积极 AI Logo 积极 AI

海螺贝壳的几何形状

海螺贝壳的几何形状
几何画板及绘图内容加载中，请稍等……
2023-03-15 19:31
圆参数方程几何作图
所属专题 geometriadinamica.es
这个 GeoGebra 范例演示了海螺贝壳的几何形状。它涉及的核心数学概念包括几何形状、圆和曲线。作图要点包括使用 Segment、Point、OrthogonalLine、Circle、Intersect、Ellipse、Angle 和 CurveCartesian 等 GeoGebra 命令/对象。这个范例适合初中或高中学生学习几何形状和曲线的概念。

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, yAxis) → zz1
  10. Circle(C, 0.62) → zz0
  11. Intersect(zz0, zz1, 1) → ZZ1
  12. Intersect(zz0, zz1, 2) → ZZ2
  13. Ellipse(ZZ1, ZZ2, 0.65) → zElipse1
  14. Intersect(zElipse1, zz1) → ZZ5, ZZ6
  15. Point(zElipse1) → XY
  16. Angle(ZZ6, C, XY) → zAngRot
  17. OrthogonalLine(C, xAxis) → zz2
  18. Intersect(zz0, zz2, 2) → ZZ3
  19. Intersect(zz0, zz2, 1) → ZZ4
  20. Ellipse(ZZ3, ZZ4, 0.65) → zElipse2
  21. Intersect(zElipse2, zz2) → ZZ7, ZZ8
  22. Point(zElipse2) → Z
  23. Angle(ZZ8, C, Z) → zAngInc
  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 * ((((exp((f * u)) * (d + (a * cos(α)))) * cos((c * u))) * sin(zAngRot)) + (((exp((f * u)) * (d + (a * cos(α)))) * sin((c * u))) * cos(zAngRot)))), (r * ((((((-exp((f * u))) * (d + (a * cos(α)))) * cos((c * u))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * u)) * (d + (a * cos(α)))) * sin((c * u))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * u)) * ((-1.4 * e) + (b * sin(α)))) * cos(zAngInc)))), u, u1, u2) → curva2
  32. CurveCartesian((r * ((((exp((f * β)) * (d + (a * cos(v)))) * cos((c * β))) * sin(zAngRot)) + (((exp((f * β)) * (d + (a * cos(v)))) * sin((c * β))) * cos(zAngRot)))), (r * ((((((-exp((f * β))) * (d + (a * cos(v)))) * cos((c * β))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * β)) * (d + (a * cos(v)))) * sin((c * β))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * β)) * ((-1.4 * e) + (b * sin(v)))) * cos(zAngInc)))), v, v1, v2) → a1
  33. CurveCartesian((r * ((((exp((f * max)) * (d + (a * cos(v)))) * cos((c * max))) * sin(zAngRot)) + (((exp((f * max)) * (d + (a * cos(v)))) * sin((c * max))) * cos(zAngRot)))), (r * ((((((-exp((f * max))) * (d + (a * cos(v)))) * cos((c * max))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * max)) * (d + (a * cos(v)))) * sin((c * max))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * max)) * ((-1.4 * e) + (b * sin(v)))) * cos(zAngInc)))), v, v1, v2) → curva1
  34. Sequence(CurveCartesian[(r * ((((exp((f * u)) * (d + (a * cos(v)))) * cos((c * u))) * sin(zAngRot)) + (((exp((f * u)) * (d + (a * cos(v)))) * sin((c * u))) * cos(zAngRot)))), (r * ((((((-exp((f * u))) * (d + (a * cos(v)))) * cos((c * u))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * u)) * (d + (a * cos(v)))) * sin((c * u))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * u)) * ((-1.4 * e) + (b * sin(v)))) * cos(zAngInc)))), v, v1, v2], u, u1, u2, paso) → list2
  35. Sequence(CurveCartesian[(r * ((((exp((f * u)) * (d + (a * cos(v)))) * cos((c * u))) * sin(zAngRot)) + (((exp((f * u)) * (d + (a * cos(v)))) * sin((c * u))) * cos(zAngRot)))), (r * ((((((-exp((f * u))) * (d + (a * cos(v)))) * cos((c * u))) * cos(zAngRot)) * sin(zAngInc)) + ((((exp((f * u)) * (d + (a * cos(v)))) * sin((c * u))) * sin(zAngRot)) * sin(zAngInc)) + ((exp((f * u)) * ((-1.4 * e) + (b * sin(v)))) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list1

AI 绘图提示语参考

画一个贝壳的几何图形，包含多个圆形和曲线，展示几何构造过程。首先绘制两条线段和四个点，然后利用正交线构造两个圆，并找到它们的交点。接着以交点为焦点绘制两个椭圆，并找到椭圆与正交线的交点。最后，利用这些点和角度信息，绘制复杂的参数曲线，形成贝壳的形状。
以上提示语为根据原始绘图命令整理而来，仅供参考。