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Square Root Spiral Animation

Square Root Spiral Animation
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2017-05-25 23:30
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the generation process of a square root spiral through animation, showing how a point moves as its distance from the origin increases by the square root. Key math concepts include square root functions, geometric constructions, coordinate geometry, and dynamic geometry. The construction utilizes GeoGebra commands and objects like Intersect, Circle, Segment, OrthogonalLine, and Polygon as outlined in the summary. It is suitable for high school and above students to understand dynamic function graphs and geometric construction techniques.

GeoGebra Commands & Parameters

  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