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Sums of Triangular Numbers

Sums of Triangular Numbers
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2017-05-17 20:01
SequenceCoordinate GeometryGeometric Construction
This example demonstrates the sum of triangular numbers and their geometric interpretation. It involves core math concepts like triangular numbers, sequence summation, and coordinate geometry. Constructed using GeoGebra's Sequence command and objects such as liste11, liste55, etc., it is suitable for high school mathematics teaching to understand the connection between sequences and geometric shapes.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Sequence[Cube[(i - 1 + (1.5 * (n * p)), j - 1, k - 1), (i + (1.5 * (n * p)), j - 1, k - 1), (i + (1.5 * (n * p)), j, k - 1)], j, 1, n + 1 - i], i, k, n], k, 1, n) → liste11
  2. Sequence(Sequence[Sequence[Cube[(i - 2 - ((1.5 * n) * p), 2 + n - k, j - 1), (i - 1 - ((1.5 * n) * p), 2 + n - k, j - 1), (i - 1 - ((1.5 * n) * p), 2 + n - k, j)], i, 1, k], j, k, n], k, 1, n) → liste55
  3. Sequence(Sequence[Sequence[Cube[(n + 1 - i, j + 1 + ((1.5 * n) * p), k), (n - i, j + 1 + ((1.5 * n) * p), k), (n - i, j + 2 + ((1.5 * n) * p), k)], i, 1, k], j, k, n], k, 1, n) → liste33
  4. Sequence(Sequence[Sequence[Cube[((-i) + 1 + n + ((1.5 * n) * p), k + ((1.5 * n) * p), j - 1), ((-i) + n + ((1.5 * n) * p), k + ((1.5 * n) * p), j - 1), ((-i) + n + ((1.5 * n) * p), k + ((1.5 * n) * p), j)], i, 1, k], j, k, n], k, 1, n) → liste22
  5. Sequence(Sequence[Sequence[Cube[(n - k - ((1.5 * n) * p), j + 1 + ((1.5 * n) * p), i - 1), (n - k - ((1.5 * n) * p), j + 1 + ((1.5 * n) * p), i), (n - k - ((1.5 * n) * p), j + 2 + ((1.5 * n) * p), i)], i, 1, k], j, k, n], k, 1, n) → liste44
  6. Sequence(Sequence[Sequence[Cube[(i - 2, 1 - j + n - ((1.5 * n) * p), k), (i - 1, 1 - j + n - ((1.5 * n) * p), k), (i - 1, (-j) + n - ((1.5 * n) * p), k)], i, 1, k], j, k, n], k, 1, n) → liste66