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Polygon and Linear Regression Animation Demo

Polygon and Linear Regression Animation Demo
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2017-01-27 20:29
CirclePolygonSolid GeometryGeometric Construction
This example demonstrates geometric relationships and transformations involving polygons, linear regression, circles, prisms, and circumcircles through animation. Key math concepts include polygon construction, linear regression analysis, circle properties, prism volume calculation, and circumcircle determination. GeoGebra commands and objects used in construction are Polygon, Midpoint, Segment, Line, OrthogonalLine, Intersect, Angle, Dilate, Rotate, Vector, and Translate. Suitable for high school and above learners to understand the integration of spatial geometry and data analysis.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(B, E, 4) → poly2, j, k, l, m, F, G
  3. Midpoint(E, F) → H
  4. Segment(A, H) → n
  5. Segment(A, F) → p
  6. Segment(A, C) → q
  7. Segment(C, B) → r
  8. Line(A, C) → s
  9. OrthogonalLine(F, s) → t
  10. OrthogonalLine(D, q) → b
  11. OrthogonalLine(C, p) → c
  12. OrthogonalLine(H, p) → d
  13. Intersect(c, p) → I
  14. Intersect(d, p) → J
  15. Line(A, H) → e
  16. OrthogonalLine(F, e) → f_1
  17. OrthogonalLine(E, n) → g_1
  18. Intersect(e, g_1) → K
  19. Intersect(e, f_1) → L
  20. Intersect(b, q) → M
  21. Angle(C, M, D) → α
  22. Angle(C, I, A) → β
  23. Angle(H, J, F) → γ
  24. Intersect(s, t) → N
  25. Angle(C, N, F) → δ
  26. Angle(F, L, H) → ε
  27. Angle(A, K, E) → ζ
  28. Polygon(A, C, D) → poly3, d_1, a_1, c_1
  29. Polygon(A, F, C) → poly4, c_2, a_2, f_2
  30. Polygon(A, H, F) → poly5, f_3, a_3, h_1
  31. Polygon(A, E, H) → poly6, h_2, a_4, e_1
  32. Dilate(E, If[0 < o ≤ 1, 1 - o, 0], H) → E'
  33. Segment(E, E') → i_1
  34. Angle(F, E, B) → η
  35. Angle(D, F, E) → θ
  36. Angle(A, D, F) → ι
  37. Angle(E, A, D) → κ
  38. Rotate(E, If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], H) → E'_1
  39. Rotate(E', If[1 < o ≤ 2, ((-(o - 1)) * π), (-π)], H) → E''
  40. Segment(E'_1, E'') → j_1
  41. Dilate(F, If[2 < o ≤ 3, 3 - o, 0], G) → F'
  42. Rotate(E, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], F) → E'_2
  43. Rotate(E', If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], F) → E''_1
  44. Rotate(E'_1, If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], F) → O
  45. Rotate(E'', If[2 < o ≤ 3, ((-(o - 2)) * π / 2), ((-π)) / 2], F) → E'''
  46. Angle(D, C, B) → λ
  47. Angle(E, B, C) → μ
  48. Segment(A, E) → n_1
  49. Segment(D, A) → p_1
  50. Segment(D, C) → k_1
  51. Rotate(D, If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], G) → D'
  52. Rotate(C, If[2 < o ≤ 3, ((o - 2) * π / 2), π / 2], G) → C'
  53. Segment(D', C') → l_1
  54. Rotate(D', If[3 < o ≤ 4, ((o - 3) * π / 2), π / 2], G) → D''
  55. Rotate(C', If[3 < o ≤ 4, ((o - 3) * π / 2), π / 2], G) → C''
  56. Segment(D'', C'') → m_1
  57. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], G) → A'
  58. Segment(A, A') → q_1
  59. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], M) → D'_1
  60. Segment(D, D'_1) → r_1
  61. Dilate(G, If[5 < o ≤ 6, 6 - o, 0], N) → G'
  62. Dilate(F, If[5 < o ≤ 6, 6 - o, 0], N) → F'_1
  63. Segment(G, G') → s_1
  64. Segment(F, F'_1) → t_1
  65. Rotate(D, If[6 < o ≤ 7, ((o - 6) * π), π], G) → D'_2
  66. Rotate(D'_1, If[6 < o ≤ 7, ((o - 6) * π), π], G) → P
  67. Dilate(D, If[6 < o ≤ 7, 7 - o, 0], N) → D'_3
  68. Vector(D, D'_3) → u
  69. Translate(D, u) → D'_4
  70. Translate(D'_1, u) → Q
  71. Segment(D'_4, Q) → b_1
  72. Dilate(A, If[7 < o ≤ 8, 8 - o, 0], F) → A'_1
  73. Segment(A, A'_1) → g_2
  74. Dilate(G, If[8 < o ≤ 9, 9 - o, 0], I) → G'_1
  75. Dilate(H, If[8 < o ≤ 9, 9 - o, 0], J) → H'
  76. Segment(G, G'_1) → i_2
  77. Segment(H, H') → j_2
  78. Dilate(A, If[7 < o ≤ 8, 8 - o, 0], H) → A'_2
  79. Segment(A, A'_2) → k_2
  80. Dilate(G, If[9 < o ≤ 10, 10 - o, 0], J) → G'_2
  81. Vector(G, G'_2) → v
  82. Translate(G, v) → G'_3
  83. Translate(G'_1, v) → R
  84. Segment(G'_3, R) → l_2
  85. Dilate(H, If[10 < o ≤ 11, 11 - o, 0], L) → H'_1
  86. Dilate(F, If[10 < o ≤ 11, 11 - o, 0], L) → F'_2
  87. Segment(F, F'_2) → n_2
  88. Dilate(E, If[10 < o ≤ 11, 11 - o, 0], K) → E'_3
  89. Segment(E, E'_3) → m_2
  90. Segment(H, H'_1) → p_2
  91. Dilate(L, If[11 < o ≤ 12, 12 - o, 0], E) → L'
  92. Vector(L, L') → w
  93. Translate(F, w) → F'_3
  94. Translate(F'_2, w) → S
  95. Segment(F'_3, S) → q_2
  96. Dilate(D, If[0 < o ≤ 1, 1 - o, 0], G) → D'_5
  97. Segment(D, D'_5) → r_2

AI Drawing Prompt Reference

Draw a quadrilateral ABCD, then draw a quadrilateral BEFG. Find the midpoint H of E and F, connect AH and AF, then draw the perpendiculars t and b to AC and BC, and the perpendiculars c and d to AH and AF, find their intersections I and J, then draw AH and its perpendiculars f_1 and g_1, find their intersections with AC and AF to get K and L, then find the intersection M of b and q, calculate angles α, β, γ, δ, ε, and ζ, then draw triangles ACD, ACF, AHF, and AEH, then rotate E and E' around H, connect E' and E'', then rotate F and F' around G, rotate E', E''_1, and E''' around F, and finally calculate angles λ and μ.
The prompt above was compiled from the original drawing commands and is for reference only.