MathPlotAI Logo MathPlotAI

Shaky Shuriken Star (Centred Slide)

Shaky Shuriken Star (Centred Slide)
Loading the math board and drawing, please wait…
2020-07-16 04:07
PolygonVectorTransformationGeometric Construction
In collections Action Modular Origami
This example demonstrates an animation of a paper model folded from the book 'Action Modular Origami' by Tarquin, showcasing dynamic transformations through centred sliding. It involves core mathematical concepts like vectors, geometric transformations, polygon construction, and linear functions. The construction utilizes commands such as Dilate, Segment, Point, Polygon, Rotate, Intersect, Vector, Translate, and OrthogonalLine. Suitable for high school students to explore geometric transformations and the integration of functional graphs with real-world models.

GeoGebra Commands & Parameters

  1. Dilate(F, frac, E) → F'
  2. Segment(E, F) → f
  3. Point(xAxis) → B
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Rotate(A, 90°, OO) → A'
  6. Rotate(B, 90°, OO) → B'
  7. Rotate(C, 90°, OO) → C'
  8. Rotate(D, 90°, OO) → D'
  9. Polygon(A', B', C', D') → poly1', a', b', c', d'
  10. Rotate(A, 180°, OO) → A'_1
  11. Rotate(B, 180°, OO) → B'_1
  12. Rotate(C, 180°, OO) → C'_1
  13. Rotate(D, 180°, OO) → D'_1
  14. Polygon(A'_1, B'_1, C'_1, D'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1
  15. Rotate(A, 270°, OO) → A'_2
  16. Rotate(B, 270°, OO) → B'_2
  17. Rotate(C, 270°, OO) → C'_2
  18. Rotate(D, 270°, OO) → D'_2
  19. Polygon(A'_2, B'_2, C'_2, D'_2) → poly1'_2, a'_2, b'_2, c'_2, d'_2
  20. Intersect(a'_2, poly1'_2) → G, H
  21. Intersect(a'_1, a'_2) → I
  22. Polygon(I, A'_1, D'_2, A'_2) → poly2, i, a'_3, d'_3, a'_4
  23. Intersect(c'_1, a'_2) → J
  24. Polygon(J, D'_1, C'_2, B'_2) → poly3, j, d'_4, c'_3, b'_3
  25. Intersect(a'_4, a) → K
  26. Polygon(A'_2, K, A, D) → poly4, a'_5, k, a_1, d_1
  27. Vector(OO, E) → u
  28. Translate(A, u) → A'_3
  29. Translate(B, u) → B'_3
  30. Translate(C, u) → C'_3
  31. Translate(D, u) → D'_3
  32. Polygon(A'_3, B'_3, C'_3, D'_3) → poly1'_3, a'_6, b'_4, c'_4, d'_5
  33. Translate(A', u) → A''
  34. Translate(B', u) → B''
  35. Translate(C', u) → C''
  36. Translate(D', u) → D''
  37. Polygon(A'', B'', C'', D'') → poly1'', a'', b'', c'', d''
  38. Translate(A'_1, u) → L
  39. Translate(B'_1, u) → M
  40. Translate(C'_1, u) → N
  41. Translate(D'_1, u) → O
  42. Polygon(L, M, N, O) → poly5, l, m, n, o
  43. Translate(I, u) → I'
  44. Translate(A'_1, u) → P
  45. Translate(D'_2, u) → Q
  46. Translate(A'_2, u) → R
  47. Polygon(I', P, Q, R) → poly2', i', p, q, r
  48. Translate(J, u) → J'
  49. Translate(D'_1, u) → S
  50. Translate(C'_2, u) → T
  51. Translate(B'_2, u) → U
  52. Polygon(J', S, T, U) → poly3', j', s, t, u_1
  53. Polygon(D'', C'', 4) → poly6, g, h, e, f_1, V, W
  54. Segment(D'', V) → g_1
  55. Dilate(C'', cut, V) → C'''
  56. OrthogonalLine(C''', h) → h_1
  57. Intersect(h_1, g_1) → Z
  58. Polygon(C''', C'', D'', Z) → poly7, c''', c''_1, d''_1, z_1
  59. Rotate(C''', 90°, E) → A_1
  60. Rotate(C'', 90°, E) → C'''_1
  61. Rotate(D'', 90°, E) → D'''
  62. Rotate(Z, 90°, E) → Z'
  63. Polygon(A_1, C'''_1, D''', Z') → poly7', a_2, c'''_1, d''', z'
  64. Rotate(C''', 180°, E) → B_1
  65. Rotate(C'', 180°, E) → C'''_2
  66. Rotate(D'', 180°, E) → D'''_1
  67. Rotate(Z, 180°, E) → Z'_1
  68. Polygon(B_1, C'''_2, D'''_1, Z'_1) → poly7'_1, b_1, c'''_2, d'''_1, z'_1
  69. Rotate(C''', 270°, E) → C_1
  70. Rotate(C'', 270°, E) → C'''_3
  71. Rotate(D'', 270°, E) → D'''_2
  72. Rotate(Z, 270°, E) → Z'_2
  73. Polygon(C_1, C'''_3, D'''_2, Z'_2) → poly7'_2, c_1, c'''_3, d'''_2, z'_2

AI Drawing Prompt Reference

Draw a dynamic origami star formed by four squares rotating around a common center. Start with a base square, then rotate it by 90, 180, and 270 degrees to create three additional squares. Use the intersections of adjacent square edges to construct four extra polygons, forming a folded star shape. Finally, translate all shapes along a fixed vector to create a set of offset overlapping copies, simulating a sliding paper animation. The composition is symmetric, layered, and demonstrates geometric transformations combined with linear motion.
The prompt above was compiled from the original drawing commands and is for reference only.