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Spiral Art Maria

Spiral Art Maria
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2019-05-26 00:55
VectorFunctionGeometric Construction
In collections EQUILATERAL TRIANGLE SPIRAL
This example demonstrates the construction of Spiral Art Maria. It involves concepts of function graphs and vectors. Using commands like Polygon, OrthogonalLine, Intersect, Segment, Vector, and Translate, a beautiful spiral pattern can be created. Suitable for high school mathematics education, particularly in coordinate geometry and function graphing.

GeoGebra Commands & Parameters

  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''