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Geometric Construction and Fitting

Geometric Construction and Fitting
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2016-06-02 03:40
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the construction of geometric figures like equilateral triangles, median lines, and squares using basic elements such as points, line segments, and circles, exploring their relationships. Core mathematical concepts include line segments, equilateral triangles, median lines, squares, and coordinate geometry. The construction involves GeoGebra commands and objects like Point, Segment, Circle, OrthogonalLine, Intersect, Polygon, and Midpoint. It is suitable for high school mathematics teaching, focusing on geometric construction practice and concept understanding.

GeoGebra Commands & Parameters

  1. Point(Circle[A, r]) → B
  2. Segment(A, B) → f
  3. Circle(A, r) → c
  4. Circle(A, (2 * r)) → d
  5. Circle(A, (3 * r)) → e
  6. OrthogonalLine(A, f) → g
  7. Intersect(c, g, 2) → C
  8. Intersect(d, g, 2) → D
  9. Intersect(e, g, 2) → E
  10. OrthogonalLine(C, g) → h
  11. OrthogonalLine(D, g) → i
  12. OrthogonalLine(E, g) → j
  13. Circle(C, r) → k
  14. Circle(C, (2 * r)) → p
  15. Intersect(k, h, 2) → F
  16. Intersect(k, h, 1) → I
  17. Intersect(p, h, 1) → J
  18. OrthogonalLine(F, h) → l
  19. OrthogonalLine(I, h) → m
  20. OrthogonalLine(J, h) → n
  21. Intersect(n, i) → G
  22. Intersect(j, m) → H
  23. Intersect(i, m) → K
  24. Intersect(i, l) → L
  25. Polygon(A, C, I, B, F, L, D, E, H, K, G, J) → poly1, a, j_1, i_1, b, c_1, f_1, l_1, d_1, e_1, h_1, k_1, g_1
  26. Segment(C, G) → q
  27. OrthogonalLine(C, q) → s
  28. Intersect(s, l_1) → M
  29. Intersect(s, f) → N
  30. Polygon(M, C, G, K, H, E, D) → poly2, m_1, c_2, g_2, k_2, h_2, e_2, d_2
  31. Polygon(N, C, G, J, I, B) → poly3, n_1, c_3, g_3, j_2, i_2, b_1
  32. Polygon(C, A, N) → poly4, n_2, c_4, a_1
  33. Polygon(L, F, C, M) → poly5, l_2, f_2, c_5, m_2
  34. Point(Circle[P, q]) → Q
  35. Segment(P, Q) → t
  36. OrthogonalLine(P, t) → p_1
  37. Circle(P, m_1) → q_1
  38. Intersect(q_1, p_1, 2) → R
  39. Segment(R, P) → r_1
  40. Segment(R, Q) → s_1
  41. OrthogonalLine(P, s_1) → t_1
  42. Intersect(t_1, s_1) → S
  43. Circle(S, r) → p_2
  44. Intersect(p_2, s_1, 1) → T
  45. Polygon(S, T, 4) → poly6, q_2, r_2, s_2, t_2, U, V
  46. Polygon(P, R, S, V, U, T, Q) → poly7, p_3, r_3, s_3, v, u, t_3, q_3
  47. Circle(W, c_3) → d_3
  48. Point(d_3) → Z
  49. Segment(W, Z) → a_2
  50. OrthogonalLine(W, a_2) → b_2
  51. Circle(W, n_1) → e_3
  52. Intersect(e_3, b_2, 1) → A_1
  53. Segment(W, A_1) → f_3
  54. Midpoint(a_2) → B_1
  55. Circle(B_1, W) → h_3
  56. Circle(W, (2 * r)) → k_3
  57. Intersect(h_3, k_3, 1) → C_1
  58. Midpoint(W, C_1) → D_1
  59. Segment(W, C_1) → i_3
  60. OrthogonalLine(D_1, i_3) → j_3
  61. Circle(D_1, r) → d_4
  62. Intersect(d_4, j_3, 1) → E_1
  63. Polygon(W, Z, C_1, D_1, E_1, A_1) → poly8, w, z_1, c_6, d_5, e_4, a_3
  64. Point(Circle[F_1, r]) → G_1
  65. Segment(F_1, G_1) → l_3
  66. OrthogonalLine(G_1, l_3) → m_3
  67. Circle(G_1, r) → f_4
  68. Intersect(f_4, m_3, 2) → H_1
  69. Segment(L, M) → n_3
  70. OrthogonalLine(F_1, l_3) → b_3
  71. Circle(F_1, n_3) → g_4
  72. Intersect(g_4, b_3, 2) → I_1
  73. Segment(I_1, H_1) → h_4
  74. Polygon(I_1, F_1, G_1, H_1) → poly9, i_4, f_5, g_5, h_5
  75. Point(Circle[J_1, r]) → K_1
  76. Segment(J_1, K_1) → j_4
  77. OrthogonalLine(K_1, j_4) → k_4
  78. Segment(A, N) → l_4
  79. Circle(K_1, Segment[A, N]) → p_4
  80. Intersect(p_4, k_4, 2) → L_1
  81. Polygon(J_1, L_1, K_1) → poly10, k_5, j_5, l_5
  82. Point(Circle[M_1, c_3]) → N_1
  83. Segment(M_1, N_1) → m_4
  84. Polygon(M_1, N_1, 4) → poly11, n_4, q_4, r_4, s_4, O_1, P_1