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3D Tetrahedral Numbers Display

3D Tetrahedral Numbers Display
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2019-05-29 19:21
FunctionSequenceSolid Geometry
This example demonstrates the 3D display of tetrahedral numbers. Tetrahedral numbers are a type of sequence representing the number of spheres that can be stacked to form a tetrahedron. Using GeoGebra commands Sequence and Sum, the generation process of tetrahedral numbers is dynamically shown. Suitable for middle school and above students to learn sequences and 3D geometry.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Sequence[A + (0, j, 0) + (((-i) * sqrt(3) / 2), 0.5, 0) + (0, 0, n - k) + (k / 2, ((-k)) / 2, 0), i, 0, j - 1], j, 0, k], k, 1, n) → list1
  2. Sequence(Sequence[Sequence[((j * cos(210°)), (j * sin(210°)) + i - 1, ((n - k) * sqrt(3) / 2)) + (((k + 1) * sqrt(3) / 4), 0.5, 0), i, 1, j], j, 1, k], k, 1, n) → list2
  3. Sequence(Length[Element[list2, i]], i, 1, n) → list3
  4. Sequence(Sum[Sequence[Length[Element[Element[list2, i], j]], j, 1, i]], i, 1, n) → list4
  5. Sum(list4) → Tet