MathPlotAI Logo MathPlotAI

11 Patterns of the Cube: Interactive 3D Demonstration

11 Patterns of the Cube: Interactive 3D Demonstration
Loading the math board and drawing, please wait…
2012-11-14 03:22
VectorTrigonometrySolid GeometryTransformationSlider Animation
This GeoGebra example demonstrates 11 geometric patterns or transformations of a cube, allowing interactive observation via sliders and 3D viewpoint adjustments. Core math concepts include solid geometry, transformations like reflection and translation, and trigonometric parameterization. Construction highlights: Utilizes commands such as Vector for vectors, OrthogonalLine for perpendicular lines, Polygon for polygons, Midpoint for midpoints, Translate for translation, Segment for segments, and Mirror for mirroring; key objects include View3D for 3D visualization and trigonometric variables like sinphi and cosphi for dynamic angle control. Suitable for high school or university students studying solid geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Vector(B_1, X) → u
  2. Vector(B_1, Z) → w
  3. OrthogonalLine(View3D, yAxis) → a_1
  4. OrthogonalLine(View3D, xAxis) → b_1
  5. Vector(B_1, Y) → v
  6. Polygon(L, K, N, M) → poly1, l, k_1, n, m
  7. Polygon(K, P, Q, N) → poly2, k_2, p, q, n_1
  8. Polygon(L, M, S, R) → poly3, l_1, m_1, s, r
  9. Polygon(N, V, W, M) → poly4, n_2, v_1, w_1, m_2
  10. Polygon(K, T, U, L) → poly5, k_3, t, u_1, l_2
  11. Polygon(B, Q, P, A) → poly6, b_2, q_1, p_1, a_2
  12. Midpoint(R, M) → D
  13. Translate(S, Vector[-(2.0 * v)]) → S'
  14. Segment(S, C) → e
  15. Translate(M, Vector[-(2.0) * v]) → M'
  16. Segment(M, E) → f
  17. Segment(E, C) → h
  18. Translate(N, Vector[-(2.0) * v]) → N'
  19. Translate(Q, Vector[-(2.0) * v]) → Q'_1
  20. Segment(Q, F) → i
  21. Segment(N, G) → j
  22. Segment(G, F) → d_1
  23. Translate(Q, Vector[-(2.0) * v]) → Q'_2
  24. Translate(B, Vector[-(2.0) * v]) → B'_1
  25. Segment(B, I) → e_1
  26. Segment(I, H) → f_1
  27. Segment(H, Q) → g_1
  28. Translate(K, Vector[2.0 * v]) → K'
  29. Translate(P, Vector[2.0 * v]) → P'_1
  30. Segment(P, J) → h_1
  31. Segment(J, A_1) → i_1
  32. Segment(A_1, K) → j_1
  33. Segment(B, H_1) → s_1
  34. Segment(H_1, C_1) → c
  35. Segment(C_1, A) → r_1
  36. Midpoint(N, P) → D_1
  37. Midpoint(k_1) → F_1
  38. Translate(A, Vector[2.0 * v]) → A'
  39. Translate(P, Vector[2.0 * v]) → P'
  40. Segment(A, G_1) → t_1
  41. Segment(G_1, I_1) → c_2
  42. Segment(I_1, P) → d_2
  43. Segment(J, K_1) → f_2
  44. Segment(P, L_1) → e_2
  45. Segment(L_1, K_1) → g_2
  46. Segment(M, W) → h_2
  47. Mirror(L_1, F_1) → O_1
  48. Mirror(K_1, F_1) → P_1
  49. Segment(M, M_1) → i_2
  50. Segment(N_1, J_1) → j_2
  51. Segment(J_1, M_1) → p_2
  52. Polygon(M, E, C, S) → poly7, q_2, r_2, s_2, t_2
  53. Polygon(Q, N, G, F) → poly8, q_3, n_3, g_3, f_3
  54. Polygon(B, Q, H, I) → poly9, b_3, q_4, h_3, i_3
  55. Polygon(J, A_1, K, P) → poly10, j_3, a_3, k_4, p_3
  56. Polygon(C_1, A, B, H_1) → poly11, c_3, a_4, b_4, h_4
  57. Polygon(G_1, I_1, P, A) → poly12, g_4, i_4, p_4, a_5
  58. Polygon(K_1, J, P, L_1) → poly13, k_5, j_4, p_5, l_3
  59. Polygon(M, M_1, J_1, N_1) → poly14, m_3, m_4, j_5, n_4