Rotation Animation to Show Circle Symmetry

Rotation Animation to Show Circle Symmetry
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2016-10-20 05:20
This example uses rotation animation to demonstrate the symmetry of a circle. Key mathematical concepts include the properties of circles and rotation transformations. Using GeoGebra commands such as Ray, Rotate, Circle, CircleSector, Dilate, etc., a dynamic display of circle symmetry is constructed. Suitable for middle school and above students to learn about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Ray(A, B') → g
  5. Circle(A, 1) → c
  6. Line(B, A) → h
  7. Intersect(c, h, 2) → C
  8. Ray(A, C) → i
  9. Ray(D, E) → j
  10. Rotate(E, α, D) → E'
  11. Angle(E, D, E') → γ
  12. Ray(D, E') → k
  13. Line(E, D) → l
  14. Circle(D, 1) → d
  15. Intersect(d, l, 2) → F
  16. Ray(D, F) → m
  17. LaTeX(B', true, true) → text1
  18. Circle(D, 2) → e
  19. Intersect(e, j, 1) → G
  20. Intersect(e, k, 1) → H
  21. Line(D, i) → n
  22. CircleSector(D, G, H) → p
  23. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], A) → D'
  24. Vector(D, D') → u
  25. Translate(p, u) → p'
  26. Point(n) → I
  27. Angle(I, D, E') → δ
  28. Line(D, g) → q
  29. Intersect(e, q, 2) → J
  30. Angle(H, D, J) → ε
  31. Rotate(p', If[0 < a ≤ 1, (a * ε), ε], D') → p''
  32. CircleArc(D, G, H) → r
  33. Intersect(e, m) → K,
  34. CircleSector(D, H, K) → s
  35. Dilate(D, If[2.75 < a ≤ 3.75, 3.75 - a, 0], A) → D'_1
  36. Vector(D, D'_1) → v
  37. Translate(s, v) → s'
  38. Rotate(s', If[2.75 < a ≤ 3.75, ((a - 2.75) * ε), ε], D'_1) → s''
  39. CircleArc(D, H, K) → t

AI Drawing Prompt Reference

Draw a circle and demonstrate its symmetry by rotating it around the center. First, draw a ray, then rotate the circle around the center, and draw tangents and arcs. Use rotation and scaling to dynamically show the circle's symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.