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Rotating Cubes

Rotating Cubes
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2019-04-02 23:19
Solid GeometryTransformationGeometric Construction
This example demonstrates rotating cubes. It involves 3D geometry transformations. Using Vector, Rotate, Sequence, Polygon, and other GeoGebra commands, dynamic rotating cubes can be constructed. Suitable for high school and above students or teachers for geometry instruction.

GeoGebra Commands & Parameters

  1. Vector((0, 0), (3^(0.5), 3)) → v
  2. Vector((0, 0), ((2 * 3^(0.5)), 0)) → u
  3. Rotate(D, α, (0, 1)) → D'
  4. Rotate(C, α, (0, 1)) → C'
  5. Rotate(B, α, (0, 1)) → B'
  6. Rotate(A, α, (0, 1)) → A'
  7. Sequence(Polygon[Translate[A', Vector[(u * mmm)]], Translate[C', Vector[(u * mmm)]], Translate[B', Vector[(u * mmm)]], Translate[D', Vector[(u * mmm)]]], mmm, -4, 4, 1) → L_9
  8. Polygon(A', C', B', D') → q1, a', c', b', d'
  9. Sequence(Translate[L_9, Vector[(v * mmm)]], mmm, -5, 5, 1) → L_2
  10. Rotate(L_2, (2 * π / 3), (0, 1)) → L_3
  11. Rotate(L_2, (4 * π / 3), (0, 1)) → L_4
  12. Rotate(L_2, 0, (0, 1)) → L_5
  13. Rotate(E, α, (0, 5)) → E'
  14. Rotate(F, α, (0, 5)) → F'
  15. Rotate(G, α, (0, 5)) → G'
  16. Rotate(H, α, (0, 5)) → H'
  17. Polygon(E', F', G', H') → q2, e', f', g', h'
  18. Sequence(Polygon[Translate[E', Vector[(u * mmm)]], Translate[F', Vector[(u * mmm)]], Translate[G', Vector[(u * mmm)]], Translate[H', Vector[(u * mmm)]]], mmm, -5, 5, 1) → L_1
  19. Sequence(Translate[L_1, Vector[(v * mmm)]], mmm, -5, 5, 1) → L_6
  20. Rotate(L_6, (2 * π / 3), (3^(0.5), 2)) → L_7
  21. Rotate(L_6, (4 * π / 3), (3^(0.5), 2)) → L_8
  22. Rotate(L_6, 0, (3^(0.5), 2)) → L_{10}
  23. If(α < (2 * π / 3) ∨ α > (4 * π / 3) ∧ α < (2 * π) ∨ α > (8 * π / 3) ∧ α < (10 * π / 3), 1, 0) → aa