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Octagon Waterwheel Origami Animation

Octagon Waterwheel Origami Animation
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2020-07-17 00:33
PolygonSolid GeometryTransformationGeometric ConstructionSlider Animation
In collections Action Modular Origami
This GeoGebra example provides a dynamic animation of an octagon waterwheel model, inspired by the paper-folding designs in 'Action Modular Origami'. The construction demonstrates key mathematical concepts including polygonal symmetry, 3D spatial transformations, and geometric folding patterns. Technically, the model is built using the Sequence and Polygon commands for structural repetition, Vector and Translate for the mechanical movement, and the extrude command to transform 2D shapes into 3D solids. It also employs Intersect and Midpoint operations to maintain geometric precision. This tool is ideal for high school students studying solid geometry, educators demonstrating spatial visualization, and enthusiasts of mathematical origami.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Line(A, B) → q
  3. Polygon(A, B, 8) → poly1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  4. Line(A, D) → n
  5. Line(H, C) → n_1
  6. Intersect(n, n_1) → N
  7. OrthogonalLine(N, n_1) → p_1
  8. Intersect(q, p_1) → O
  9. Line(O, n) → q_1
  10. Line(B, E) → p
  11. Intersect(n, p) → I
  12. Intersect(q_1, p) → Q
  13. Line(B, C) → t
  14. OrthogonalLine(I, t) → a_1
  15. Intersect(t, a_1) → S
  16. Midpoint(A, E) → OO
  17. Vector(OO, OO') → u
  18. Translate(C, u) → C'
  19. OrthogonalLine(C, t) → d
  20. Intersect(p, d) → R
  21. Translate(R, u) → R'
  22. Point(q) → K
  23. Intersect(n, d) → M
  24. OrthogonalLine(K, d) → e
  25. Intersect(d, e) → L
  26. Translate(M, u) → M'
  27. Translate(L, u) → L'
  28. Line(C, D) → r
  29. Polygon(O, Q, I, S, B) → poly2, a, b, i_1, r_1, s_1
  30. Intersect(r, q) → J
  31. Polygon(O, Q, I, N) → poly3, c, f_1, g_1, h_1
  32. Sequence(Rotate[ListPoly1, β + (n * α), OO], n, 0, 3) → List1Poly
  33. Sequence(Rotate[ListPoly1, β + (0.5 * α) + (n * α), OO], n, 0, 3) → List2Poly
  34. OrthogonalLine(OO, xOyPlane) → s
  35. Translate(List1Poly, u) → List1Poly'
  36. Polygon(R, C, C', R') → poly4, j_1, k_1, l_1, m_1
  37. Translate(List2Poly, u) → List2Poly'
  38. Translate(J, u) → J'
  39. Sequence(Rotate[poly4, β + (0.5 * α) + (n * α), OO], n, 0, 3) → List2Side
  40. Sequence(Rotate[poly4, β + (n * α), OO], n, 0, 3) → List1Side
  41. Intersect(p_1, n) → P
  42. Sequence(Rotate[ListPoly3, β + α / 2 + (n * α), OO], n, 0, 3) → List4Poly
  43. Sequence(Rotate[ListPoly3, β + (n * α), OO], n, 0, 3) → List3Poly
  44. Translate(List3Poly, u) → List3Poly'
  45. Translate(List4Poly, u) → List4Poly'

AI Drawing Prompt Reference

Create an animated octagon waterwheel model, demonstrating dynamic movement. Start by constructing an octagonal base, then simulate the motion of the wheel's blades using rotation and translation. The animation showcases symmetry, 3D spatial transformations, and geometric folding patterns as the blades rotate around a central axis while maintaining precise geometric shapes.
The prompt above was compiled from the original drawing commands and is for reference only.