积极 AI Logo 积极 AI

Nefroide：线性函数与椭圆作图示例

Nefroide：线性函数与椭圆作图示例
几何画板及绘图内容加载中，请稍等……
2023-03-15 20:51
函数几何作图
所属专题 geometriadinamica.es
这个范例展示了如何通过线性函数和椭圆的几何构造来演示数学关系。核心数学概念包括线性函数、椭圆方程和几何作图方法。作图要点涉及使用GeoGebra命令如Segment、Circle、Ellipse和Intersect来构建图形。适合初中或高中数学学习，用于理解函数与几何的结合。

GeoGebra 命令及参数

  1. Segment(Q3, Q4) → p2
  2. Point(p2) → P3
  3. Segment(P3, Q4) → p4
  4. Point(p4) → P4
  5. Segment(Q1, Q2) → p1
  6. Point(p1) → P1
  7. Segment(P1, Q2) → p3
  8. Point(p3) → P2
  9. OrthogonalLine(C, xAxis) → zz2
  10. Circle(C, 0.62) → zz0
  11. Intersect(zz0, zz2, 1) → ZZ4
  12. Intersect(zz0, zz2, 2) → ZZ3
  13. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  14. Point(zElipse2) → Z
  15. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  16. Angle(ZZ8, C, Z) → zAngInc
  17. OrthogonalLine(C, yAxis) → zz1
  18. Intersect(zz0, zz1, 2) → ZZ2
  19. Intersect(zz0, zz1, 1) → ZZ1
  20. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  21. Point(zElipse1) → XY
  22. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  23. Angle(ZZ6, C, XY) → zAngRot
  24. Segment(Q5, Q6) → p5
  25. Point(p5) → P5
  26. Segment(ZZ5, ZZ6) → zz4
  27. Segment(ZZ7, ZZ8) → zz3
  28. Intersect(zElipse2, zElipse1, 1) → zPunto1
  29. Intersect(zElipse2, zElipse1, 4) → zPunto2
  30. Segment(zPunto1, zPunto2) → zSeg2
  31. CurveCartesian((r / 2.5 * (((cos(α) * ((3 * cos(v)) - cos((3 * v)))) * sin(zAngRot)) + ((sin(α) * ((3 * cos(v)) - cos((3 * v)))) * cos(zAngRot)))), (r / 2.5 * (((((-cos(α)) * ((3 * cos(v)) - cos((3 * v)))) * cos(zAngRot)) * sin(zAngInc)) + (((sin(α) * ((3 * cos(v)) - cos((3 * v)))) * sin(zAngRot)) * sin(zAngInc)) + (((3 * sin(v)) - sin((3 * v))) * cos(zAngInc)))), v, v1, v2) → curva2
  32. CurveCartesian((r / 2.5 * (((cos(u) * 2) * sin(zAngRot)) + ((sin(u) * 2) * cos(zAngRot)))), (r / 2.5 * (((((-cos(u)) * 2) * cos(zAngRot)) * sin(zAngInc)) + (((sin(u) * 2) * sin(zAngRot)) * sin(zAngInc)))), u, u1, u2) → curva1
  33. CurveCartesian((r / 2.5 * (((cos(u) * ((3 * cos(β - 3.14159 / 2)) - cos((3 * (β - 3.14159 / 2))))) * sin(zAngRot)) + ((sin(u) * ((3 * cos(β - 3.14159 / 2)) - cos((3 * (β - 3.14159 / 2))))) * cos(zAngRot)))), (r / 2.5 * (((((-cos(u)) * ((3 * cos(β - 3.14159 / 2)) - cos((3 * (β - 3.14159 / 2))))) * cos(zAngRot)) * sin(zAngInc)) + (((sin(u) * ((3 * cos(β - 3.14159 / 2)) - cos((3 * (β - 3.14159 / 2))))) * sin(zAngRot)) * sin(zAngInc)) + (((3 * sin(β - 3.14159 / 2)) - sin((3 * (β - 3.14159 / 2)))) * cos(zAngInc)))), u, u1, u2) → a1
  34. Sequence(CurveCartesian[(r / 2.5 * (((cos(u) * ((3 * cos(v)) - cos((3 * v)))) * sin(zAngRot)) + ((sin(u) * ((3 * cos(v)) - cos((3 * v)))) * cos(zAngRot)))), (r / 2.5 * (((((-cos(u)) * ((3 * cos(v)) - cos((3 * v)))) * cos(zAngRot)) * sin(zAngInc)) + (((sin(u) * ((3 * cos(v)) - cos((3 * v)))) * sin(zAngRot)) * sin(zAngInc)) + (((3 * sin(v)) - sin((3 * v))) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list3
  35. Sequence(CurveCartesian[(r / 2.5 * (((cos(u) * ((3 * cos(v)) - cos((3 * v)))) * sin(zAngRot)) + ((sin(u) * ((3 * cos(v)) - cos((3 * v)))) * cos(zAngRot)))), (r / 2.5 * (((((-cos(u)) * ((3 * cos(v)) - cos((3 * v)))) * cos(zAngRot)) * sin(zAngInc)) + (((sin(u) * ((3 * cos(v)) - cos((3 * v)))) * sin(zAngRot)) * sin(zAngInc)) + (((3 * sin(v)) - sin((3 * v))) * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list1

AI 绘图提示语参考

画一个几何图形，展示线性函数与椭圆的关系。首先构建两条线段和两个点，然后以其中一个点为圆心画一个圆，与垂直于x轴的直线相交得到两个点。利用这两个点画一个椭圆，再以另一个点为圆心画另一个圆，同样与垂直于x轴的直线相交得到两个点，并以此画另一个椭圆。最后，连接两个椭圆的交点，并绘制两条曲线，展示函数与几何的融合。
以上提示语为根据原始绘图命令整理而来，仅供参考。