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Circumference Animation

Circumference Animation
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2015-11-27 03:18
CircleTransformationSlider Animation
This example demonstrates an animation of a circle's circumference. Key mathematical concepts include the circumference formula and rotation transformations. Using GeoGebra commands such as Rotate, CircleArc, and Dilate, the animation dynamically shows the changes in the circle's circumference. Suitable for middle school and above students to learn basic properties of circles and geometric transformations.

GeoGebra Commands & Parameters

  1. Center(c) → A
  2. Segment(C, B) → b
  3. Rotate(B, 114.59155902616465°, A) → B'
  4. Angle(B, A, B') → α
  5. Rotate(B', 114.59155902616465°, A) → B''
  6. Angle(B', A, B'') → β
  7. Rotate(B'', 114.59155902616465°, A) → B'''
  8. Angle(B'', A, B''') → γ
  9. Rotate(B, If[0 < d < 1, (d * α), α], A) → B'_1
  10. CircleArc(A, B, B'_1) → e
  11. Dilate(C, If[0 < d < 1, 1 - d, 0], B) → C'
  12. Segment(C', B) → f
  13. Segment(C', C) → g
  14. Rotate(e, If[1.2 ≤ d ≤ 2.2, ((d - 1.2) * α), α], A) → e'
  15. Dilate(C, If[1.2 < d < 2.2, 2.2 - d, 0], B) → C'_1
  16. Segment(C'_1, B) → h
  17. Segment(C, C'_1) → i
  18. Rotate(B, If[1.2 < d < 2.2, ((d - 1.2) * α), α], A) → B'_2
  19. CircleArc(A, B, B'_2) → k
  20. Dilate(C, If[2.4 < d < 3.4, 3.4 - d, 0], B) → C'_2
  21. Segment(C'_2, B) → j
  22. Segment(C, C'_2) → l
  23. Rotate(B, If[2.4 < d < 3.4, ((d - 2.4) * α), α], A) → B'_3
  24. CircleArc(A, B, B'_3) → p
  25. Rotate(e', If[2.4 ≤ d ≤ 3.4, ((d - 2.4) * α), α], A) → e''
  26. Rotate(k, If[2.4 ≤ d ≤ 3.4, ((d - 2.4) * α), α], A) → k'
  27. CircleArc(A, B, B') → q
  28. CircleArc(A, B''', B) → r
  29. CircleArc(A, B, B') → s
  30. CircleArc(A, B', B'') → t
  31. CircleArc(A, B'', B''') → c_1
  32. CircleArc(A, B''', B) → d_1