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巴瓦雷螺旋打印

巴瓦雷螺旋打印
几何画板及绘图内容加载中，请稍等……
2018-12-27 21:35
圆变换几何作图
①本范例演示了如何通过动态几何工具构建巴瓦雷螺旋图形，该图形由一系列连续的圆和三角形组成，展现几何变换与序列的和谐美；②涉及的核心数学概念包括几何变换、旋转、相似三角形、数列、解析几何等；③作图要点提炼自GeoGebra命令：Intersect（交点）、Point（点）、Polygon（多边形）、Circle（圆）；④适合高中及以上数学学习者，用于理解复杂几何图形的构造与性质，提升空间想象能力。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Point(f) → E
  5. Circle(B, Distance[A, E]) → c
  6. Intersect(c, g, 1) → F
  7. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  8. Circle(E, (Distance[A, E] / Distance[A, B] * Distance[E, F])) → d
  9. Intersect(d, j, 1) → I
  10. Circle(F, Radius[d]) → e
  11. Intersect(e, k, 1) → J
  12. Polygon(I, J, 4) → poly3, n, p, q, r, K, L
  13. Circle(I, (Distance[A, E] / Distance[A, B] * Distance[I, J])) → s
  14. Intersect(poly1, poly2) → M, N, O, P, Q, R, S, T
  15. Intersect(s, n) → U,
  16. Circle(J, (Distance[A, E] / Distance[A, B] * Distance[I, J])) → t
  17. Intersect(t, p) → V,
  18. Polygon(U, V, 4) → poly4, a, b, f_1, g_1, W, Z
  19. Circle(U, (Distance[A, E] / Distance[A, B] * Distance[U, V])) → c_1
  20. Intersect(c_1, a) → A_1,
  21. Circle(V, Radius[c_1]) → d_1
  22. Intersect(d_1, b, 1) → B_1
  23. Polygon(A_1, B_1, 4) → poly5, h_1, i_1, j_1, k_1, C_1, D_1
  24. Circle(A_1, (Distance[A, E] / Distance[A, B] * Distance[A_1, B_1])) → e_1
  25. Intersect(e_1, h_1) → E_1,
  26. Circle(B_1, Radius[e_1]) → p_1
  27. Intersect(p_1, i_1, 1) → F_1
  28. Polygon(E_1, F_1, 4) → poly6, l_1, m_1, n_1, q_1, G_1, H_1
  29. Circle(E_1, (Distance[A, E] / Distance[A, B] * Distance[E_1, F_1])) → r_1
  30. Circle(F_1, Radius[r_1]) → s_1
  31. Intersect(r_1, m_1) → I_1,
  32. Intersect(s_1, m_1) → J_1,
  33. Intersect(r_1, l_1) → K_1,
  34. Polygon(K_1, J_1, 4) → poly7, t_1, a_1, b_1, f_2, L_1, M_1
  35. Circle(K_1, (Distance[A, E] / Distance[A, B] * Distance[K_1, J_1])) → c_2
  36. Circle(J_1, (Distance[A, E] / Distance[A, B] * Distance[K_1, J_1])) → d_2
  37. Intersect(c_2, t_1, 1) → O_1
  38. Intersect(d_2, a_1, 1) → P_1
  39. Polygon(O_1, P_1, 4) → poly8, g_2, h_2, i_2, j_2, Q_1, R_1
  40. Circle(O_1, (Distance[A, E] / Distance[A, B] * Distance[O_1, P_1])) → e_2
  41. Circle(P_1, (Distance[A, E] / Distance[A, B] * Distance[O_1, P_1])) → k_2
  42. Intersect(k_2, h_2) → N_1,
  43. Intersect(e_2, g_2) → S_1,
  44. Polygon(S_1, N_1, 4) → poly9, l_2, m_2, n_2, p_2, T_1, U_1
  45. Circle(S_1, (Distance[A, E] / Distance[A, B] * Distance[S_1, N_1])) → q_2
  46. Circle(N_1, (Distance[A, E] / Distance[A, B] * Distance[S_1, N_1])) → r_2
  47. Intersect(r_2, m_2) → V_1,
  48. Intersect(q_2, l_2) → W_1,
  49. Polygon(W_1, V_1, 4) → poly10, s_2, t_2, a_2, b_2, Z_1, A_2
  50. Polygon(E, I, N_1, P_1, J_1, F_1, B_1, V, J, F, B, U, A_1, E_1, K_1, O_1, S_1, W_1, V_1) → poly11, e_3, v_1, k_3, l_3, m_3, n_3, p_3, v, j_4, f_4, b_3, i_3, u, f_3, g_3, h_3, o_1, j_3, w_1