不规则镶嵌 by JM Arranz, JA Mora, M Sada y R Losada

不规则镶嵌 by JM Arranz, JA Mora, M Sada y R Losada
几何画板及绘图内容加载中,请稍等……
2023-03-13 20:55
所属专题 geometriadinamica.es
这个范例展示了不规则镶嵌的构造过程。涉及的核心数学概念包括变换(如相似变换)和几何作图。通过使用向量、圆、线段等GeoGebra对象,可以构造出不规则镶嵌图案。适合初中及以上学生或教师使用,用于几何作图和变换教学。

GeoGebra 命令及参数

  1. Vector(A, B) → u
  2. Circle(B, A) → c2
  3. Circle(A, B) → c1
  4. Intersect(c1, c2, 1) → C1
  5. Circle(C1, A) → c3
  6. Intersect(c2, c3, 2) → P2
  7. Circle(P2, C1) → c5
  8. Segment(A, B) → l
  9. OrthogonalLine(A, l) → r0
  10. Intersect(c3, r0, 2) → P1
  11. Circle(P1, C1) → c4
  12. Intersect(c3, c4, 2) → P3
  13. Line(P3, P2) → r1
  14. OrthogonalLine(P2, r1) → r2
  15. Intersect(c5, r2, 2) → A2
  16. Intersect(c4, r0, 2) → A1
  17. Vector(A, A1) → v1
  18. OrthogonalLine(P3, r1) → r3
  19. OrthogonalLine(A2, r2) → r4
  20. Intersect(r3, r4) → P4
  21. Circle(A2, P4) → c6
  22. Circle(P4, A2) → c7
  23. Intersect(c6, c7, 2) → C2
  24. Circle(C2, A2) → c8
  25. Intersect(c8, r2, 2) → P5
  26. Line(B2, P5) → r5
  27. OrthogonalLine(B2, r5) → r7
  28. OrthogonalLine(P5, r5) → r8
  29. Circle(B2, P5) → c9
  30. Intersect(c9, r7, 1) → P6
  31. Line(P6, r4) → r6
  32. Circle(P6, B2) → c9b
  33. Intersect(c9b, r6, 1) → A3
  34. Vector(A, A3) → v3
  35. Vector(A, A2) → v2
  36. Hex(A, B) → h1
  37. Hex(A2, B2) → h2
  38. Sequence(Sequence[Hex[A + (n * v1) + (k * v3), B + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list1, {{2.598076211353302}}
  39. Sequence(Sequence[Hex[A2 + (n * v1) + (k * v3), B2 + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list2, {{2.598076211353323}}
  40. Cua(P1, P3) → cua1
  41. Sequence(Sequence[Cua[P1 + (n * v1) + (k * v3), P3 + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list3, {{1.0000000000000284}}
  42. Intersect(c1, c4, 2) → P7
  43. Cua(P7, P1) → cua2
  44. Sequence(Sequence[Cua[P7 + (n * v1) + (k * v3), P1 + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list4, {{0.9999999999999432}}
  45. Cua(A, P7) → cua3
  46. Sequence(Sequence[Cua[A + (n * v1) + (k * v3), P7 + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list5, {{0.9999999999999716}}
  47. Cua(P2, B) → cua4
  48. Sequence(Sequence[Cua[P2 + (n * v1) + (k * v3), B + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list6, {{1.0000000000000284}}
  49. Cua(P3, P2) → cua5
  50. Sequence(Sequence[Cua[P3 + (n * v1) + (k * v3), P2 + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list7, {{1.0000000000000284}}
  51. Cua(B2, A2) → cua6
  52. Sequence(Sequence[Cua[B2 + (n * v1) + (k * v3), A2 + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list8, {{1}}
  53. Sequence(Sequence[Hex[A + (n * v1) + (k * v3), B + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list1b, {{2.598076211353302}}
  54. Sequence(Sequence[Hex[A2 + (n * v1) + (k * v3), B2 + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list2b, {{2.598076211353323}}
  55. Sequence(Sequence[Cua[P1 + (n * v1) + (k * v3), P3 + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list3b, {{1.0000000000000284}}
  56. Sequence(Sequence[Cua[B2 + (n * v1) + (k * v3), A2 + (n * v1) + (k * v3)], n, (-m), m], k, (-m), m) → list8b, {{1}}

AI 绘图提示语参考

在平面内先给定一条底边与两端点,先作以这两点为圆心、彼此为半径的两圆取交点,再用交点与原端点作圆、连同圆与已作直线的交点形成多个关键点。由若干点连成多条直线,其中至少两条相互垂直的引导线用于确定后续交点;再围绕某些点作圆并与这些垂线相交得到更多顶点。最终把两侧的方向向量反复叠加,对用六边形平铺的单元作平移与重复,得到不规则马赛克图案。
以上提示语为根据原始绘图命令整理而来,仅供参考。