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黄金数坐标的120面体动画

黄金数坐标的120面体动画
几何画板及绘图内容加载中，请稍等……
2015-07-14 19:58
三角函数数列解析几何立体几何矩阵
所属专题 Polyeder, whose coordinates are golden numbers
①本范例演示了一个由黄金数坐标构成的120面体动画，该多面体具有120个三角形面、180条边和62个顶点；②涉及的核心数学概念包括黄金数、坐标几何、立体几何和三角函数；③作图要点运用了If, Sequence, Length, Join, Sort, Element, LaTeX等GeoGebra命令和对象，如matrix2, a_40, r, a_4, a_4scale等；④适合高中及以上数学学习者，用于理解复杂几何体的构造和黄金数的应用。

GeoGebra 命令及参数

  1. If(b, 1, a_4scale) → scalefactor
  2. If(b, q1, 1 + q1) → q
  3. Sequence(((scalefactor * Element[Element[matrix2, i], 1]), (scalefactor * Element[Element[matrix2, i], 2]), (scalefactor * Element[Element[matrix2, i], 3])), i, 1, Length[matrix2]) → A0
  4. If(b, lb, lnb) → l00qqb
  5. Sequence(Segment[((scalefactor * Element[Element[A00, x(Element[l00qqb, i])], 1]), (scalefactor * Element[Element[A00, x(Element[l00qqb, i])], 2]), (scalefactor * Element[Element[A00, x(Element[l00qqb, i])], 3])), ((scalefactor * Element[Element[A00, y(Element[l00qqb, i])], 1]), (scalefactor * Element[Element[A00, y(Element[l00qqb, i])], 2]), (scalefactor * Element[Element[A00, y(Element[l00qqb, i])], 3]))], i, 1, 300) → list1
  6. Length(matrix2) → lämx2
  7. Join(Sequence[Sequence[Segment[Element[A0, i], Element[A0, j]], j, i + 1, lämx2], i, 1, lämx2 - 1]) → l00r
  8. Sort(Union[l01r, l01r]) → l01sortr
  9. Sequence(KeepIf[If[i ≟ 1, x ≤ Element[l01sortr, i], If[i ≟ lämx2, Element[l01sortr, i - 1] < x, Element[l01sortr, i - 1] < x ≤ Element[l01sortr, i]]], l00r], i, 1, lämx2) → la00r
  10. Element(la00r, 1) → la11
  11. Element(la00r, 2) → la12
  12. Element(la00r, 3) → la13
  13. Element(la00r, 4) → la14
  14. Element(la00r, 5) → la15
  15. Element(la00r, 6) → la16
  16. Element(la00r, 7) → la17
  17. Element(la00r, 8) → la18
  18. Element(la00r, a) → la1a
  19. Sequence(((scalefactor * Element[Element[A00, i], 1]), (scalefactor * Element[Element[A00, i], 2]), (scalefactor * Element[Element[A00, i], 3])), i, 1, 62) → A000
  20. Element(A0, Vertex) → AAAr
  21. Length(l01sortr) → läl01sortr
  22. Length(la1a) → läla1a
  23. Element(Element[list2, iq + 1], Vertex) → zzz1
  24. Element(list5, zzz1) → zzz2
  25. If(iq ≟ 0, "120 Polyhedron", If[(iq > 0) ∧ (iq < 11), "Tetrahedra", If[(iq > 10) ∧ (iq < 16), "Cube", If[(iq > 15) ∧ (iq < 21), "Octahedra", If[(iq > 20) ∧ (iq < 26), " rhombic Dodecahedra", If[iq ≟ 26, " Icosahedron", If[iq ≟ 27, " regular Dodecahedron", " rhombic Triacontahedron"]]]]]]) → zzz3
  26. LaTeX(If[b, " \frac{\sqrt{5}-1}{2}", " \frac{\sqrt{5}+1}{2}"], true) → tx3
  27. LaTeX(If[iq ≟ 0, "120\; Polyhedron", If[(iq > 0) ∧ (iq < 11), "Tetrahedron", If[(iq > 10) ∧ (iq < 16), "Cube", If[(iq > 15) ∧ (iq < 21), "Octahedron", If[(iq > 20) ∧ (iq < 26), " rhombic\; Dodecahedron", If[iq ≟ 26, " Icosahedron", If[iq ≟ 27, " regular\; Dodecahedron", " rhombic\; Triacontahedron"]]]]]]], true) → zzz3a