MathPlotAI Logo MathPlotAI

Cube Cutting: Square of Triangular Numbers

Cube Cutting: Square of Triangular Numbers
Loading the math board and drawing, please wait…
2017-10-21 03:13
SequenceSolid Geometry
This example demonstrates the formation of a square of triangular numbers after cutting a cube. Key mathematical concepts include sequences, solid geometry, and geometric construction. Using GeoGebra commands such as Point, Cube, Sequence, and Flatten, the construction of the cut cube is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]) → A
  2. Cube((0, 0), (1, 0), A) → a, B, faceABFE, faceCDEF, edge2, edge1, edge4, edgeAB, edge3, edgeBF, edgeCF, edgeCD, C, edge5, edgeDE, edgeAE, edgeEF, D, E, F, face1, face3, face2, face4
  3. Sequence(Translate[a, Vector[(i, 0)]], i, 1, 2) → l1
  4. Sequence(Translate[a, Vector[(0, i)]], i, 1, 2) → l2
  5. Flatten(Sequence[Translate[l1, Vector[(0, i)]], i, 1, 2]) → l3
  6. Flatten(Translate[{a, l1, l2, l3}, Vector[(0, 3)]]) → l4
  7. Flatten(Translate[l4, Vector[(3, 0)]]) → l5
  8. Flatten(Translate[{a, l1, l2, l3}, Vector[(3, 0)]]) → l6
  9. Sequence(Translate[a, Vector[(i, 0)]], i, 6, 9) → l7
  10. Flatten(Sequence[Translate[l7, Vector[(0, i)]], i, 1, 9]) → l8
  11. Polygon((3, 2, 0), (1, 2, 0), (1, 2, 1), (3, 2, 1)) → q1, f, g, h, i
  12. Flatten(Sequence[Sequence[Translate[a, Vector[(j, i)]], i, 6, 9, 1], j, 0, 5, 1]) → l9
  13. Polygon((6, 0, 0), (6, 4, 0), (6, 4, 1), (6, 0, 1)) → q3, n, p, q, r
  14. Polygon((1, 1, 0), (1, 3, 0), (1, 3, 1), (1, 1, 1)) → q2, j, k, l, m
  15. Polygon((6, 3, 0), (3, 3, 0), (3, 3, 1), (6, 3, 1)) → q4, s, t, b, c
  16. Polygon((3, 3, 0), (3, 3, 1), (3, 6, 1), (3, 6, 0)) → q5, d, e, f_1, g_1
  17. Polygon((6, 4, 0), (10, 4, 0), (10, 4, 1), (6, 4, 1)) → q6, h_1, i_1, j_1, k_1
  18. Polygon((6, 6, 0), (6, 10, 0), (6, 10, 1), (6, 6, 1)) → q9, a_1, b_1, c_1, d_1
  19. Polygon((6, 8, 0), (10, 8, 0), (10, 8, 1), (6, 8, 1)) → q7, l_1, m_1, n_1, p_1
  20. Polygon((4, 6, 0), (4, 10, 0), (4, 10, 1), (4, 6, 1)) → q8, q_1, r_1, s_1, t_1
  21. Translate(a, Vector[(-2, 0)]) → a'
  22. Translate(l3, Vector[(-4, 1)]) → l3'
  23. Translate(l3', Vector[(0, 0, 1)]) → l3''
  24. Translate(l4, Vector[(-3, -7)]) → l10
  25. Flatten(Sequence[Translate[l10, Vector[(0, 0, i)]], i, 1, 2, 1]) → l11
  26. Translate(l7, Vector[(-3, -2)]) → l12
  27. Flatten(Sequence[Translate[l12, Vector[(0, i)]], i, -1, -3, -1]) → l13
  28. Flatten(Sequence[Translate[Flatten[{l12, l13}], Vector[(0, 0, i)]], i, 1, 3, 1]) → l14