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Figurate Numbers Demo

Figurate Numbers Demo
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2017-04-15 22:21
PolygonSequenceGeometric Construction
This example demonstrates the generation and properties of figurate numbers, visually representing sequences of different dimensional polygons through dynamic construction; core math concepts include sequences, geometry, transformations, and parametrization; construction highlights involve GeoGebra commands like Intersect, Point, Polygon, If, Take, Dilate, Sequence, LaTeX, RemoveUndefined, TableText for visualization and interaction; suitable for high school and above mathematics learning, exploring the connection between sequences and geometry and dynamic geometry demonstrations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, If[a, 3, If[b, 4, If[c, 5, 6]]]) → poly1, f, J, g, h, q, r, s, C, H, I
  4. If(a, 3, If[b, 4, If[c, 5, 6]]) → i
  5. Take(list1_1, 1, i) → list1
  6. Take(list1_1, 1, 1) → list0
  7. Dilate(list1, 2) → list2
  8. Dilate(list2, 3 / 2) → list3
  9. Dilate(list3, 4 / 3) → list4
  10. Dilate(list4, 5 / 4) → list5
  11. Sequence(Sequence[Dilate[Element[list5, i], j / 5, Element[list5, i + 1]], i, 2, Length[list5] - 1], j, 1, 5) → list55
  12. Sequence(Sequence[Dilate[Element[list2, i], j / 2, Element[list2, i + 1]], i, 2, Length[list2] - 1], j, 1, 1) → list22
  13. Sequence(Sequence[Dilate[Element[list3, i], j / 3, Element[list3, i + 1]], i, 2, Length[list3] - 1], j, 1, 2) → list33
  14. Sequence(Sequence[Dilate[Element[list4, i], j / 4, Element[list4, i + 1]], i, 2, Length[list4] - 1], j, 1, 3) → list44
  15. Dilate(list5, 6 / 5) → list6
  16. Sequence(Sequence[Dilate[Element[list6, i], j / 6, Element[list6, i + 1]], i, 2, Length[list6] - 1], j, 1, 6) → list66
  17. If(a, 3, If[b, 4, If[c, 5, If[d, 6, 7]]]) → j
  18. LaTeX("P_{" + i + "}(n)") → C1
  19. LaTeX("n") → B1
  20. If(n ≥ A2, A2, NaN) → B2
  21. If(n ≥ A3, A3, NaN) → B3
  22. If(n ≥ A4, A4, NaN) → B4
  23. If(n ≥ A5, A5, NaN) → B5
  24. If(n ≥ A6, A6, NaN) → B6
  25. If(n ≥ A7, A7, NaN) → B7
  26. If(n ≥ A8, A8, NaN) → B8
  27. RemoveUndefined(list7) → list77
  28. RemoveUndefined(list8) → list88
  29. TableText({list77, list88}, "c_|v") → text1