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General Model for Polygonal Numbers

General Model for Polygonal Numbers
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2015-07-15 19:18
PolygonSequenceTransformation
This example demonstrates the geometric model of polygonal numbers. It involves concepts such as polygons, sequences, and transformations. Using GeoGebra commands like Segment, Rotate, and Sequence, it dynamically shows the generation process of polygonal numbers. Suitable for middle school and above students or teachers to help understand the properties and generation rules of polygonal numbers.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Rotate(B, (2 * π / u), A) → B'
  3. Sequence(Rotate[B, ((2 * π / u) * k), A], k, 1, u) → список1
  4. Polygon(B, B', u) → многоугольник2, m, c_1, d_1, b, c, d, e, f, g, h, i, n_1, j, N, O, P, Q, R, S, T, U, V, p, C, D, E, F, G, H, I, J, K, q, r, s, t, a_1, b_1
  5. Sequence(Dilate[многоугольник2, l, B], l, 1, n) → список2
  6. Sequence(Dilate[список1, l, B], l, 1, n) → список3
  7. Sequence(Dilate[список1, l, A], l, 1, n) → список4
  8. Sequence(Segment[Element[список1, s], Element[список1, s + 1]], s, 1, u - 1) → список5
  9. Element(список3, 1) → список10
  10. Sequence(Element[Element[список3, n], 1] + (i * (Element[Element[список3, n], 2] - Element[Element[список3, n], 1])), i, 0, 1, 1 / n) → список8
  11. Sequence(Element[Element[список3, n], 1] + (i * (Element[Element[список3, n], 2] - Element[Element[список3, n], 1])), i, 0, 1, 1 / n) → список9
  12. Sequence(Sequence[Element[Element[список3, n], k] + (i * (Element[Element[список3, n], k + 1] - Element[Element[список3, n], k])), i, 0, 1, 1 / n], k, 1, u - 1) → список11
  13. Sequence(Sequence[Sequence[Element[Element[список3, s], k] + (i * (Element[Element[список3, s], k + 1] - Element[Element[список3, s], k])), i, 0, 1, 1 / s], k, 1, u - 1], s, 1, n) → список12