勾股螺旋线

勾股螺旋线
几何画板及绘图内容加载中,请稍等……
2014-12-26 10:13
勾股螺旋线是一种由直角三角形组成的螺旋图形,每个三角形的斜边是下一个三角形的直角边。它展示了勾股定理的应用,涉及直角三角形和根号的概念。通过使用GeoGebra的Intersect、Sequence、Point、Polygon、Circle等命令,可以构造出这种螺旋图形。适合初中及以上学生学习勾股定理和根号的概念。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Sequence(Circle[A, i^(1 / 2)], i, 2, 17) → list1
  3. Point(xAxis) → B
  4. Point(list1) → C
  5. Polygon(A, B, C) → poly1, c, a, b
  6. Circle(C, 1) → d
  7. Circle(A, B2) → C2
  8. Intersect(d, C2) → D, E, ,
  9. Circle(A, B3) → C3
  10. Circle(A, B4) → C4
  11. Circle(A, B5) → C5
  12. Circle(A, B6) → C6
  13. Circle(A, B7) → C7
  14. Circle(A, B8) → C8
  15. Circle(A, B9) → C9
  16. Circle(A, B10) → C10
  17. Circle(A, B11) → C11
  18. Circle(A, B12) → C12
  19. Circle(A, B13) → C13
  20. Circle(A, B14) → C14
  21. Circle(A, B15) → C15
  22. Circle(A, B16) → C16
  23. Circle(A, B17) → C17
  24. Circle(A, B18) → C18
  25. Circle(C, 1) → e
  26. Intersect(C4, e, 1) → F
  27. Polygon(A, C, F) → poly2, f, a_1, c_1
  28. Circle(F, 1) → g
  29. Intersect(C5, g, 1) → G
  30. Polygon(A, F, G) → poly3, g_1, a_2, f_1
  31. Circle(G, 1) → h
  32. Intersect(C6, h, 1) → H
  33. Polygon(A, G, H) → poly4, h_1, a_3, g_2
  34. Circle(H, 1) → k
  35. Intersect(C7, k, 1) → I
  36. Circle(I, 1) → p
  37. Intersect(C8, p, 1) → J
  38. Circle(J, 1) → q
  39. Intersect(C9, q, 1) → K
  40. Circle(K, 1) → r
  41. Intersect(C10, r, 1) → L
  42. Circle(L, 1) → s
  43. Intersect(C11, s, 1) → M
  44. Circle(M, 1) → t
  45. Intersect(C12, t, 1) → N
  46. Circle(N, 1) → d_1
  47. Intersect(C13, d_1, 1) → O
  48. Circle(O, 1) → e_1
  49. Intersect(C14, e_1, 1) → P
  50. Circle(P, 1) → k_1
  51. Intersect(C15, k_1, 1) → Q
  52. Circle(Q, 1) → p_1
  53. Intersect(C16, p_1, 1) → R
  54. Circle(R, 1) → q_1
  55. Intersect(C17, q_1, 1) → S
  56. Circle(S, 1) → r_1
  57. Intersect(C18, r_1, 1) → T
  58. Polygon(A, H, I) → poly5, i, a_4, h_2
  59. Polygon(A, I, J) → poly6, j, a_5, i_1
  60. Polygon(A, J, K) → poly7, k_2, a_6, j_1
  61. Polygon(L, A, K) → poly8, k_3, l, a_7
  62. Polygon(M, A, L) → poly9, l_1, m, a_8
  63. Polygon(N, A, M) → poly10, m_1, n_2, a_9
  64. Polygon(O, A, N) → poly11, n_1, o, a_{10}
  65. Polygon(P, A, O) → poly12, o_1, p_2, a_{11}
  66. Polygon(Q, A, P) → poly13, p_3, q_2, a_{12}
  67. Polygon(R, A, Q) → poly14, q_3, r_2, a_{13}
  68. Polygon(S, A, R) → poly15, r_3, s_1, a_{14}
  69. Polygon(T, A, S) → poly16, s_2, t_1, a_{15}

AI 绘图提示语参考

绘制一个由多个直角三角形组成的螺旋,每个三角形的斜边是下一个三角形的直角边。首先在坐标轴上创建点A和B,然后以A为圆心,以连续的平方根值为半径画一系列圆,每个圆与前一个圆相切,形成一系列直角三角形,最后连接这些三角形的顶点形成螺旋状的多边形。
以上提示语为根据原始绘图命令整理而来,仅供参考。