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Pursuit Curve Triangle

Pursuit Curve Triangle
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2018-10-15 21:59
TriangleCircleSequenceGeometric ConstructionSlider Animation
This example demonstrates the dynamic trajectory of pursuit curves within a triangle. Key math concepts include isosceles triangles, median value, circles, and sequences and series. Construction highlights involve commands like Polygon, Point, Circle, Centroid, Rotate, and Intersect in GeoGebra. Suitable for high school and above students exploring geometric dynamic changes and locus problems.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Point(f) → D
  3. Circle(A, D) → c
  4. Centroid(poly1) → E
  5. Rotate(c, 120°, E) → c'
  6. Intersect(c', g, 1) → F
  7. Polygon(D, F, 3) → poly2, i, j, k, G
  8. Circle(D, A) → d
  9. Circle(F, B) → e
  10. Intersect(d, i, 1) → H
  11. Intersect(e, j, 1) → I
  12. Polygon(H, I, 3) → poly3, l, m, n, J
  13. Circle(H, D) → p
  14. Circle(I, F) → q
  15. Intersect(p, l, 1) → K
  16. Intersect(q, m, 1) → L
  17. Polygon(K, L, 3) → poly4, r, s, t, M
  18. Circle(K, H) → c_1
  19. Circle(L, I) → d_1
  20. Intersect(c_1, r, 1) → N
  21. Intersect(d_1, s, 1) → P
  22. Polygon(N, P, 3) → poly5, a, b, f_1, O
  23. Circle(N, K) → e_1
  24. Circle(P, L) → g_1
  25. Intersect(e_1, a, 1) → Q
  26. Intersect(g_1, b, 1) → R
  27. Polygon(Q, R, 3) → poly6, h_1, i_1, j_1, S
  28. Circle(Q, N) → k_1
  29. Circle(R, P) → p_1
  30. Intersect(k_1, h_1, 1) → T
  31. Intersect(p_1, i_1, 1) → U
  32. Polygon(T, U, 3) → poly7, l_1, m_1, n_1, V
  33. Circle(T, Q) → q_1
  34. Circle(U, R) → r_1
  35. Intersect(q_1, l_1, 1) → W
  36. Intersect(r_1, m_1, 1) → Z
  37. Polygon(W, Z, 3) → poly8, s_1, t_1, a_1, A_1
  38. Circle(W, T) → c_2
  39. Circle(Z, U) → d_2
  40. Intersect(c_2, s_1, 1) → B_1
  41. Intersect(d_2, t_1, 1) → C_1
  42. Polygon(B_1, C_1, 3) → poly9, b_1, f_2, g_2, D_1
  43. Circle(B_1, W) → e_2
  44. Circle(C_1, Z) → h_2
  45. Intersect(e_2, b_1, 1) → E_1
  46. Intersect(h_2, f_2, 1) → F_1
  47. Polygon(E_1, F_1, 3) → poly10, i_2, j_2, k_2, G_1
  48. Circle(E_1, B_1) → p_2
  49. Intersect(p_2, i_2, 1) → H_1
  50. Circle(F_1, C_1) → q_2
  51. Intersect(q_2, j_2, 1) → J_1
  52. Polygon(H_1, J_1, 3) → poly11, l_2, m_2, n_2, I_1
  53. Circle(H_1, E_1) → r_2
  54. Circle(J_1, F_1) → s_2
  55. Intersect(r_2, l_2, 1) → K_1
  56. Intersect(s_2, m_2, 1) → L_1
  57. Polygon(K_1, L_1, 3) → poly12, t_2, a_2, b_2, M_1
  58. Circle(K_1, H_1) → c_3
  59. Circle(L_1, J_1) → d_3
  60. Intersect(c_3, t_2, 1) → N_1
  61. Intersect(d_3, a_2, 1) → O_1
  62. Polygon(N_1, O_1, 3) → poly13, f_3, g_3, h_3, P_1
  63. Circle(N_1, K_1) → e_3
  64. Circle(O_1, L_1) → k_3
  65. Intersect(e_3, f_3, 1) → Q_1
  66. Intersect(k_3, g_3, 1) → R_1
  67. Polygon(Q_1, R_1, 3) → poly14, i_3, j_3, l_3, S_1

AI Drawing Prompt Reference

Draw a triangle ABC, then construct a series of rotated and intersected circles and points inside the triangle to form a complex closed shape sequence. Start by constructing a triangle with vertices A, B, and C, then take a point D on side AB and draw a circle centered at D. Rotate this circle 120 degrees to get circle c', and find the intersection of c' with another side of the triangle to get point F. Continue this process to construct a series of circles and points, ultimately forming a complex closed shape sequence composed of multiple triangles.
The prompt above was compiled from the original drawing commands and is for reference only.