MathPlotAI Logo MathPlotAI

Animation 205

Animation 205
Loading the math board and drawing, please wait…
2017-02-21 12:49
CircleTransformationGeometric Construction
This example demonstrates an animation involving a circle and a rectangle. Key mathematical concepts include circle, rectangle, congruence, distance, and slope. Using GeoGebra commands such as Circle, Point, Segment, Intersect, etc., dynamic geometric shapes can be constructed. Suitable for middle school and above students to learn geometric transformations and dynamic geometry.

GeoGebra Commands & Parameters

  1. Circle(A_1, A) → c
  2. Circle(C, A) → d
  3. Semicircle(A, D_1) → e
  4. Semicircle(D_1, A) → f
  5. Point(e) → D
  6. Segment(A, D) → g
  7. Intersect(d, g, 2) → P
  8. OrthogonalLine(D, h) → i
  9. Intersect(d, i, 2) → F
  10. Intersect(h, i) → E
  11. Ray(A, F) → j
  12. Intersect(e, j, 2) → G
  13. OrthogonalLine(G, h) → k
  14. Intersect(d, k, 2) → M
  15. Segment(A, M) → l
  16. Intersect(i, l) → N
  17. Distance(A, g) → distanceAg
  18. Distance(A, N) → distanceAN
  19. Distance(P, A) → distancePA
  20. Dilate(A, If[0 < m ≤ 1, 1 - m, 0], P) → A'
  21. Segment(A, A') → n
  22. Dilate(P, If[1 < m ≤ 2, 2 - m, 0], D) → P'
  23. Segment(P, P') → p
  24. Dilate(D, If[2 < m ≤ 3, 3 - m, 0], F) → D'
  25. Segment(D, D') → q
  26. Intersect(k, xAxis) → B
  27. Angle(G, B, A) → β
  28. Angle(D, E, A) → α
  29. Dilate(F, If[3 < m ≤ 4, 4 - m, 0], E) → F'
  30. Segment(F, F') → r
  31. Dilate(A, If[4 < m ≤ 5, 5 - m, 0], F) → A'_1
  32. Segment(A, A'_1) → s
  33. Dilate(F, If[5 < m ≤ 6, 6 - m, 0], G) → F'_1
  34. Segment(F, F'_1) → t
  35. Dilate(G, If[6 < m ≤ 7, 7 - m, 0], M) → G'
  36. Segment(G, G') → f_1
  37. Dilate(M, If[7 < m ≤ 8, 8 - m, 0], B) → M'
  38. Segment(M, M') → g_1
  39. Dilate(A, If[8 < m ≤ 9, 9 - m, 0], N) → A'_2
  40. Segment(A, A'_2) → h_1
  41. Dilate(N, If[9 < m ≤ 10, 10 - m, 0], M) → N'
  42. Segment(N, N') → i_1
  43. Intersect(e, j_1, 1) → I
  44. Angle(N, A, P) → γ
  45. Rotate(A, If[11 < m ≤ 12, ((m - 11) * γ), γ], A) → A'_3
  46. Rotate(A'_2, If[11 < m ≤ 12, ((m - 11) * γ), γ], A) → J
  47. Segment(A'_3, J) → k_1
  48. Semicircle(A, H) → c_1
  49. Line(P, N) → l_1
  50. Line(D, M) → m_1
  51. Line(P, D) → n_1
  52. Circle(D, 2) → d_1
  53. Intersect(d_1, n_1, 2) → K
  54. Ray(D, K) → p_1
  55. Intersect(l_1, s) → L
  56. Circle(P, (0.5 * Distance[P, L])) → e_1
  57. Intersect(e_1, k_1, 1) → O
  58. Intersect(e_1, l_1, 2) → Q
  59. Intersect(e_1, l_1, 1) → R
  60. Ray(P, R) → q_1
  61. Circle(D, 2) → r_1
  62. Intersect(r_1, m_1, 1) → S
  63. Ray(D, S) → s_1
  64. Dilate(N, If[12 < m ≤ 13, 13 - m, 0], P) → N'_1
  65. Dilate(M, If[12 < m ≤ 13, 13 - m, 0], D) → M'_1
  66. Segment(N, N'_1) → t_1
  67. Segment(M, M'_1) → a_1
  68. Angle(R, P, O) → δ
  69. Rotate(R, If[13 < m ≤ 14, ((m - 13) * δ), δ], P) → R'
  70. CircleSector(P, R, R') → c_2
  71. Dilate(P, If[14 < m ≤ 15, 15 - m, 0], D) → P'_1
  72. Vector(P, P'_1) → u
  73. Translate(c_2, u) → d_2
  74. Segment(A, D_1) → b_1