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Stairs (Optical Illusion)

Stairs (Optical Illusion)
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2024-06-09 03:38
PolygonSolid GeometryTransformationGeometric ConstructionLocus
This GeoGebra example demonstrates a classic optical illusion of stairs, where a 2D arrangement of polygons creates the visual effect of a 3D staircase, tricking the viewer into perceiving continuous ascending or descending steps. Core mathematical concepts include polygons, rectangles, squares, solid geometry (perspective and projection), and dilation/transformation. Construction highlights: using GeoGebra commands Segment, Point, and Polygon, multiple points (A through V) and segments are created, and polygons (such as q1, l_1, m_1) are formed to build the stair steps; by adjusting point positions and segment connections, the illusion of depth is achieved. Suitable for middle or high school mathematics and geometry classes, this example helps explain optical illusions, polygon composition, spatial reasoning, and geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(E, B) → f
  2. Segment(E, F) → g
  3. Segment(F, G) → h
  4. Segment(G, B) → i
  5. Segment(H, I) → j
  6. Segment(I, J) → k
  7. Segment(J, K) → l
  8. Segment(K, H) → m
  9. Point(j) → L
  10. Point(k) → N
  11. Polygon(L, M, N, I) → q1, l_1, m_1, n, i_1
  12. Segment(E, A) → p
  13. Segment(O, P) → q
  14. Segment(Q, R) → r
  15. Segment(S, T) → s
  16. Segment(U, V) → t
  17. Segment(W, Z) → a
  18. Segment(A_1, B_1) → b
  19. Segment(C_1, D_1) → c
  20. Segment(E_1, F_1) → d
  21. Segment(F, D) → e
  22. Segment(G, C) → f_1
  23. Segment(D, C) → g_1
  24. Segment(A, D) → h_1
  25. Point(g_1) → H_1
  26. Segment(G_1, H_1) → j_1
  27. Point(g_1) → J_1
  28. Segment(I_1, J_1) → k_1
  29. Point(g_1) → L_1
  30. Segment(K_1, L_1) → n_1
  31. Point(g_1) → N_1
  32. Segment(M_1, N_1) → p_1
  33. Point(g_1) → P_1
  34. Segment(O_1, P_1) → q_1
  35. Point(g_1) → R_1
  36. Segment(Q_1, R_1) → r_1
  37. Point(g_1) → T_1
  38. Segment(S_1, T_1) → s_1
  39. Point(g_1) → V_1
  40. Segment(U_1, V_1) → t_1
  41. Segment(G, G_1) → a_1
  42. Segment(G_1, I_1) → b_1
  43. Segment(I_1, K_1) → c_1
  44. Segment(K_1, M_1) → d_1
  45. Segment(M_1, O_1) → e_1
  46. Segment(O_1, Q_1) → f_2
  47. Segment(Q_1, S_1) → g_2
  48. Segment(S_1, U_1) → h_2
  49. Segment(E, O) → i_2
  50. Segment(O, Q) → j_2
  51. Segment(Q, S) → k_2
  52. Segment(S, U) → l_2
  53. Segment(U, W) → m_2
  54. Segment(W, A_1) → n_2
  55. Segment(A_1, C_1) → p_2
  56. Segment(C_1, E_1) → q_2
  57. Polygon(G, G_1, H_1, C) → q2, g_3, t_2, a_2, c_2
  58. Polygon(I_1, K_1, L_1, J_1) → q3, b_2, d_2, e_2, f_3
  59. Polygon(M_1, O_1, P_1, N_1) → q4, h_3, o_1, i_3, j_3
  60. Polygon(S_1, T_1, R_1, Q_1) → q5, k_3, l_3, m_3, n_3
  61. Point(g_1) → W_1
  62. Segment(U_1, W_1) → s_2
  63. Polygon(U_1, V_1, W_1) → t1, w_1, u_1, v_1
  64. Point(h_1) → Z_1
  65. Polygon(A, P, O, E) → q6, a_3, p_3, o, e_3
  66. Polygon(R, T, S, Q) → q7, r_3, t_3, s_3, q_3
  67. Polygon(V, U, W, Z) → q8, v, u, w, z_1
  68. Polygon(B_1, A_1, C_1, D_1) → q9, b_3, c_3, d_3, f_4
  69. Segment(E_1, Z_1) → r_2
  70. Polygon(F_1, E_1, Z_1) → t2, g_4, h_4, i_4
  71. Segment(K, M) → j_4
  72. Polygon(H, K, M, L) → q10, h_5, k_4, m_4, l_4
  73. Polygon(F, D, G_1, G, W_1, U_1, S_1, Q_1, O_1, M_1, K_1, I_1) → poly1, f_5, b_4, c_4, g_5, d_4, n_4, p_4, q_4, r_4, s_4, t_4, a_4

AI Drawing Prompt Reference

Create an optical illusion of stairs using multiple rectangles and squares. Start by creating points E, B, F, G, H, I, J, K, L, M, N, and then connect these points to form multiple rectangles and squares, such as q1, l1, m1, to achieve a depth illusion effect through adjusting point positions and line segment connections.
The prompt above was compiled from the original drawing commands and is for reference only.