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平方根螺旋

平方根螺旋
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2019-03-02 02:58
圆多边形数列几何作图
①本范例演示了通过连续构造等腰三角形和正方形，形成平方根螺旋的图形现象；②涉及的核心数学概念包括平方根、等腰三角形、几何作图、数列与序列；③作图要点——从下方『构造摘要』提炼用到了 Circle（圆）、Point（点）、Segment（线段）、OrthogonalLine（垂线）、Intersect（交点）、Polygon（多边形）等 GeoGebra 命令/对象；④适合初中及以上学段，用于学习几何作图、平方根概念及数列生成的可视化。

GeoGebra 命令及参数

  1. Circle(A, 1) → c
  2. Point(c) → B
  3. Segment(A, B) → f
  4. OrthogonalLine(A, f) → g
  5. Intersect(c, g, 1) → C
  6. Segment(C, B) → h
  7. Circle(C, 1) → d
  8. OrthogonalLine(C, h) → i
  9. Polygon(C, B, A) → t1, a, c_1, b
  10. Intersect(d, i, 1) → D
  11. Segment(D, B) → j
  12. Segment(C, D) → k
  13. Polygon(B, C, D) → t2, d_1, b_1, c_2
  14. Polygon(B, A, C) → t3, c_3, b_2, a_1
  15. Polygon(B, C, D) → t4, d_2, b_3, c_4
  16. Circle(D, 1) → e
  17. OrthogonalLine(D, j) → l
  18. Intersect(e, l) → E, F
  19. Segment(E, B) → m
  20. Polygon(D, E, B) → t5, b_4, d_3, e_1
  21. Circle(E, 1) → p
  22. OrthogonalLine(E, m) → n
  23. Intersect(p, n) → G, H
  24. Segment(G, B) → q
  25. Segment(B, D) → r
  26. Segment(E, B) → s
  27. Segment(B, E) → t
  28. Polygon(B, E, G) → t6, g_1, b_5, e_2
  29. Circle(G, 1) → f_1
  30. Circle(G, 1) → h_1
  31. OrthogonalLine(G, q) → i_1
  32. Intersect(h_1, i_1) → I, J
  33. Segment(B, I) → j_1
  34. Polygon(B, G, I) → t7, i_2, b_6, g_2
  35. Circle(I, 1) → k_1
  36. OrthogonalLine(I, j_1) → l_1
  37. Intersect(k_1, l_1) → K, L
  38. Segment(B, L) → m_1
  39. Polygon(B, I, L) → t8, l_2, b_7, i_3
  40. Circle(L, 1) → p_1
  41. OrthogonalLine(L, m_1) → n_1
  42. Intersect(m_1, i_3) → M
  43. Intersect(p_1, n_1) → N, O
  44. Segment(B, O) → q_1
  45. Polygon(B, L, O) → t9, o, b_8, l_3
  46. Circle(O, 1) → r_1
  47. OrthogonalLine(O, q_1) → s_1
  48. Intersect(r_1, s_1) → P, Q
  49. Segment(B, Q) → t_1
  50. Polygon(B, O, Q) → t10, q_2, b_9, o_1
  51. Circle(Q, 1) → f_2
  52. OrthogonalLine(Q, t_1) → h_2
  53. Intersect(f_2, h_2) → R, S
  54. Segment(B, S) → j_2
  55. Polygon(B, Q, S) → t11, s_2, b_{10}, q_3
  56. Polygon(B, Q, S) → t12, s_3, b_{11}, q_4
  57. Circle(S, 1) → k_2
  58. OrthogonalLine(S, j_2) → m_2
  59. Intersect(k_2, m_2) → T, U
  60. Segment(B, U) → n_2
  61. Polygon(B, S, U) → t13, u, b_{12}, s_4