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螺旋艺术 Maria

螺旋艺术 Maria
几何画板及绘图内容加载中，请稍等……
2019-05-26 00:55
向量函数几何作图
所属专题 EQUILATERAL TRIANGLE SPIRAL
这个范例展示了螺旋艺术 Maria 的构造过程。它涉及函数图像和向量的概念。通过使用 Polygon, OrthogonalLine, Intersect, Segment, Vector, Translate 等命令，可以构造出精美的螺旋图案。适合高中数学教学，特别是解析几何和函数图像的教学。

GeoGebra 命令及参数

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. OrthogonalLine(C, f) → i
  3. Intersect(i, poly1) → D, E
  4. Segment(C, D) → j
  5. Polygon(C, D, 3) → poly2, k, l, m, F
  6. OrthogonalLine(F, j) → n
  7. Intersect(j, k) → G
  8. Intersect(g, l) → H
  9. Polygon(C, H, 3) → poly3, p, q, r, I
  10. Intersect(q, m) → J
  11. Polygon(C, J, 3) → poly4, s, t, a, K
  12. Intersect(r, t) → L
  13. Polygon(C, L, 3) → poly5, b, c, d, M
  14. Intersect(a, c) → N
  15. Polygon(C, N, 3) → poly6, e, f_1, g_1, O
  16. Intersect(d, f_1) → P
  17. Polygon(C, P, 3) → poly7, h_1, i_1, j_1, Q
  18. Intersect(i_1, g_1) → R
  19. Polygon(C, R, 3) → poly8, k_1, l_1, m_1, S
  20. Intersect(l_1, j_1) → T
  21. Polygon(C, T, 3) → poly9, n_1, p_1, q_1, U
  22. Intersect(m_1, p_1) → V
  23. Polygon(C, V, 3) → poly10, r_1, s_1, t_1, W
  24. Intersect(s_1, poly9) → Z, Z_1
  25. Polygon(C, Z_1, 3) → poly11, a_1, b_1, c_1, A_1
  26. Intersect(t_1, poly11) → B_1, C_1
  27. Polygon(C_1, B_1, 3) → poly12, d_1, e_1, f_2, D_1
  28. Intersect(c_1, e_1) → E_1
  29. Polygon(C_1, E_1, 3) → poly13, g_2, h_2, i_2, F_1
  30. Vector(J_1, K_1) → u
  31. Translate(poly1, u) → poly1'
  32. Translate(poly2, u) → poly2'
  33. Translate(poly3, u) → poly3'
  34. Translate(poly4, u) → poly4'
  35. Translate(poly5, u) → poly5'
  36. Translate(poly6, u) → poly6'
  37. Translate(poly7, u) → poly7'
  38. Translate(poly8, u) → poly8'
  39. Translate(poly9, u) → poly9'
  40. Translate(poly10, u) → poly10'
  41. Translate(C, u) → C'
  42. Translate(D, u) → D'
  43. Segment(C', D') → j'
  44. Translate(E, u) → E'
  45. Translate(Z, u) → Z'
  46. Translate(poly11, u) → poly11'
  47. Translate(poly12, u) → poly12'
  48. Translate(poly13, u) → poly13'
  49. Translate(poly1', u) → poly1''
  50. Translate(poly2', u) → poly2''
  51. Translate(poly3', u) → poly3''
  52. Translate(poly4', u) → poly4''
  53. Translate(poly5', u) → poly5''
  54. Translate(poly6', u) → poly6''
  55. Translate(poly7', u) → poly7''
  56. Translate(poly8', u) → poly8''
  57. Translate(poly9', u) → poly9''
  58. Translate(poly10', u) → poly10''
  59. Translate(poly11', u) → poly11''
  60. Translate(poly12', u) → poly12''
  61. Translate(poly13', u) → poly13''
  62. Translate(C', u) → C''
  63. Translate(D', u) → D''
  64. Segment(C'', D'') → j''
  65. Translate(E', u) → E''
  66. Translate(Z', u) → Z''