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Wiegand Spiral

Wiegand Spiral
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2017-03-06 23:46
FunctionTrigonometrySolid GeometryGeometric Construction
This example demonstrates the beautiful square and rectangle spiral created by Charmion von Wiegand, involving concepts like dilation, hypergeometric distribution, cuboid, cone, tangent function, and means. It is constructed using GeoGebra commands such as Point, Polygon, and objects like r_1, a_1, r_0, a_0, A, B, etc. Suitable for high school and above learning geometric constructions and solid geometry.

GeoGebra Commands & Parameters

  1. Point(Ray[A, A + (1, 0)]) → B
  2. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  3. Point(Ray[D, (2 * D) - A]) → E
  4. Polygon(D, C, F, E) → poly2, d, c, f_1, e
  5. Polygon(A, G, H, I) → poly3, a_3, g_1, h_1, i_1
  6. Polygon(I, H, 4) → poly4, j, k, l, m, J, K
  7. Polygon(N, M, 4) → poly5, n_3, p, q, s, O, P
  8. Polygon(J, L, M, N) → poly6, j_1, l_1, m_1, n_1
  9. Polygon(O, Q, R, S) → poly7, o, q_1, r_4, s_1
  10. Polygon(S, R, 4) → poly8, t, b, k_1, p_1, T, U
  11. Polygon(Z, W, 4) → poly9, t_1, b_1, c_1, d_1, A_1, B_1
  12. Polygon(V, W, Z, T) → poly10, v, w, z_1, t_2
  13. Polygon(C_1, D_1, E_1, A_1) → poly11, c_2, d_2, e_1, a_2
  14. Polygon(E_1, D_1, 4) → poly12, f_2, g_2, h_2, i_2, F_1, G_1
  15. Polygon(J_1, I_1, 4, xOyPlane) → poly13, j_2, k_2, l_2, m_2, K_1, L_1
  16. Polygon(F_1, H_1, I_1, J_1) → poly14, f_3, h_3, i_3, j_3
  17. Polygon(O_1, K_1, M_1, N_1) → poly15, o_1, k_3, m_3, n_2
  18. Polygon(O_1, N_1, 4, xOyPlane) → poly16, p_2, q_2, r_2, s_2, P_1, Q_1
  19. Polygon(T_1, S_1, 4, xOyPlane) → poly17, b_2, e_2, g_3, l_3, U_1, V_1
  20. Polygon(T_1, P_1, R_1, S_1) → poly18, t_3, p_3, r_3, s_3

AI Drawing Prompt Reference

Draw a spiral composed of squares and rectangles to demonstrate geometric construction and solid geometry concepts. Start with a ray, sequentially create multiple squares and rectangles by combining points, edges, and faces, forming a gradually expanding spiral structure that showcases symmetry and layering.
The prompt above was compiled from the original drawing commands and is for reference only.