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Geometric Transformations of a Cube

Geometric Transformations of a Cube
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2018-06-02 23:59
VectorSolid GeometryTransformation
This example demonstrates geometric transformations of a cube, including rotation, translation, and similarity. Key mathematical concepts include vectors, functions, and transformations. Using GeoGebra commands such as Segment, Rotate, Translate, etc., it dynamically illustrates these transformations. Suitable for high school mathematics education and learning about solid geometry transformations.

GeoGebra Commands & Parameters

  1. Segment(A_1, B_1) → f
  2. Rotate(D_1, 30°, B_1) → D'
  3. Angle(D_1, B_1, D') → β
  4. Rotate(A_1, 60°, B_1) → A'
  5. Rotate(B_1, 60°, B_1) → B'
  6. Segment(A', B') → f'
  7. Rotate(A_1, (-(60°)), B_1) → A'_1
  8. Rotate(B_1, (-(60°)), B_1) → B'_1
  9. Segment(A'_1, B'_1) → f'_1
  10. Vector(B_1, A') → u
  11. Vector(B_1, A'_1) → v
  12. Translate(A_1, u) → A'_2
  13. Translate(B_1, u) → B'_2
  14. Segment(A'_2, B'_2) → f'_2
  15. Translate(A_1, v) → A'_3
  16. Translate(B_1, v) → B'_3
  17. Segment(A'_3, B'_3) → f'_3
  18. Segment(A_1, A'_3) → h
  19. Vector(A_1, A'_2) → w
  20. Translate(A_1, w) → A'_4
  21. Translate(A'_3, w) → E_1
  22. Segment(A'_4, E_1) → h'
  23. Vector(A_1, A'_3) → a
  24. Translate(A_1, a) → A'_5
  25. Translate(A'_2, a) → F_1
  26. Segment(A'_5, F_1) → g'
  27. Sequence((i / n * A_1) + ((n - i) / n * B'_1), i, 0, n) → L_1
  28. Segment(A_1, A'_2) → g
  29. Sequence((i / n * A'_4) + ((n - i) / n * A_1), i, 0, n) → L_2
  30. Sequence((i / n * B'_2) + ((n - i) / n * A'_4), i, 0, n) → L_3
  31. Sequence((i / n * B'_1) + ((n - i) / n * B'_2), i, 0, n) → L_4
  32. Sequence((i / n * A'_5) + ((n - i) / n * A_1), i, 0, n) → L_5
  33. Sequence((i / n * B'_3) + ((n - i) / n * A'_5), i, 0, n) → L_6
  34. Sequence((i / n * B'_1) + ((n - i) / n * B'_3), i, 0, n) → L_7
  35. Sequence((i / n * E_1) + ((n - i) / n * A'_4), i, 0, n) → L_8
  36. Sequence((i / n * A'_5) + ((n - i) / n * E_1), i, 0, n) → L_9
  37. Sequence(Segment[Element[L_1, i], Element[L_2, i]], i, 1, n + 1) → L_{10}
  38. Sequence(Segment[Element[L_2, i], Element[L_3, i]], i, 1, n + 1) → L_{11}
  39. Sequence(Segment[Element[L_3, i], Element[L_4, i]], i, 1, n + 1) → L_{12}
  40. Sequence(Segment[Element[L_4, i], Element[L_1, i]], i, 1, n + 1) → L_{13}
  41. Sequence(Segment[Element[L_1, i], Element[L_5, i]], i, 1, n + 1) → L_{14}
  42. Sequence(Segment[Element[L_5, i], Element[L_6, i]], i, 1, n + 1) → L_{15}
  43. Sequence(Segment[Element[L_6, i], Element[L_7, i]], i, 1, n + 1) → L_{16}
  44. Sequence(Segment[Element[L_7, i], Element[L_1, i]], i, 1, n + 1) → L_{17}
  45. Sequence(Segment[Element[L_2, i], Element[L_8, i]], i, 1, n + 1) → L_{18}
  46. Sequence(Segment[Element[L_8, i], Element[L_9, i]], i, 1, n + 1) → L_{19}
  47. Sequence((i / n * F_1) + ((n - i) / n * A'_5), i, 0, n) → L_{21}
  48. Sequence(Segment[Element[L_{21}, i], Element[L_5, i]], i, 1, n + 1) → L_{20}
  49. Sequence(Segment[Element[L_5, i], Element[L_2, i]], i, 1, n + 1) → L_{22}
  50. Sequence((i / n * A_1) + ((n - i) / n * A'_3), i, 0, n) → L_{23}
  51. Sequence(Segment[Element[L_{23}, i], Element[L_2, i]], i, 1, n + 1) → L_{24}