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Rectangle Transformation Demo

Rectangle Transformation Demo
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2020-12-03 21:02
VectorCoordinate GeometryTransformation
This example demonstrates geometric transformations of a rectangle through dynamic interaction, helping students intuitively understand transformation effects. Core math concepts include geometry transformation, vector, and coordinate geometry. Construction highlights the use of commands like Segment, Vector, Translate, Rotate in GeoGebra. Suitable for high school mathematics teaching on transformations and geometric properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Slope(a) → c
  3. OrthogonalLine(A, a) → e
  4. Point(e) → C
  5. Ray(A, C) → d
  6. Point(d) → D
  7. Segment(A, D) → f
  8. Line(D, a) → g
  9. Line(B, f) → h
  10. Intersect(g, h) → E
  11. Segment(D, E) → i
  12. Segment(E, B) → j
  13. Midpoint(A, E) → F
  14. Circle(A, (0.2 * Min[f, i])) → k
  15. Intersect(k, f) → G,
  16. Intersect(k, a, 1) → H
  17. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → A'
  18. Vector(A, A') → u
  19. CircleSector(A, H, G) → p
  20. Translate(p, u) → p'
  21. Rotate(p', If[1 < l ≤ 2, ((l - 1) * π / 2), 1.5707963267948966], B) → p''
  22. Dilate(B, If[2 < l ≤ 3, 3 - l, 0], E) → B'
  23. Vector(B, B') → v
  24. Translate(p'', v) → p'''
  25. Rotate(p''', If[3 < l ≤ 4, ((l - 3) * π / 2), 1.5707963267948966], E) → q
  26. Dilate(E, If[4 < l ≤ 5, 5 - l, 0], D) → E'
  27. Vector(E, E') → w
  28. Translate(q, w) → q'
  29. Rotate(q', If[5 < l ≤ 6, ((l - 5) * π / 2), 1.5707963267948966], D) → q''
  30. Dilate(D, If[6 < l ≤ 7, 7 - l, 0], F) → D'
  31. Vector(D, D') → m
  32. Segment(D, D') → n
  33. Dilate(F, If[7 < l ≤ 8, 8 - l, 0], B) → F'
  34. Segment(F, F') → r
  35. Dilate(A, If[8 < l ≤ 9, 9 - l, 0], F) → A'_1
  36. Segment(A, A'_1) → s
  37. Dilate(F, If[9 < l ≤ 10, 10 - l, 0], E) → F'_1
  38. Segment(F, F'_1) → t
  39. Polygon(A, B, E, D) → poly1, a_1, b_1, e_1, d_1
  40. Angle(E, F, D) → α
  41. Angle(B, A, F) → γ
  42. Angle(F, A, D) → δ
  43. Rotate(F, If[10 < l ≤ 11, ((l - 10) * α), α], F) → F'_2
  44. Rotate(F'_1, If[10 < l ≤ 11, ((l - 10) * α), α], F) → I
  45. Segment(F'_2, I) → t'
  46. Rotate(F'_2, If[11 < l ≤ 12, ((l - 11) * (π - α)), π - α], F) → J
  47. Rotate(I, If[11 < l ≤ 12, ((l - 11) * (π - α)), π - α], F) → I'
  48. Segment(J, I') → t''
  49. Rotate(J, If[12 < l ≤ 13, ((l - 12) * α), α], F) → J'
  50. Rotate(I', If[12 < l ≤ 13, ((l - 12) * α), α], F) → I''
  51. Segment(J', I'') → t'''
  52. Segment(A, F) → c_1
  53. Intersect(k, c_1) → K,
  54. CircleSector(A, H, K) → f_1
  55. CircleSector(A, K, G) → g_1
  56. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], E) → A'_2
  57. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], B) → A'_3
  58. Dilate(A, If[16 < l ≤ 17, 17 - l, 0], D) → A'_4
  59. Vector(A, A'_3) → u_1
  60. Vector(A, A'_2) → v_1
  61. Vector(A, A'_4) → w_1
  62. Translate(f_1, u_1) → h_1
  63. Translate(f_1, v_1) → k_1
  64. Translate(f_1, w_1) → p_1
  65. Rotate(h_1, If[17 < l ≤ 18, ((l - 17) * (π / 2 + δ)), π / 2 + δ], B) → q_1
  66. Rotate(p_1, If[17 < l ≤ 18, ((l - 17) * ((3 * π / 2) + δ)), (3 * π / 2) + δ], D) → r_1
  67. Rotate(k_1, If[17 < l ≤ 18, ((l - 17) * π), 3.141592653589793], E) → s_1
  68. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], E) → A'_5
  69. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], D) → A'_6
  70. Dilate(A, If[18 < l ≤ 19, 19 - l, 0], B) → A'_7
  71. Vector(A, A'_7) → i_1
  72. Vector(A, A'_5) → j_1
  73. Vector(A, A'_6) → l_1
  74. Translate(g_1, l_1) → t_1
  75. Translate(g_1, j_1) → c_2
  76. Translate(g_1, i_1) → d_2
  77. Rotate(d_2, If[19 < l ≤ 20, ((l - 19) * δ), δ], B) → e_2
  78. Rotate(c_2, If[19 < l ≤ 20, ((-(l - 19)) * π), -3.141592653589793], E) → f_2
  79. Rotate(t_1, If[19 < l ≤ 20, ((l - 19) * (π + δ)), π + δ], D) → g_2

AI Drawing Prompt Reference

Draw a rectangle ABCD, then perform a scaling transformation around point A, followed by a rotation transformation around point B, and then a rotation and scaling transformation around point D, and finally a rotation and scaling transformation around point E, to form a series of transformed rectangles and triangles, resulting in a complex geometric shape.
The prompt above was compiled from the original drawing commands and is for reference only.