勾股螺旋

勾股螺旋
几何画板及绘图内容加载中,请稍等……
2016-01-15 15:00
①本范例演示了勾股定理在构建螺旋形多边形中的应用;②涉及核心数学概念包括勾股定理、直角三角形、多边形构造;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)、Angle(角度)等 GeoGebra 命令/对象;④适合初中及以上学生学习几何作图与勾股定理的实践应用。

GeoGebra 命令及参数

  1. Circle(A, a) → c
  2. Point(Circle[A, 1]) → C
  3. Segment(A, C) → e
  4. OrthogonalLine(A, e) → b
  5. Intersect(c, b) → B, D
  6. Polygon(D, C, A) → poly1, a_1, d, c_1
  7. OrthogonalLine(D, a_1) → f
  8. Circle(D, a) → g
  9. Intersect(g, f) → E, F
  10. Polygon(D, F, C) → poly2, c_2, d_1, f_1
  11. Circle(F, a) → k
  12. OrthogonalLine(F, d_1) → h
  13. Intersect(k, h, 2) → G
  14. Polygon(G, C, F) → poly3, f_2, g_1, c_3
  15. OrthogonalLine(G, f_2) → i
  16. Circle(G, a) → p
  17. Intersect(p, i, 2) → H
  18. Polygon(H, C, G) → poly4, g_2, h_1, c_4
  19. OrthogonalLine(H, g_2) → j
  20. Circle(H, a) → q
  21. Intersect(q, j, 2) → I
  22. Polygon(I, C, H) → poly5, h_2, i_1, c_5
  23. OrthogonalLine(I, h_2) → l
  24. Circle(I, a) → r
  25. Intersect(r, l, 2) → J
  26. Polygon(I, J, C) → poly6, c_6, i_2, j_1
  27. OrthogonalLine(J, i_2) → m
  28. Circle(J, a) → s
  29. Intersect(s, m, 2) → K
  30. Polygon(J, K, C) → poly7, c_7, j_2, k_1
  31. OrthogonalLine(K, j_2) → n
  32. Circle(K, a) → t
  33. Intersect(t, n, 2) → L
  34. Polygon(K, L, C) → poly8, c_8, k_2, l_1
  35. OrthogonalLine(L, k_2) → b_1
  36. Circle(L, a) → e_1
  37. Intersect(e_1, b_1, 2) → M
  38. Polygon(L, M, C) → poly9, c_9, l_2, m_1
  39. OrthogonalLine(M, l_2) → n_1
  40. Circle(M, a) → p_1
  41. Intersect(p_1, n_1, 2) → N
  42. Polygon(M, N, C) → poly10, c_{10}, m_2, n_2
  43. OrthogonalLine(N, m_2) → q_1
  44. Circle(N, a) → r_1
  45. Intersect(r_1, q_1, 2) → O
  46. Polygon(N, O, C) → poly11, c_{11}, n_3, o
  47. OrthogonalLine(O, n_3) → s_1
  48. Circle(O, a) → t_1
  49. Intersect(t_1, s_1, 2) → P
  50. Polygon(O, P, C) → poly12, c_{12}, o_1, p_2
  51. OrthogonalLine(P, o_1) → a_2
  52. Circle(P, a) → d_2
  53. Intersect(d_2, a_2, 2) → Q
  54. Polygon(P, Q, C) → poly13, c_{13}, p_3, q_2
  55. Angle(C, A, D) → α
  56. Angle(C, D, F) → β
  57. Angle(C, F, G) → γ
  58. Angle(C, G, H) → δ
  59. Angle(C, H, I) → ε
  60. Angle(C, I, J) → ζ
  61. Angle(C, J, K) → η
  62. Angle(C, K, L) → θ
  63. Angle(C, L, M) → ι
  64. Angle(C, M, N) → κ
  65. Angle(C, N, O) → λ
  66. Angle(C, O, P) → μ
  67. Angle(C, P, Q) → ν