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Geometric and Data Analysis Animation

Geometric and Data Analysis Animation
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2017-03-25 00:36
CircleAngleMatrixOptimizationGeometric Construction
This example demonstrates dynamic changes in geometric figures like circles, angles, and polygons, alongside data analysis through animation. Core math concepts include angles, circles, congruence, incircle, pie charts, linear programming, matrices, and linear regression. Construction highlights the use of GeoGebra commands such as Circle, Point, Segment, Intersect, Midpoint, CircleArc, Min, CircleSector, Dilate, Rotate, Vector, Translate, Line, and Angle. Suitable for high school and above, ideal for teaching geometric constructions, data analysis, and algorithm visualization.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. Segment(C, D) → f
  5. Point(c) → I
  6. Circle(I, f) → k
  7. Intersect(c, k, 2) → J
  8. Segment(I, J) → i
  9. Midpoint(f) → K
  10. Midpoint(i) → N
  11. CircleArc(A, I, C) → d
  12. Point(d) → E
  13. Circle(E, f) → e
  14. Intersect(d, e, 2) → F
  15. Segment(E, F) → g
  16. CircleArc(A, I, E) → h
  17. Point(h) → G
  18. Circle(G, f) → p
  19. Intersect(c, p, 2) → H
  20. Segment(G, H) → j
  21. Midpoint(g) → L
  22. Midpoint(j) → M
  23. Segment(M, L) → l
  24. Segment(M, K) → m
  25. Segment(N, L) → n
  26. Segment(N, K) → q
  27. Min({l, n, m, q}) → a
  28. Circle(M, (0.2 * a)) → r
  29. Intersect(r, l, 1) → O
  30. Intersect(r, m, 1) → P
  31. CircleSector(M, O, P) → s
  32. Dilate(C, If[0 < b ≤ 1, 1 - b, 0], K) → C'
  33. Segment(C, C') → t
  34. Dilate(K, If[1 < b ≤ 2, 2 - b, 0], D) → K'
  35. Segment(K, K') → f_1
  36. Rotate(C, If[2 < b ≤ 3, ((b - 2) * π), π], K) → C'_1
  37. Rotate(C', If[2 < b ≤ 3, ((b - 2) * π), π], K) → C''
  38. Segment(C'_1, C'') → t'
  39. Dilate(E, If[3 < b ≤ 4, 4 - b, 0], L) → E'
  40. Dilate(G, If[3 < b ≤ 4, 4 - b, 0], M) → G'
  41. Dilate(I, If[3 < b ≤ 4, 4 - b, 0], N) → I'
  42. Segment(E, E') → g_1
  43. Segment(G, G') → h_1
  44. Segment(I, I') → i_1
  45. Dilate(M, If[4 < b ≤ 5, 5 - b, 0], H) → M'
  46. Dilate(N, If[4 < b ≤ 5, 5 - b, 0], J) → N'
  47. Dilate(L, If[4 < b ≤ 5, 5 - b, 0], F) → L'
  48. Segment(L, L') → j_1
  49. Segment(M, M') → k_1
  50. Segment(N, N') → l_1
  51. Dilate(C, If[5 < b ≤ 6, 6 - b, 0], J) → C'_2
  52. Dilate(C, If[5 < b ≤ 6, 6 - b, 0], H) → C'_3
  53. Dilate(C, If[5 < b ≤ 6, 6 - b, 0], F) → C'_4
  54. Vector(C, C'_2) → u
  55. Vector(C, C'_3) → v
  56. Vector(C, C'_4) → w
  57. Translate(C, w) → C'_5
  58. Translate(C', w) → C''_1
  59. Segment(C'_5, C''_1) → t'_1
  60. Translate(C, v) → C'_6
  61. Translate(C', v) → C''_2
  62. Segment(C'_6, C''_2) → t'_2
  63. Translate(C, u) → C'_7
  64. Translate(C', u) → C''_3
  65. Segment(C'_7, C''_3) → t'_3
  66. Line(J, t) → m_1
  67. Line(F, t) → n_1
  68. Line(H, t) → p_1
  69. Point(m_1) → Q
  70. Angle(N, J, Q) → α
  71. Point(p_1) → R
  72. Point(n_1) → S
  73. Angle(S, F, L) → β
  74. Angle(R, H, G) → γ
  75. Rotate(C'_7, If[6 < b ≤ 7, ((-(b - 6)) * α), (-α)], J) → T
  76. Rotate(C''_3, If[6 < b ≤ 7, ((-(b - 6)) * α), (-α)], J) → U
  77. Segment(T, U) → q_1
  78. Rotate(C'_5, If[6 < b ≤ 7, ((b - 6) * β), β], F) → V
  79. Rotate(C''_1, If[6 < b ≤ 7, ((b - 6) * β), β], F) → W
  80. Segment(V, W) → r_1
  81. Rotate(C'_6, If[6 < b ≤ 7, ((b - 6) * γ), γ], H) → Z
  82. Rotate(C''_2, If[6 < b ≤ 7, ((b - 6) * γ), γ], H) → A_1
  83. Segment(Z, A_1) → s_1
  84. Rotate(T, If[7 < b ≤ 8, ((-(b - 7)) * π), (-π)], N) → T'
  85. Rotate(U, If[7 < b ≤ 8, ((b - 7) * π), π], N) → U'
  86. Segment(T', U') → t_1
  87. Rotate(V, If[7 < b ≤ 8, ((-(b - 7)) * π), (-π)], L) → V'
  88. Rotate(W, If[7 < b ≤ 8, ((b - 7) * π), π], L) → W'
  89. Segment(V', W') → a_1
  90. Rotate(Z, If[7 < b ≤ 8, ((-(b - 7)) * π), (-π)], M) → Z'
  91. Rotate(A_1, If[7 < b ≤ 8, ((b - 7) * π), π], M) → B_1
  92. Segment(Z', B_1) → b_1
  93. Dilate(M, If[8 < b ≤ 9, 9 - b, 0], L) → M'_1
  94. Dilate(N, If[8 < b ≤ 9, 9 - b, 0], K) → N'_2
  95. Segment(M, M'_1) → c_1
  96. Segment(N, N'_2) → f_2
  97. Dilate(M, If[8 < b ≤ 9, 9 - b, 0], K) → M'_2
  98. Segment(M, M'_2) → d_1
  99. Dilate(N, If[8 < b ≤ 9, 9 - b, 0], L) → N'_1
  100. Segment(N, N'_1) → e_1
  101. Angle(L, M, K) → δ
  102. Rotate(O, If[9 < b ≤ 10, ((b - 9) * δ), δ], M) → O'
  103. CircleSector(M, O, O') → c_2
  104. Dilate(M, If[10.5 < b ≤ 11.5, 11.5 - b, 0], N) → M'_3
  105. Vector(M, M'_3) → u_1
  106. Translate(s, u_1) → s'
  107. Line(N, d_1) → g_2
  108. Point(g_2) → C_1
  109. Angle(K, N, C_1) → ε
  110. Rotate(s', If[11.5 < b ≤ 12.5, ((b - 11.5) * ((2 * π) - ε)), (2 * π) - ε], N) → s''