MathPlotAI Logo MathPlotAI

Spiral George B

Spiral George B
Loading the math board and drawing, please wait…
2019-05-26 00:48
FunctionParametric EquationGeometric Construction
In collections EQUILATERAL TRIANGLE SPIRAL
This example demonstrates a spiral using function and parametric equations. It involves constructing complex spiral shapes using GeoGebra commands such as Polygon, OrthogonalLine, and Intersect. Suitable for high school and above students to explore.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. OrthogonalLine(C, f) → i
  3. Intersect(i, f) → D
  4. Segment(C, D) → j
  5. Polygon(C, D, 3) → poly2, k, l, m, E
  6. Intersect(g, l) → F
  7. Segment(C, F) → n
  8. Polygon(C, F, 3) → poly3, p, q, r, G
  9. Intersect(m, q) → H
  10. Segment(C, H) → s
  11. Polygon(C, H, 3) → poly4, t, a, b, I
  12. Intersect(r, a) → J
  13. Segment(C, J) → c
  14. Polygon(C, J, 3) → poly5, d, e, f_1, K
  15. Intersect(b, e) → L
  16. Segment(C, L) → g_1
  17. Polygon(C, L, 3) → poly6, h_1, i_1, j_1, M
  18. Intersect(f_1, i_1) → N
  19. Segment(C, N) → k_1
  20. Polygon(C, N, 3) → poly7, l_1, m_1, n_1, O
  21. Intersect(j_1, m_1) → P
  22. Segment(C, P) → p_1
  23. Polygon(C, P, 3) → poly8, q_1, r_1, s_1, Q
  24. Intersect(n_1, r_1) → R
  25. Segment(C, R) → t_1
  26. Polygon(C, R, 3) → poly9, a_1, b_1, c_1, S
  27. Intersect(s_1, b_1) → T
  28. Segment(C, T) → d_1
  29. Polygon(C, T, 3) → poly10, e_1, f_2, g_2, U
  30. Intersect(c_1, f_2) → V
  31. Segment(C, V) → h_2
  32. Intersect(j, k) → D_1
  33. Intersect(j, k) → E_1
  34. Intersect(g, n) → H_1
  35. Intersect(m, s) → K_1
  36. Intersect(b, g_1) → P_1
  37. Intersect(f_1, k_1) → S_1
  38. Polygon(K, C, J) → t1, j_4, k_4, c_4
  39. Polygon(M, C, L) → t2, l_4, m_4, c_5
  40. Polygon(Q, C, P) → t3, p_4, q_4, c_6
  41. Polygon(O, C, N) → t4, n_4, o, c_7
  42. Polygon(C, S, R) → t5, r_4, c_8, s_4
  43. Polygon(C, S, R) → t6, r_5, c_9, s_5
  44. Polygon(Q, C, P) → t7, p_5, q_5, c_{10}
  45. Distance(A, B) → distanceAB
  46. Distance(D, E) → distanceDE
  47. Distance(F, G) → distanceFG
  48. Distance(H, I) → distanceHI
  49. Polygon(C, V, 3) → poly11, i_2, j_2, k_2, W
  50. Intersect(poly10, poly11) → Z, A_1, B_1, C_1, F_1, G_1, I_1
  51. Polygon(I_1, G_1, 3) → poly12, l_2, m_2, n_2, J_1

AI Drawing Prompt Reference

Draw a complex spiral shape using function and parametric equations. Start by constructing a triangle, then create multiple subsequent triangles, each connecting to the previous triangle's vertex and forming a perpendicular line to its edge, creating a spiraling effect. Pay attention to the size and positional relationships of each triangle to ensure the overall spiral pattern is clear and ascending.
The prompt above was compiled from the original drawing commands and is for reference only.