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Animation 212

Animation 212
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2017-03-05 06:22
CircleTrigonometryGeometric Construction
This example demonstrates the geometric mean on the unit circle. Key mathematical concepts include circle, geometric mean, and unit circle. Using GeoGebra commands such as Point, Ray, OrthogonalLine, etc., dynamic geometric figures are constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(y = 0) → A
  2. Ray(A, B) → f
  3. Point(f) → C
  4. OrthogonalLine(C, p) → q
  5. Ray(C, F) → i
  6. Point(i) → G
  7. Ray(G, H) → j
  8. Point(j) → I
  9. Segment(I, G) → k
  10. Circle(I, G) → c
  11. Ray(C, D) → h
  12. Intersect(l, h) → E
  13. Ray(E, J) → m
  14. Intersect(c, m, 1) → K
  15. Ray(K, I) → n
  16. Intersect(n, y = 0) → L
  17. Circle(L, K) → d
  18. Intersect(d, y = 0) → M, N
  19. Segment(K, N) → r
  20. Intersect(c, r, 2) → O
  21. Line(O, G) → s
  22. Intersect(q, s) → P
  23. Segment(K, P) → q_1
  24. Segment(K, P) → t
  25. Segment(P, O) → a
  26. Dilate(N, If[0 < b ≤ 1, 1 - b, 0], O) → N'
  27. Segment(N, N') → e
  28. Dilate(O, If[1 < b ≤ 2, 2 - b, 0], K) → O'
  29. Segment(O, O') → f_1
  30. Dilate(K, If[2 < b ≤ 3, 3 - b, 0], C) → K'
  31. Angle(K, C, A) → α
  32. Segment(K, K') → g_1
  33. Dilate(O, If[3 < b ≤ 4, 4 - b, 0], G) → O'_1
  34. Segment(O, O'_1) → h_1
  35. Dilate(G, If[4 < b ≤ 5, 5 - b, 0], P) → G'
  36. Dilate(C, If[4 < b ≤ 5, 5 - b, 0], P) → C'
  37. Segment(G, G') → i_1
  38. Segment(C, C') → j_1
  39. Segment(M, N) → k_1
  40. Circle(G, g_1 + j_1) → c_1
  41. Segment(M, G) → l_1
  42. Segment(G, Q) → m_1
  43. Segment(Q, N) → n_1
  44. Dilate(M, If[5 < b ≤ 6, 6 - b, 0], G) → M'
  45. Segment(M, M') → p_1
  46. Rotate(K, If[6 < b ≤ 7, ((-(b - 6)) * π / 2), ((-π)) / 2], P) → K'_1
  47. Rotate(P, If[6 < b ≤ 7, ((-(b - 6)) * π / 2), ((-π)) / 2], P) → P'
  48. Segment(K'_1, P') → r_1
  49. Dilate(P, If[7 < b ≤ 8, 8 - b, 0], G) → P'_1
  50. Vector(P, P'_1) → u
  51. Translate(K'_1, u) → R
  52. Translate(P', u) → P''
  53. Segment(R, P'') → s_1
  54. Midpoint(M, Q) → S
  55. Rotate(Q, If[8 < b ≤ 9, ((-(b - 8)) * π), (-π)], S) → Q'
  56. CircleArc(S, Q', Q) → d_1
  57. OrthogonalLine(G, n_1) → t_1
  58. Intersect(d_1, t_1) → T,
  59. Angle(T, G, S) → β
  60. Dilate(T, If[10 < b ≤ 11, 11 - b, 0], G) → T'
  61. Segment(T, T') → a_1
  62. Dilate(K, If[11 < b ≤ 12, 12 - b, 0], G) → K'_2
  63. Segment(K, K'_2) → b_1
  64. Angle(T, G, K) → γ
  65. Rotate(K, If[13 < b ≤ 14, ((-(b - 13)) * γ), (-γ)], G) → K'_3
  66. Rotate(K'_2, If[13 < b ≤ 14, ((-(b - 13)) * γ), (-γ)], G) → U
  67. Segment(K'_3, U) → f_2
  68. Segment(S, Q') → g_2
  69. Segment(M, N) → h_2
  70. CircleArc(S, M, Q) → e_1
  71. CircleSector(S, Q', Q) → c_2