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Möbius 几何作图示例

Möbius 几何作图示例
几何画板及绘图内容加载中，请稍等……
2023-03-15 20:48
圆向量解析几何几何作图
所属专题 geometriadinamica.es
该范例演示了通过几何构造展示变量、向量和圆的交互关系。核心数学概念包括变量、向量、圆和几何作图。作图要点涉及使用GeoGebra命令如Segment、Point、OrthogonalLine、Circle、Intersect、Ellipse、Angle和CurveCartesian等对象。适合初中或高中数学学习，用于理解几何变换和图形关系。

GeoGebra 命令及参数

  1. Segment(Q5, Q6) → p5
  2. Point(p5) → P5
  3. Segment(Q3, Q4) → p2
  4. Point(p2) → P3
  5. Segment(P3, Q4) → p4
  6. Point(p4) → P4
  7. Segment(Q1, Q2) → p1
  8. Point(p1) → P1
  9. Segment(P1, Q2) → p3
  10. Point(p3) → P2
  11. OrthogonalLine(C, yAxis) → zz1
  12. Circle(C, 0.62) → zz0
  13. Intersect(zz0, zz1, 1) → ZZ1
  14. Intersect(zz0, zz1, 2) → ZZ2
  15. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  16. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  17. Point(zElipse1) → XY
  18. Angle(ZZ6, C, XY) → zAngRot
  19. OrthogonalLine(C, xAxis) → zz2
  20. Intersect(zz0, zz2, 2) → ZZ3
  21. Intersect(zz0, zz2, 1) → ZZ4
  22. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  23. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  24. Point(zElipse2) → Z
  25. Angle(ZZ8, C, Z) → zAngInc
  26. CurveCartesian((r * ((((1 + (v * cos(3.14159 / 2))) * cos(3.14159)) * sin(zAngRot)) + (((1 + (v * cos(3.14159 / 2))) * sin(3.14159)) * cos(zAngRot)))), (r * (((((-(1 + (v * cos(3.14159 / 2)))) * cos(3.14159)) * cos(zAngRot)) * sin(zAngInc)) + ((((1 + (v * cos(3.14159 / 2))) * sin(3.14159)) * sin(zAngRot)) * sin(zAngInc)) + ((v * sin(3.14159 / 2)) * cos(zAngInc)))), v, v1, v2) → curva1
  27. Segment(ZZ5, ZZ6) → zz4
  28. Segment(ZZ7, ZZ8) → zz3
  29. Intersect(zElipse2, zElipse1, 1) → zPunto1
  30. Intersect(zElipse2, zElipse1, 4) → zPunto2
  31. Segment(zPunto1, zPunto2) → zSeg2
  32. CurveCartesian((r * ((((1 + (β * cos(u / 2))) * cos(u)) * sin(zAngRot)) + (((1 + (β * cos(u / 2))) * sin(u)) * cos(zAngRot)))), (r * (((((-(1 + (β * cos(u / 2)))) * cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((1 + (β * cos(u / 2))) * sin(u)) * sin(zAngRot)) * sin(zAngInc)) + ((β * sin(u / 2)) * cos(zAngInc)))), u, u1, (2 * u2)) → curva2
  33. CurveCartesian((r * ((((1 + (v * cos(α / 2))) * cos(α)) * sin(zAngRot)) + (((1 + (v * cos(α / 2))) * sin(α)) * cos(zAngRot)))), (r * (((((-(1 + (v * cos(α / 2)))) * cos(α)) * cos(zAngRot)) * sin(zAngInc)) + ((((1 + (v * cos(α / 2))) * sin(α)) * sin(zAngRot)) * sin(zAngInc)) + ((v * sin(α / 2)) * cos(zAngInc)))), v, v1, v2) → a1
  34. Sequence(CurveCartesian[(r * ((((1 + (v * cos(u / 2))) * cos(u)) * sin(zAngRot)) + (((1 + (v * cos(u / 2))) * sin(u)) * cos(zAngRot)))), (r * (((((-(1 + (v * cos(u / 2)))) * cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((1 + (v * cos(u / 2))) * sin(u)) * sin(zAngRot)) * sin(zAngInc)) + ((v * sin(u / 2)) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list2
  35. Sequence(CurveCartesian[(r * ((((1 + (v * cos(u / 2))) * cos(u)) * sin(zAngRot)) + (((1 + (v * cos(u / 2))) * sin(u)) * cos(zAngRot)))), (r * (((((-(1 + (v * cos(u / 2)))) * cos(u)) * cos(zAngRot)) * sin(zAngInc)) + ((((1 + (v * cos(u / 2))) * sin(u)) * sin(zAngRot)) * sin(zAngInc)) + ((v * sin(u / 2)) * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list1

AI 绘图提示语参考

绘制一个莫比乌斯带的几何构造，包括两个椭圆（zElipse1 和 zElipse2），它们通过交点（ZZ1, ZZ2, ZZ3, ZZ4, ZZ5, ZZ6, ZZ7, ZZ8, zPunto1, zPunto2）相连。首先画出两个圆（C），然后构造垂直线和椭圆，接着通过交点和角度构造曲线，最后用曲线和椭圆生成莫比乌斯带的表面。
以上提示语为根据原始绘图命令整理而来，仅供参考。