平面镶嵌 by Ben Sparks

平面镶嵌 by Ben Sparks
几何画板及绘图内容加载中,请稍等……
2016-11-02 21:36
这个范例演示了平面镶嵌的概念。涉及的核心数学概念包括多边形和向量。通过使用GeoGebra命令如Segment, Line, Vector, Translate等,可以构造出各种多边形的镶嵌图案。适合初中及以上学生学习几何作图和变换。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Line(A, g) → h
  4. Line(C, f) → i
  5. Vector(A, B) → u
  6. Vector(B, C) → v
  7. Segment(A, E) → k
  8. Segment(E, F) → m
  9. Segment(F, G) → n_1
  10. Segment(G, B) → p
  11. Segment(B, H) → q
  12. Segment(H, I) → r
  13. Segment(I, J) → s
  14. Segment(J, K) → t
  15. Segment(K, L) → a
  16. Segment(L, C) → b
  17. Translate(edge1, v) → edge1'
  18. Translate(edge2, Vector[(-u)]) → edge2'
  19. Flatten(Sequence[Sequence[(tt * u) + (ss * v), tt, (-n), n], ss, (-n), n]) → veclist
  20. Intersect(i, h) → D
  21. Segment(A, D) → j
  22. Segment(D, C) → l
  23. Polygon(Join[{edge1, edge2, Reverse[edge1'], Reverse[edge2']}]) → poly1
  24. Zip(Translate[poly1, Vector[vec]], Vector[vec], veclist) → tessel
  25. Polygon(A, B, C, D) → pshape, a_1, b_1, c_1, d_1
  26. Zip(Polygon[Translate[A, Vector[vec]], Translate[B, Vector[vec]], Translate[C, Vector[vec]], Translate[D, Vector[vec]]], Vector[vec], veclist) → ptessel