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Cubes Illusion III

Cubes Illusion III
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2018-11-19 18:27
PolygonSolid GeometryTransformationParametric EquationGraphing
This example demonstrates the projection and illusion phenomena of 3D cubes onto 2D planes. Core math concepts include solid geometry, polygons, geometric transformations, parametric equations, and function graphing. Construction highlights involve GeoGebra commands like If, Sequence, Polygon, Rotate, utilizing objects such as n, t, taux1, PtsC1, taux, Pts, PtsC, C1, f, g, h, i, j, etc., for dynamic visualization. Suitable for high school and above students studying applications of solid geometry, geometric transformations, and parametric equations.

GeoGebra Commands & Parameters

  1. If(0 ≤ t ≤ 1, 1.0E-5, If[1 < t ≤ 2, t - 1, 1]) → taux1
  2. Sequence(Rotate[((taux1 * cos(((i / n * 2) * π))), (taux1 * sin(((i / n * 2) * π)))), π / 6, (0, 0)], i, 1, n) → PtsC1
  3. If(0 ≤ t ≤ 1, t, 1) → taux
  4. Sequence(Rotate[(cos(((i / n * 2) * π)), sin(((i / n * 2) * π))), π / 6, (0, 0)], i, 1, n) → Pts
  5. Sequence(Rotate[((taux * cos(((i / n * 2) * π))), (taux * sin(((i / n * 2) * π)))), π / 6, (0, 0)], i, 1, n) → PtsC
  6. Polygon(Element[Pts, 2], Element[Pts, 3], Element[Pts, 4], (0, 0), Element[Pts, 2]) → C1, f, g, h, i, j
  7. Rotate(C1, (2 * π / 3), (0, 0)) → L1
  8. Rotate(C1, ((2 * 2) * π / 3), (0, 0)) → L2
  9. Rotate(C1, ((3 * 2) * π / 3), (0, 0)) → L3
  10. Polygon(Element[PtsC, 3], Element[PtsC, 4], Element[PtsC, 5], (0, 0), Element[PtsC, 3]) → C2, k, l, m, p, q
  11. Rotate(C2, (2 * π / 3), (0, 0)) → M1
  12. Rotate(C2, ((2 * 2) * π / 3), (0, 0)) → M2
  13. Polygon(Element[PtsC1, 2], Element[PtsC1, 3], Element[PtsC1, 4], (0, 0), Element[PtsC1, 2]) → C3, r, s, a, b, c
  14. Rotate(C2, ((3 * 2) * π / 3), (0, 0)) → M3
  15. Rotate(C3, (2 * π / 3), (0, 0)) → N1
  16. Rotate(C3, ((2 * 2) * π / 3), (0, 0)) → N2
  17. Rotate(C3, ((3 * 2) * π / 3), (0, 0)) → N3
  18. Sequence(Sequence[Translate[Translate[L1, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → L_1
  19. Sequence(Sequence[Translate[Translate[L2, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → L_2
  20. Sequence(Sequence[Translate[Translate[L3, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → L_3
  21. Sequence(Sequence[Translate[Translate[M1, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → M_1
  22. Sequence(Sequence[Translate[Translate[M2, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → M_2
  23. Sequence(Sequence[Translate[Translate[M3, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → M_3
  24. Sequence(Sequence[Translate[Translate[N1, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → N_1
  25. Sequence(Sequence[Translate[Translate[N2, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → N_2
  26. Sequence(Sequence[Translate[Translate[N3, Vector[(i * Vector[(0, 0), (0.43, 0.75)])]], Vector[(0, 0), (((j * 2) * 0.87), 0)]], i, 2, width, 2], j, 0, height) → N_3

AI Drawing Prompt Reference

Draw a 3D projection of a cube, including three rotated cube faces, each made up of four vertices. Use rotations and translations to generate multiple repeated cube faces, creating a 3D illusion of a cube.
The prompt above was compiled from the original drawing commands and is for reference only.