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Polyhedron Computer Constructions n=10

Polyhedron Computer Constructions n=10
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2015-03-27 19:30
VectorTrigonometrySolid GeometryCalculusGeometric Construction
This example demonstrates random oscillations on a spherical surface near equilibrium positions, involving key math concepts like constructions, continuity, calculus, 2D vectors, trigonometric functions, and distributions. It uses GeoGebra commands such as Sequence, Sort, Element, TableText, Length, Intersect, and Sphere for dynamic visualization, suitable for high school and above learners/teachers exploring spatial geometry and dynamic systems.

GeoGebra Commands & Parameters

  1. Sequence(((zoom * Element[Element[A00, i], 1]), (zoom * Element[Element[A00, i], 2]), (zoom * Element[Element[A00, i], 3])), i, 1, Length[A00]) → A0
  2. Sort(Sequence[Segment[Element[A0, Element[Element[nom, i], 1]], Element[A0, Element[Element[nom, i], 2]]], i, 1, Length[nom]]) → Segments
  3. Sequence(Element[Segments, i], i, 1, i_s) → Segments_o
  4. Sort(Union[{}, ceil((Segments * 10^(k))) / 10^(k)]) → Segn
  5. Sequence(KeepIf[If[i ≟ 1, x ≤ Element[Segn, i], If[i ≟ Length[Segn], Element[Segn, i - 1] < x, Element[Segn, i - 1] < x ≤ Element[Segn, i]]], Segments], i, 1, Length[Segn]) → la0
  6. Sequence(Length[Element[la0, i]], i, 1, Length[Segn]) → lLength
  7. Element(la0, 1) → la1
  8. Element(la0, 2) → la2
  9. Element(la0, 3) → la3
  10. Element(la0, 4) → la4
  11. Sequence(((zoom * Element[Element[A00d, i], 1]), (zoom * Element[Element[A00d, i], 2]), (zoom * Element[Element[A00d, i], 3])), i, 1, Length[A00d]) → A0d
  12. Sort(Sequence[Segment[Element[A0d, Element[Element[nomd, i], 1]], Element[A0d, Element[Element[nomd, i], 2]]], i, 1, Length[nomd]]) → Segmentsd
  13. Sequence(Element[Segmentsd, i], i, 1, id_s) → Segmentsd_o
  14. Sort(Union[{}, ceil((Segmentsd * 10^(k_d))) / 10^(k_d)]) → Segnd
  15. Sequence(KeepIf[If[i ≟ 1, x ≤ Element[Segnd, i], If[i ≟ Length[Segnd], Element[Segnd, i - 1] < x, Element[Segnd, i - 1] < x ≤ Element[Segnd, i]]], Segmentsd], i, 1, Length[Segnd]) → la0d
  16. Sequence(Length[Element[la0d, i]], i, 1, Length[Segnd]) → lLengthd
  17. TableText({mm5ad, mm7ad}, "hr") → text2
  18. Element(la0d, 1) → la1d
  19. Element(la0d, 2) → la2d
  20. Element(la0d, 3) → la3d
  21. Element(la0d, 4) → la4d
  22. TableText({Segn, lLength}, "hr") → text8
  23. TableText({Segnd, lLengthd}, "hr") → text9
  24. TableText({Append["n=", mm5a], Append["N=", mm7a]}, "hr") → text1
  25. Sequence(Polygon[Element[A0, Element[Element[mm1, f], 1]], Element[A0, Element[Element[mm1, f], 2]], Element[A0, Element[Element[mm1, f], 3]]], f, 1, Length[mm1]) → poly_3
  26. Sequence(Polygon[Element[A0d, Element[Element[mm1d, f], 1]], Element[A0d, Element[Element[mm1d, f], 2]], Element[A0d, Element[Element[mm1d, f], 3]]], f, 1, Length[mm1d]) → polyd_3
  27. Length(a00) → n
  28. Intersect(xAxis, zAxis) → A
  29. Sphere(A, (r_0 * zoom)) → a
  30. Sequence(((((r_0 * zoom) * cos(Element[a01, i])) * sin(Element[b01, i])), (((r_0 * zoom) * sin(Element[a01, i])) * sin(Element[b01, i])), ((r_0 * zoom) * cos(Element[b01, i]))), i, 1, n) → A0w
  31. Sequence(Polygon[Element[A0d, Element[Element[Element[mm6d, 1], i], 1]], Element[A0d, Element[Element[Element[mm6d, 1], i], 2]], Element[A0d, Element[Element[Element[mm6d, 1], i], 3]], Element[A0d, Element[Element[Element[mm6d, 1], i], 4]]], i, 1, 2) → polyd_{4}