Mathematical Modeling of the Oblation Statue

Mathematical Modeling of the Oblation Statue
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2022-01-21 21:53
This example demonstrates the geometric construction of the Oblation statue using GeoGebra, involving concepts like solid geometry, symmetry, rotation, and mirroring. Key commands used include Polygon, Rotate, and Mirror to create and manipulate the shape. Suitable for high school and above to understand 3D figure construction.

GeoGebra Commands & Parameters

  1. Polygon(K_1, J_1, A_1, Z, W, V, U, T, S, R, Q, O, I_1, N, P, M, L, G, F, E, D, C, M_1, H_1, G_1, F_1, E_1, D_1, C_1, B_1) → poly1, k_1, b_1, a_1, z_1, w, v, u, t, s, r, q, j_1, o, n, p, m, l, g, f, e, d, c, i_1, m_1, h_1, g_1, f_1, e_1, d_1, c_1
  2. Polygon(C, M_1, L_1, K, J, H, I) → poly2, c_2, h, l_1, k, j, h_2, i
  3. Rotate(K_1, 90°, xAxis) → N_1
  4. Rotate(J_1, 90°, xAxis) → O_1
  5. Rotate(I_1, 90°, xAxis) → P_1
  6. Rotate(H_1, 90°, xAxis) → Q_1
  7. Rotate(G_1, 90°, xAxis) → R_1
  8. Rotate(F_1, 90°, xAxis) → S_1
  9. Rotate(E_1, 90°, xAxis) → T_1
  10. Rotate(D_1, 90°, xAxis) → U_1
  11. Rotate(C_1, 90°, xAxis) → V_1
  12. Rotate(B_1, 90°, xAxis) → W_1
  13. Rotate(A_1, 90°, xAxis) → Z_1
  14. Rotate(Z, 90°, xAxis) → Z'
  15. Rotate(W, 90°, xAxis) → W'
  16. Rotate(V, 90°, xAxis) → V'
  17. Rotate(U, 90°, xAxis) → U'
  18. Rotate(T, 90°, xAxis) → T'
  19. Rotate(S, 90°, xAxis) → S'
  20. Rotate(R, 90°, xAxis) → R'
  21. Rotate(Q, 90°, xAxis) → Q'
  22. Rotate(O, 90°, xAxis) → O'
  23. Rotate(N, 90°, xAxis) → N'
  24. Rotate(P, 90°, xAxis) → P'
  25. Rotate(M, 90°, xAxis) → M'
  26. Rotate(L, 90°, xAxis) → L'
  27. Rotate(G, 90°, xAxis) → G'
  28. Rotate(F, 90°, xAxis) → F'
  29. Rotate(E, 90°, xAxis) → E'
  30. Rotate(D, 90°, xAxis) → D'
  31. Rotate(C, 90°, xAxis) → C'
  32. Rotate(M_1, 90°, xAxis) → A_2
  33. Polygon(N_1, O_1, Z_1, Z', W', V', U', T', S', R', Q', O', P_1, N', P', M', L', G', F', E', D', C', A_2, Q_1, R_1, S_1, T_1, U_1, V_1, W_1) → poly1', n_1, w_1, a, z', w', v', u', t', s', r', q', o_1, o', n', p', m', l', g', f', e', d', c', p_1, a_2, q_1, r_1, s_1, t_1, u_1, v_1
  34. Rotate(poly2, 90°, xAxis) → poly2'
  35. Mirror(poly1', eq1) → poly1''
  36. Mirror(poly2', eq1) → poly2''

AI Drawing Prompt Reference

Construct a 3D solid-like sculpture silhouette in 2D by combining rotation and mirroring of polygon faces. First, create a main polygon surface using a large ordered set of points to form the primary body, then create a second polygon surface from another set of points to serve as a paired side piece. Choose one horizontal axis and rotate the first polygon around it by 90 degrees repeatedly to produce several corresponding side copies; rotate the second polygon around the same axis in the same way to obtain its matching copies. Finally, mirror the rotated copies of both polygons across a given symmetry line to complete the overall symmetric statue shape.
The prompt above was compiled from the original drawing commands and is for reference only.