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Eleven Patterns of the Cube

Eleven Patterns of the Cube
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2018-06-07 02:25
PolygonVectorTrigonometrySolid GeometryGeometric Construction
This example demonstrates eleven distinct patterns of a cube and their spatial arrangements. It involves core mathematical concepts such as solid geometry, vectors, polygons, and trigonometric functions (sine and cosine). The construction utilizes GeoGebra commands and objects like Vector, OrthogonalLine, Polygon, Midpoint, Translate, Segment, and Mirror, as outlined in the summary. It is suitable for high school students and math enthusiasts studying spatial geometry and transformations.

GeoGebra Commands & Parameters

  1. Vector(B_1, X) → u
  2. Vector(B_1, Z) → w
  3. OrthogonalLine(Vues, yAxis) → a_1
  4. OrthogonalLine(Vues, 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 * v)))]) → S'
  14. Segment(S, C) → e
  15. Translate(M, Vector[(-2 * v)]) → M'
  16. Segment(M, E) → f
  17. Segment(E, C) → h
  18. Translate(N, Vector[(-2 * v)]) → N'
  19. Translate(Q, Vector[(-2 * v)]) → Q'_1
  20. Segment(Q, F) → i
  21. Segment(N, G) → j
  22. Segment(G, F) → d_1
  23. Translate(Q, Vector[(-2 * v)]) → Q'_2
  24. Translate(B, Vector[(-2 * 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 * v)]) → K'
  29. Translate(P, Vector[(2 * 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 * v)]) → A'
  39. Translate(P, Vector[(2 * 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