MathPlotAI Logo MathPlotAI

Penrose Triangle

Penrose Triangle
Loading the math board and drawing, please wait…
2018-01-16 16:26
VectorSolid GeometryGeometric Construction
This example demonstrates the construction and properties of the Penrose triangle, a famous visual paradox consisting of three mutually connected but non-interlocking triangles that cannot form a three-dimensional space. The core mathematical concepts involved include polygon construction, solid geometry, vector operations, and spatial geometric relationships. The construction highlights commands and objects in GeoGebra such as Polygon, Prism, Vector, Plane, IntersectPath, and Segment. It is suitable for high school students and above to explore spatial geometry, visualization skills, and geometric construction techniques, as well as for mathematical competitions or enrichment purposes.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Prism(poly1, l) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  3. Polygon(I, H, G, J) → poly2, i, h, g, j
  4. Prism(poly2, l - 1) → f, K, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, L, M, N, face1, face2, face3, face4, face5
  5. Polygon(C, O, P, B) → poly3, c_1, o, p, b_1
  6. Prism(poly3, l) → k, Q, edgeCQ, edgeOR, edgePS, edgeBT, edgeQR, edgeRS, edgeST, edgeQT, R, S, T, faceCORQ, faceOPSR, faceBPST, faceBCQT, faceQRST
  7. Vector(N, Q) → u
  8. Plane(N, edgeCQ) → m
  9. Plane(S, m) → n
  10. IntersectPath(n, f) → poly4, U, V, W, Z, q, r, s, t
  11. Polygon(A, E, V, U, I, D) → poly5, a_1, e_1, v, u_1, i_1, d_1
  12. Polygon(E, F, W, V) → poly6, e_2, f_1, w, v_1
  13. Polygon(Q, D, I, J, O, R) → poly7, q_1, d_2, i_2, j_1, o_1, r_1
  14. Polygon(O, P, S, R) → poly8, o_2, p_1, s_1, r_2
  15. Polygon(W, Z, J, O, P, F) → poly9, w_1, z_1, j_2, o_3, p_2, f_2
  16. Polygon(R, S, T, Q) → poly10, r_3, s_2, t_1, q_2
  17. Polygon(T, A, D, Q) → poly11, t_2, a_2, d_3, q_3
  18. Polygon(E, A, T, S, P, F) → poly12, e_3, a_3, t_3, s_3, p_3, f_3
  19. Polygon(J, I, U, Z) → poly13, j_3, i_3, u_2, z_2
  20. Polygon(Q, R, O, D) → poly14, q_4, r_4, o_4, d_4
  21. Polygon(D, I, J, O) → poly15, d_5, i_4, j_4, o_5
  22. Polygon(A, E, I, D) → poly16, a_4, e_4, i_5, d_6
  23. Polygon(I, E, V, U) → poly17, i_6, e_5, v_2, u_3
  24. Polygon(W, Z, J, F) → poly18, w_2, z_3, j_5, f_4
  25. Polygon(J, O, P, F) → poly19, j_6, o_6, p_4, f_5
  26. Polygon(F, E, A, P) → poly20, f_6, e_6, a_5, p_5
  27. Polygon(P, A, T, S) → poly21, p_6, a_6, t_4, s_4
  28. Segment(P, A_1) → g_1