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Dissecting Cubes Demo

Dissecting Cubes Demo
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2019-05-11 23:42
VectorCoordinate GeometrySolid GeometryTransformationGeometric Construction
This example demonstrates the dissection and reassembly of cubes, illustrating spatial transformations and relationships in geometry. It involves core concepts like solid geometry, vector operations, and geometric transformations (translation, rotation). Construction highlights include commands like Point, Polygon, Segment, Midpoint, Centroid, Circle, Intersect, Vector, Translate, Prism. Suitable for high school students and above learning spatial reasoning and GeoGebra dynamic geometry software.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  5. Segment(H, F) → n
  6. Segment(E, G) → p
  7. Midpoint(i) → I
  8. Midpoint(m) → J
  9. Midpoint(l) → K
  10. Midpoint(k) → L
  11. Midpoint(j) → M
  12. Midpoint(n) → N
  13. Midpoint(h) → O
  14. Midpoint(g) → P
  15. Centroid(poly1) → Q
  16. Centroid(poly1) → R
  17. Midpoint(f) → S
  18. Polygon(D, I, J, E, N, H, K, O) → poly3, d, i_1, j_1, e, n_1, h_1, k_1, o
  19. Polygon(O, K, H, N, G, L, P, C) → poly4, o_1, k_2, h_2, n_2, g_1, l_1, p_1, c
  20. Polygon(L, G, N, F, M, S, B, P) → poly5, l_2, g_2, n_3, f_1, m_1, s, b, p_2
  21. Polygon(I, A, S, M, F, N, E, J) → poly6, i_2, a, s_1, m_2, f_2, n_4, e_1, j_2
  22. Circle(N, r) → q
  23. Intersect(q, h_2) → T,
  24. Intersect(q, g_2) → U,
  25. Vector(N, T) → u
  26. Vector(N, U) → v
  27. Translate(O, v) → O'
  28. Translate(K, v) → K'
  29. Translate(H, v) → H'
  30. Translate(N, v) → N'
  31. Translate(G, v) → G'
  32. Translate(L, v) → L'
  33. Translate(P, v) → P'
  34. Translate(C, v) → C'
  35. Polygon(O', K', H', N', G', L', P', C') → poly4', o', k', h', n', g', l', p', c'
  36. Translate(D, u) → D'
  37. Translate(I, u) → I'
  38. Translate(J, u) → J'
  39. Translate(E, u) → E'
  40. Translate(N, u) → N'_1
  41. Translate(H, u) → H'_1
  42. Translate(K, u) → K'_1
  43. Translate(O, u) → O'_1
  44. Polygon(D', I', J', E', N'_1, H'_1, K'_1, O'_1) → poly3', d', i', j', e', n'_1, h'_1, k'_1, o'_1
  45. Translate(I, Vector[(-v)]) → I'_1
  46. Translate(A, Vector[(-v)]) → A'
  47. Translate(S, Vector[(-v)]) → S'
  48. Translate(M, Vector[(-v)]) → M'
  49. Translate(F, Vector[(-v)]) → F'
  50. Translate(N, Vector[(-v)]) → N'_2
  51. Translate(E, Vector[(-v)]) → E'_1
  52. Translate(J, Vector[(-v)]) → J'_1
  53. Polygon(I'_1, A', S', M', F', N'_2, E'_1, J'_1) → poly6', i'_1, a', s', m', f', n'_2, e'_1, j'_1
  54. Translate(L, Vector[(-u)]) → L'_1
  55. Translate(G, Vector[(-u)]) → G'_1
  56. Translate(N, Vector[(-u)]) → N'_3
  57. Translate(F, Vector[(-u)]) → F'_1
  58. Translate(M, Vector[(-u)]) → M'_1
  59. Translate(S, Vector[(-u)]) → S'_1
  60. Translate(B, Vector[(-u)]) → B'
  61. Translate(P, Vector[(-u)]) → P'_1
  62. Polygon(L'_1, G'_1, N'_3, F'_1, M'_1, S'_1, B', P'_1) → poly5', l'_1, g'_1, n'_3, f'_1, m'_1, s'_1, b', p'_1
  63. Prism(poly3', a_1) → b_1, F_1, face10, face11, face12, face13, face14, face15, face9, face16, edge12, edge13, G_1, edge14, edge15, edge16, edge17, edge18, edge19, edge20, edge22, edge23, edge24, H_1, edge25, edge26, edge27, edge21, I_1, J_1, K_1, L_1, M_1, face8
  64. Prism(poly4', q_1) → r_1, V_1, face28, face29, face30, face31, face32, face33, face27, face34, edge28, edge45, W_1, edge46, edge47, edge48, edge49, edge50, edge51, edge52, edge54, edge55, edge56, Z_1, edge57, edge58, edge59, edge53, A_2, B_2, C_2, D_2, E_2, face17
  65. Prism(poly6', d_1) → t_1, N_1, face21, face22, face23, face24, face25, face26, face20, face35, edge30, edge31, O_1, edge32, edge33, edge34, edge35, edge36, edge37, edge38, edge40, edge41, edge42, P_1, edge43, edge44, edge60, edge39, Q_1, R_1, S_1, T_1, U_1, face19
  66. Prism(poly5', u_1) → v_1, F_2, face39, face40, face41, face42, face43, face44, face38, face45, edge63, edge64, G_2, edge65, edge66, edge67, edge68, edge69, edge70, edge71, edge73, edge74, edge75, H_2, edge76, edge77, edge78, edge72, I_2, J_2, K_2, L_2, M_2, face37