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n=40 Polyhedron Computer Constructions

n=40 Polyhedron Computer Constructions
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2015-12-28 01:18
SequenceSolid GeometryGeometric Construction
This example demonstrates the computer construction of a polyhedron with n=40. Key math concepts involved include constructions, pie chart or circle chart, incircle or inscribed circle, median value, similarity transformation or similarity, and quadratic functions. The construction utilizes GeoGebra commands such as Sequence, Sort, Element, and TableText, along with objects like r_n, A00r, A00, zoom, opacity_3, k, A0, A00d, i_s, nom, mm5a, Segments, Segments_o, Segn, la0, lLength, mm1, la1, la2, la3, la4, opacityd_3, id_s, k_1, k_d, Vol, A0d, nomd, Segmentsd, Segmentsd_o, Segnd, la0d, lLengthd, mm1d, Vold, mm6d, läSegments, läSegmentsd, mm7a, and mm1läd. Suitable for high school and above, focusing on solid geometry and computer-aided geometric constructions.

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. 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]], Element[A0d, Element[Element[Element[mm6d, 1], i], 5]]], i, 1, 12) → polyd_{5}
  28. Sequence(Polygon[Element[A0d, Element[Element[Element[mm6d, 2], i], 1]], Element[A0d, Element[Element[Element[mm6d, 2], i], 2]], Element[A0d, Element[Element[Element[mm6d, 2], i], 3]], Element[A0d, Element[Element[Element[mm6d, 2], i], 4]], Element[A0d, Element[Element[Element[mm6d, 2], i], 5]], Element[A0d, Element[Element[Element[mm6d, 2], i], 6]]], i, 1, 28) → polyd_{6}