → d_1
  42. Segment(B, E) → m_1
  43. Segment(B, A) → n_1
  44. Segment(H, E) → p_1
  45. OrthogonalLine(G, s') → r_1
  46. OrthogonalLine(B, s) → s_1
  47. Intersect(r_1, s') → L
  48. OrthogonalLine(H, s'') → q_1
  49. Intersect(q_1, s'') → M
  50. Intersect(s_1, s) → N
  51. Dilate(G, If[4 < o ≤ 5, 5 - o, 0], L) → G'
  52. Segment(G, L) → t_1
  53. Circle(H, t_1) → c_2
  54. Segment(H, M) → b_1
  55. Intersect(c_2, b_1) → O, U
  56. Segment(G, G') → g_2
  57. Dilate(B, If[5 < o ≤ 6, 6 - o, 0], N) → B'_1
  58. Segment(B, B'_1) → h_2
  59. Dilate(H, If[6 < o ≤ 7, 7 - o, 0], O) → H'
  60. Segment(H, H') → i_2
  61. Dilate(O, If[7 < o ≤ 8, 8 - o, 0], M) → O'
  62. Segment(O, O') → j_2
  63. Line(O, g_2) → k_2
  64. Point(k_2) → P
  65. Angle(H, O, P) → ζ
  66. Dilate(L, If[8 < o ≤ 9, 9 - o, 0], O) → L'
  67. Vector(L, L') → u
  68. Translate(G, u) → G'_1
  69. Translate(G', u) → G''
  70. Segment(G'_1, G'') → l_2
  71. Rotate(G'_1, If[9 < o ≤ 10, (((-(o - 9)) * 2) * π / 3), (-2 * π / 3)], O) → Q
  72. Rotate(G'', If[9 < o ≤ 10, (((-(o - 9)) * 2) * π / 3), (-2 * π / 3)], O) → G'''
  73. Segment(Q, G''') → m_2
  74. Line(M, h_2) → n_2
  75. Point(n_2) → R
  76. Angle(H, M, R) → η
  77. Dilate(N, If[10 < o ≤ 11, 11 - o, 0], M) → N'
  78. Vector(N, N') → v
  79. Translate(B, v) → B'_2
  80. Dilate(B, If[10 < o ≤ 11, 11 - o, 0], M) → B'_3
  81. Vector(B, B'_3) → w
  82. Translate(B, w) → B'_4
  83. Translate(B'_1, w) → S
  84. Segment(B'_4, S) → p_2
  85. Rotate(B'_4, If[11 < o ≤ 12, ((-(o - 11)) * π / 3), ((-π)) / 3], M) → T
  86. Rotate(S, If[11 < o ≤ 12, ((-(o - 11)) * π / 3), ((-π)) / 3], M) → S'
  87. Segment(T, S') → q_2
  88. Angle(G, L, A) → θ
  89. Angle(A, N, B) → ι
  90. Angle(H, M, A'') → κ