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Animated Rotations Sequences with Color Changes

Animated Rotations Sequences with Color Changes
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2019-08-27 07:56
SequenceCoordinate GeometryTransformation
This example demonstrates the dynamic sequences of arcs rotating and moving, with color changes to enhance visual effects. Key mathematical concepts include rotation, sequences, and coordinate geometry. Using GeoGebra commands such as Rotate, Midpoint, Circle, CircumcircleArc, Sequence, Vector, Translate, Element, and Mirror, a series of rotating, translating, and reflecting arcs can be constructed. Suitable for high school mathematics education and learning, particularly in coordinate geometry and transformation geometry.

GeoGebra Commands & Parameters

  1. Rotate(B, α, A) → B'
  2. Midpoint(A, B) → C
  3. Circle(A, B) → c
  4. CircumcircleArc(A, C, B') → d
  5. Sequence(CircumcircleArc[Rotate[A, k, A], Rotate[C, k, A], Rotate[B', k, A]], k, 0, (2 * π), ((2 * π)) / n) → L_1
  6. Vector(A, D) → u
  7. Translate(L_1, u) → L_2
  8. Element(L_1, 2) → e
  9. Element(L_1, 1) → f
  10. Mirror(L_1, D) → l1
  11. Sequence(CircumcircleArc[Rotate[A, k, A], Rotate[C, k, A], Rotate[B', k, A]], k, 0, (2 * π), ((2 * π)) / n) → l2
  12. Sequence(CircumcircleArc[Rotate[A, (-k), A], Rotate[C, (-k), A], Rotate[B', (-k), A]], k, 0, (2 * π), ((2 * π)) / n) → l3
  13. Sequence(Ellipse[Rotate[A, k, A], Rotate[C, k, A], Rotate[B', k, A]], k, 0, (2 * π), ((2 * π)) / n) → l4
  14. Sequence(Ellipse[Rotate[A, k, A], Rotate[C, k, A], Rotate[B', k, A]], k, 0, (2 * π), ((2 * π)) / n) → l5
  15. Sequence(Hyperbola[Rotate[A, k, A], Rotate[C, k, A], Rotate[B', k, A]], k, 0, (2 * π), ((2 * π)) / n) → l6