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Square Root Spiral

Square Root Spiral
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2019-03-02 02:58
CirclePolygonSequenceGeometric Construction
This example demonstrates the creation of a square root spiral by continuously constructing isosceles triangles and squares, visually representing the concept of square roots. It involves core mathematical concepts such as square roots, isosceles triangles, geometric constructions, and sequences. The construction utilizes GeoGebra commands like Circle, Point, Segment, OrthogonalLine, Intersect, and Polygon. It is suitable for middle school and above, serving as a visual aid for understanding geometric constructions, square roots, and sequence generation.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Point(c) → B
  3. Segment(A, B) → f
  4. OrthogonalLine(A, f) → g
  5. Intersect(c, g, 1) → C
  6. Segment(C, B) → h
  7. Circle(C, 1) → d
  8. OrthogonalLine(C, h) → i
  9. Polygon(C, B, A) → t1, a, c_1, b
  10. Intersect(d, i, 1) → D
  11. Segment(D, B) → j
  12. Segment(C, D) → k
  13. Polygon(B, C, D) → t2, d_1, b_1, c_2
  14. Polygon(B, A, C) → t3, c_3, b_2, a_1
  15. Polygon(B, C, D) → t4, d_2, b_3, c_4
  16. Circle(D, 1) → e
  17. OrthogonalLine(D, j) → l
  18. Intersect(e, l) → E, F
  19. Segment(E, B) → m
  20. Polygon(D, E, B) → t5, b_4, d_3, e_1
  21. Circle(E, 1) → p
  22. OrthogonalLine(E, m) → n
  23. Intersect(p, n) → G, H
  24. Segment(G, B) → q
  25. Segment(B, D) → r
  26. Segment(E, B) → s
  27. Segment(B, E) → t
  28. Polygon(B, E, G) → t6, g_1, b_5, e_2
  29. Circle(G, 1) → f_1
  30. Circle(G, 1) → h_1
  31. OrthogonalLine(G, q) → i_1
  32. Intersect(h_1, i_1) → I, J
  33. Segment(B, I) → j_1
  34. Polygon(B, G, I) → t7, i_2, b_6, g_2
  35. Circle(I, 1) → k_1
  36. OrthogonalLine(I, j_1) → l_1
  37. Intersect(k_1, l_1) → K, L
  38. Segment(B, L) → m_1
  39. Polygon(B, I, L) → t8, l_2, b_7, i_3
  40. Circle(L, 1) → p_1
  41. OrthogonalLine(L, m_1) → n_1
  42. Intersect(m_1, i_3) → M
  43. Intersect(p_1, n_1) → N, O
  44. Segment(B, O) → q_1
  45. Polygon(B, L, O) → t9, o, b_8, l_3
  46. Circle(O, 1) → r_1
  47. OrthogonalLine(O, q_1) → s_1
  48. Intersect(r_1, s_1) → P, Q
  49. Segment(B, Q) → t_1
  50. Polygon(B, O, Q) → t10, q_2, b_9, o_1
  51. Circle(Q, 1) → f_2
  52. OrthogonalLine(Q, t_1) → h_2
  53. Intersect(f_2, h_2) → R, S
  54. Segment(B, S) → j_2
  55. Polygon(B, Q, S) → t11, s_2, b_{10}, q_3
  56. Polygon(B, Q, S) → t12, s_3, b_{11}, q_4
  57. Circle(S, 1) → k_2
  58. OrthogonalLine(S, j_2) → m_2
  59. Intersect(k_2, m_2) → T, U
  60. Segment(B, U) → n_2
  61. Polygon(B, S, U) → t13, u, b_{12}, s_4