积极 AI Logo 积极 AI

平方根螺旋动画

平方根螺旋动画
几何画板及绘图内容加载中，请稍等……
2017-05-25 23:30
函数三角函数解析几何几何作图
①本范例通过动画演示了平方根螺旋的生成过程，展示了点随着距离原点距离的平方根增长而运动形成的轨迹；②涉及的核心数学概念包括平方根函数、几何作图、解析几何和动态几何；③作图要点提炼自构造摘要，使用了Intersect（交点）、Circle（圆）、Segment（线段）、OrthogonalLine（垂线）、Polygon（多边形）等GeoGebra命令和对象；④适合高中及以上数学学习者，用于理解函数图像的动态变化和几何作图的技巧。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → B
  2. Circle(B, 1) → c
  3. Intersect(c, yAxis) → B_2, Z
  4. Intersect(c, xAxis) → D_2, C
  5. Segment(Z, B) → a_4
  6. Segment(B, C) → b
  7. Segment(Z, C) → d
  8. OrthogonalLine(C, d) → e
  9. Circle(C, 1) → f
  10. Intersect(f, e) → F_2, D
  11. Segment(Z, D) → g
  12. OrthogonalLine(D, g) → h
  13. Circle(D, 1) → k
  14. Intersect(k, h) → H_2, E
  15. Segment(C, D) → i
  16. Segment(D, E) → j
  17. Segment(Z, E) → l
  18. OrthogonalLine(E, l) → m
  19. Circle(E, 1) → p
  20. Intersect(p, m) → J_1, F
  21. Segment(E, F) → n
  22. Segment(Z, F) → q
  23. OrthogonalLine(F, q) → r
  24. Circle(F, 1) → s
  25. Intersect(s, r) → L_1, G
  26. Segment(F, G) → t
  27. Segment(Z, G) → a_1
  28. OrthogonalLine(G, a_1) → b_1
  29. Circle(G, 1) → c_1
  30. Intersect(c_1, b_1) → N_1, H
  31. Segment(Z, H) → d_1
  32. OrthogonalLine(H, d_1) → e_1
  33. Circle(H, 1) → f_1
  34. Intersect(f_1, e_1) → P_1, I
  35. Segment(Z, I) → g_1
  36. Segment(G, H) → h_1
  37. Segment(H, I) → i_1
  38. OrthogonalLine(I, g_1) → j_1
  39. Circle(I, 1) → k_1
  40. Intersect(k_1, j_1) → R, J
  41. Segment(I, J) → l_1
  42. Segment(J, Z) → m_1
  43. OrthogonalLine(J, m_1) → n_1
  44. Circle(J, 1) → p_1
  45. Intersect(p_1, n_1) → K, U
  46. Segment(K, Z) → q_1
  47. Segment(J, K) → r_1
  48. OrthogonalLine(K, q_1) → s_1
  49. Circle(K, 1) → t_1
  50. Intersect(t_1, s_1) → L, W
  51. Segment(K, L) → a_2
  52. Segment(L, Z) → b_2
  53. OrthogonalLine(L, b_2) → c_2
  54. Circle(L, 1) → d_2
  55. Intersect(d_2, c_2) → M, A_1
  56. Segment(L, M) → e_2
  57. Segment(M, Z) → f_2
  58. OrthogonalLine(M, f_2) → g_2
  59. Circle(M, 1) → h_2
  60. Intersect(h_2, g_2) → N, C_1
  61. Segment(M, N) → i_2
  62. Segment(N, Z) → j_2
  63. OrthogonalLine(N, j_2) → k_2
  64. Circle(N, 1) → p_2
  65. Intersect(p_2, k_2) → O, E_1
  66. Segment(N, O) → l_2
  67. Segment(O, Z) → m_2
  68. OrthogonalLine(O, m_2) → n_2
  69. Circle(O, 1) → q_2
  70. Intersect(q_2, n_2) → P, G_1
  71. Segment(O, P) → r_2
  72. Segment(P, Z) → s_2
  73. OrthogonalLine(P, s_2) → t_2
  74. Circle(P, 1) → c_3
  75. Intersect(c_3, t_2) → Q, I_1
  76. Segment(P, Q) → a_3
  77. Segment(Q, Z) → b_3
  78. Polygon(B, C, Z) → poly1, z_1, b_4, c_4
  79. Polygon(C, D, Z) → poly2, z_2, c_5, d_3
  80. Polygon(D, E, Z) → poly3, z_3, d_4, e_3
  81. Polygon(E, F, Z) → poly4, z_4, e_4, f_3
  82. Polygon(F, G, Z) → poly5, z_5, f_4, g_3
  83. Polygon(G, H, Z) → poly6, z_6, g_4, h_3
  84. Polygon(H, I, Z) → poly7, z_7, h_4, i_3
  85. Polygon(I, J, Z) → poly8, z_8, i_4, j_3
  86. Polygon(J, K, Z) → poly9, z_9, j_4, k_3
  87. Polygon(K, L, Z) → poly10, z_{10}, k_4, l_3
  88. Polygon(L, M, Z) → poly11, z_{11}, l_4, m_3
  89. Polygon(M, N, Z) → poly12, z_{12}, m_4, n_3
  90. Polygon(N, O, Z) → poly13, z_{13}, n_4, o
  91. Polygon(O, P, Z) → poly14, z_{14}, o_1, p_3
  92. Polygon(P, Q, Z) → poly15, z_{15}, p_4, q_3