MathPlotAI Logo MathPlotAI

Animation Demonstrating Polygons and Geometric Transformations

Animation Demonstrating Polygons and Geometric Transformations
Loading the math board and drawing, please wait…
2017-02-14 20:13
PolygonVectorCalculusGeometric Construction
This example demonstrates the rotation, translation, and dilation of polygons and triangles through animation. It involves core mathematical concepts such as polygon construction, vector operations, angle calculations, function graphs, and calculus. GeoGebra commands like Rotate, Ray, Point, Segment, Circle, Intersect, Line, Angle, Min, CircleSector, Dilate, Vector, Translate, Polygon, and OrthogonalLine are used in the construction. Suitable for high school and above students to understand geometric transformations and advanced mathematical applications.

GeoGebra Commands & Parameters

  1. Rotate(A, 108°, B) → A'
  2. Ray(B, A') → g
  3. Ray(B, A) → f
  4. Point(f) → C
  5. Segment(C, B) → n
  6. Circle(C, n) → d_1
  7. Rotate(B, (-(108°)), C) → B'
  8. Ray(C, B') → h
  9. Intersect(d_1, h, 1) → G
  10. Circle(G, n) → e_1
  11. Point(h) → D
  12. Rotate(C, (-(108°)), D) → C'
  13. Ray(D, C') → i
  14. Point(i) → E
  15. Rotate(D, (-(108°)), E) → D'
  16. Ray(E, D') → j
  17. Intersect(g, j) → F
  18. Segment(F, E) → k
  19. Segment(E, D) → l
  20. Line(G, l) → g_1
  21. Intersect(e_1, g_1, 1) → J
  22. Line(J, k) → h_1
  23. Intersect(h_1, g) → K
  24. Angle(A, B, A') → α
  25. Angle(B', C, B) → β
  26. Angle(C', D, C) → γ
  27. Angle(D', E, D) → δ
  28. Segment(D, C) → m
  29. Segment(B, F) → p
  30. Min(list) → a
  31. Circle(B, (0.2 * n)) → q
  32. Intersect(q, p) → H,
  33. Intersect(q, n) → I,
  34. CircleSector(B, I, H) → r
  35. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], C) → B'_1
  36. Vector(B, B'_1) → u
  37. Translate(r, u) → r'
  38. Rotate(r', If[1 < o ≤ 2, (((o - 1) * 2) * π / 5), (2 * π / 5)], C) → r''
  39. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], G) → C'_1
  40. Vector(C, C'_1) → v
  41. Translate(r'', v) → r'''
  42. Rotate(r''', If[3 < o ≤ 4, (((o - 3) * 2) * π / 5), (2 * π / 5)], G) → s
  43. Dilate(G, If[4 < o ≤ 5, 5 - o, 0], J) → D'_1
  44. Vector(G, D'_1) → w
  45. Translate(s, w) → s'
  46. Rotate(s', If[5 < o ≤ 6, (((o - 5) * 2) * π / 5), (2 * π / 5)], J) → s''
  47. Dilate(J, If[6 < o ≤ 7, 7 - o, 0], K) → E'
  48. Vector(J, E') → t
  49. Translate(s'', t) → s'''
  50. Circle(J, n) → k_1
  51. Rotate(s''', If[7 < o ≤ 8, (((o - 7) * 2) * π / 5), (2 * π / 5)], K) → c_1
  52. Segment(B, B'_1) → b
  53. Segment(C, C'_1) → c
  54. Segment(G, D'_1) → d
  55. Segment(J, E') → e
  56. Dilate(K, If[8 < o ≤ 9, 9 - o, 0], B) → K'
  57. Segment(K, K') → f_1
  58. Polygon(B, C, G, J, K) → poly1, b_1, c_2, g_2, j_1, k_2
  59. Rotate(B, If[9 < o ≤ 10, ((-(o - 9)) * α), (-α)], C) → B'_2
  60. Rotate(B'_1, If[9 < o ≤ 10, ((-(o - 9)) * α), (-α)], C) → L
  61. Segment(B'_2, L) → b'
  62. Rotate(B'_2, If[10 < o ≤ 11, ((-(o - 10)) * α), (-α)], G) → M
  63. Rotate(L, If[10 < o ≤ 11, ((-(o - 10)) * α), (-α)], G) → L'
  64. Segment(M, L') → b''
  65. Rotate(M, If[11 < o ≤ 12, ((-(o - 11)) * α), (-α)], J) → M'
  66. Rotate(L', If[12 < o ≤ 13, ((-(o - 12)) * α), (-α)], J) → L''
  67. Segment(M', L'') → b'''
  68. Rotate(M', If[12 < o ≤ 13, ((-(o - 12)) * α), (-α)], K) → M''
  69. Rotate(L'', If[12 < o ≤ 13, ((-(o - 12)) * α), (-α)], K) → L'''
  70. Segment(M'', L''') → i_1
  71. Segment(J, B) → l_1
  72. Segment(C, J) → m_1
  73. Point(b'') → N
  74. Segment(K, C) → n_1
  75. Segment(N, C) → p_1
  76. Segment(N, K) → q_1
  77. OrthogonalLine(N, n_1) → r_1
  78. Intersect(r_1, n_1) → O
  79. OrthogonalLine(B, m_1) → s_1
  80. Intersect(s_1, m_1) → P
  81. Polygon(B, C, J) → poly2, j_2, b_2, c_3
  82. Segment(N, O) → t_1
  83. Segment(B, P) → a_1
  84. Dilate(B, If[15 < o ≤ 16, 16 - o, 0], J) → B'_3
  85. Segment(B, B'_3) → f_2
  86. Dilate(C, If[15 < o ≤ 16, 16 - o, 0], J) → C'_2
  87. Segment(C, C'_2) → h_2
  88. Angle(J, P, B) → ε
  89. Rotate(B, If[16 < o ≤ 17, ((o - 16) * α / 3), α / 3], J) → B'_4
  90. Rotate(B'_3, If[16 < o ≤ 17, ((o - 16) * α / 3), α / 3], J) → Q
  91. Segment(B'_4, Q) → i_2
  92. Dilate(B, If[17 < o ≤ 18, 18 - o, 0], P) → B'_5
  93. Segment(B, B'_5) → l_2
  94. Rotate(B'_4, If[18 < o ≤ 19, ((o - 18) * α / 3), α / 3], C) → R
  95. Rotate(Q, If[18 < o ≤ 19, ((o - 18) * α / 3), α / 3], C) → Q'
  96. Segment(R, Q') → m_2
  97. Dilate(K, If[19 < o ≤ 20, 20 - o, 0], N) → K'_1
  98. Dilate(C, If[19 < o ≤ 20, 20 - o, 0], N) → C'_3
  99. Segment(K, K'_1) → n_2
  100. Segment(C, C'_3) → p_2
  101. Polygon(K, C, N) → poly3, n_3, k_3, c_4
  102. Line(O, l_2) → q_2
  103. Circle(O, 5) → d_2
  104. Intersect(d_2, q_2, 2) → S
  105. Angle(S, O, N) → ζ
  106. Dilate(N, If[20.5 < o ≤ 21.5, 21.5 - o, 0], O) → N'
  107. Segment(N, N') → r_2
  108. Angle(N, O, K) → η
  109. Dilate(B, If[21.5 < o ≤ 22.5, 22.5 - o, 0], O) → B'_6
  110. Vector(B, B'_6) → u_1
  111. Translate(B, u_1) → B'_7
  112. Translate(B'_5, u_1) → T
  113. Segment(B'_7, T) → s_2
  114. Rotate(B'_7, If[22.5 < o ≤ 23.5, ((o - 22.5) * α / 3), α / 3], O) → U
  115. Rotate(T, If[22.5 < o ≤ 23.5, ((o - 22.5) * α / 3), α / 3], O) → T'
  116. Segment(U, T') → t_2

AI Drawing Prompt Reference

Draw a triangle ABC, then rotate it 108 degrees around point B to get A', and draw rays from B to A' and from B to A, finding their intersection point C. Use C as the center and BC as the radius to draw a circle, then rotate B around C to get B', and draw a ray from C to B', finding their intersection point G. Continue this process to construct a series of related shapes, including circles, line segments, angles, and scaling transformations, ultimately forming a dynamic geometric transformation animation.
The prompt above was compiled from the original drawing commands and is for reference only.