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Rotating Planes

Rotating Planes
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2015-07-29 11:08
VectorSequenceTransformationGeometric Construction
This example demonstrates dynamic symmetry and design involving rotating planes. The core math concepts include vector, point, sequence, and rotation. It is constructed using GeoGebra commands like Vector, Point, Sequence, and Rotate. Suitable for high school and above students to understand dynamic geometry and symmetric design.

GeoGebra Commands & Parameters

  1. Vector(C, B) → u
  2. Point(Ray[C, Vector[Rotate[u, (360 * ° / m), C]]]) → D
  3. Sequence(Dilate[A, (N - i) / N, E], i, 0, N) → list1
  4. Sequence(Dilate[B, (N - i) / N, E], i, 0, N) → list2
  5. Sequence(Dilate[C, (N - i) / N, E], i, 0, N) → list3
  6. Sequence(Dilate[D, (N - i) / N, E], i, 0, N) → list4
  7. Sequence(Polygon[Between[Element[list1, i], Element[list2, i], (r * (i - 1) / N)], Between[Element[list2, i], Element[list3, i], (r * (i - 1) / N)], Between[Element[list3, i], Element[list4, i], (r * (i - 1) / N)], Between[Element[list4, i], Element[list1, i], (r * (i - 1) / N)]], i, 1, N + 1) → list6
  8. Rotate(list6, (360 * ° / m), C) → list6'
  9. Rotate(list6, (720 * ° / m), C) → list6'_1
  10. Rotate(list6, (1080 * ° / m), C) → list6'_2
  11. Rotate(list6, (1440 * ° / m), C) → list6'_3
  12. Rotate(list6, (1800 * ° / m), C) → list6'_4
  13. Rotate(list6, (2160 * ° / m), C) → list6'_5
  14. Rotate(list6, (2520 * ° / m), C) → list6'_6