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Circle Circumference Animation

Circle Circumference Animation
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2015-11-27 10:33
CircleFunctionGeometric Construction
This example demonstrates the calculation and geometric transformations of a circle's circumference through animation. Key math concepts include circle, linear functions, polynomial functions, Pythagorean theorem, and linear transformations. GeoGebra commands used in construction are Center, Rotate, Angle, CircleArc, Dilate, Segment, and Point. Suitable for high school mathematics education to understand the circumference formula and applications of geometric transformations.

GeoGebra Commands & Parameters

  1. Center(c) → B
  2. Rotate(A, 1, B) → A'
  3. Angle(A, B, A') → α
  4. Rotate(A', 1, B) → A''
  5. Angle(A', B, A'') → β
  6. Rotate(A'', 1, B) → A'''
  7. Angle(A'', B, A''') → γ
  8. Rotate(A''', 1, B) → C
  9. Angle(A''', B, C) → δ
  10. Rotate(C, 1, B) → C'
  11. Angle(C, B, C') → ε
  12. Rotate(C', 1, B) → C''
  13. Angle(C', B, C'') → ζ
  14. CircleArc(B, A, A') → d
  15. CircleArc(B, A', A'') → e
  16. CircleArc(B, A'', A''') → f
  17. CircleArc(B, A''', C) → g
  18. CircleArc(B, C, C') → h
  19. CircleArc(B, C', C'') → k
  20. Rotate(A, If[0 ≤ a ≤ 1, (a * α), α], B) → A'_1
  21. CircleArc(B, A, A'_1) → p
  22. Dilate(B, If[0 ≤ a ≤ 1, 1 - a, 0], A) → B'
  23. Segment(B', A) → b
  24. CircleArc(B, C'', A) → q
  25. CircleArc(B, A'_1, A') → s
  26. Segment(B, B') → j
  27. Segment(B, A') → l
  28. Point(h) → D
  29. Segment(B, D) → Radius
  30. Rotate(B', If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → B''
  31. Rotate(d, If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → d'
  32. CircleArc(B, A, B'') → t
  33. Dilate(B, If[1.2 ≤ a ≤ 2.2, 2.2 - a, 0], A) → B'_1
  34. Segment(B'_1, A) → m
  35. Segment(B, B'_1) → n
  36. Dilate(B, If[2.4 ≤ a ≤ 3.4, 3.4 - a, 0], A) → B'_2
  37. Segment(B, B'_2) → a_1
  38. Segment(B'_2, A) → b_1
  39. Rotate(d', If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → d''
  40. Rotate(t, If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → t'
  41. Rotate(A, If[2.4 < a < 3.4, ((a - 2.4) * β), β], B) → A'_2
  42. CircleArc(B, A, A'_2) → c_1
  43. Dilate(B, If[3.6 ≤ a ≤ 4.6, 4.6 - a, 0], A) → B'_3
  44. Segment(B'_3, A) → d_1
  45. Segment(B, B'_3) → e_1
  46. Rotate(A, If[3.6 < a < 4.6, ((a - 3.6) * β), β], B) → A'_3
  47. CircleArc(B, A, A'_3) → f_1
  48. Rotate(d'', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → d'''
  49. Rotate(t', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → t''
  50. Rotate(c_1, If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → g_1
  51. Dilate(B, If[4.8 ≤ a ≤ 5.8, 5.8 - a, 0], A) → B'_4
  52. Segment(B, B'_4) → h_1
  53. Segment(B'_4, A) → i_1
  54. Rotate(d''', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → k_1
  55. Rotate(t'', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → t'''
  56. Rotate(g_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → p_1
  57. Rotate(f_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → q_1
  58. Rotate(A, If[4.8 < a < 5.8, ((a - 4.8) * β), β], B) → A'_4
  59. CircleArc(B, A, A'_4) → r_1
  60. Dilate(B, If[6 ≤ a ≤ 7, 7 - a, 0], A) → B'_5
  61. Segment(B'_5, A) → j_1
  62. Segment(B, B'_5) → l_1
  63. Rotate(A, If[6 < a < 7, ((a - 6) * β), β], B) → A'_5
  64. CircleArc(B, A, A'_5) → s_1
  65. Rotate(k_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → t_1
  66. Rotate(t''', If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → c_2
  67. Rotate(p_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → d_2
  68. Rotate(q_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → e_2
  69. Rotate(r_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → f_2
  70. CircleArc(B, C'', A) → g_2