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双曲八面体

双曲八面体
几何画板及绘图内容加载中，请稍等……
2023-03-15 20:55
解析几何立体几何几何作图
所属专题 geometriadinamica.es
这个范例展示了双曲八面体的几何构造。它涉及双曲几何中的核心概念，如双曲平面中的多边形。通过使用GeoGebra命令如Segment, Point, OrthogonalLine等，可以构造出双曲八面体的各个面。适合高中或大学的几何学课程，特别是立体几何和双曲几何的学习。

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(((1.5 * r) * ((((cos(u) * cos(α)))^(3) * sin(zAngRot)) + (((sin(u) * cos(α)))^(3) * cos(zAngRot)))), ((1.5 * r) * ((((-((cos(u) * cos(α)))^(3)) * cos(zAngRot)) * sin(zAngInc)) + ((((sin(u) * cos(α)))^(3) * sin(zAngRot)) * sin(zAngInc)) + ((sin(α))^(3) * cos(zAngInc)))), u, u1, u2) → curva2
  32. CurveCartesian((((1.5 * r) * (cos(v))^(3)) * sin(zAngRot)), ((1.5 * r) * ((((-(cos(v))^(3)) * cos(zAngRot)) * sin(zAngInc)) + ((sin(v))^(3) * cos(zAngInc)))), v, v1, v2) → curva1
  33. CurveCartesian(((1.5 * r) * ((((cos(β) * cos(v)))^(3) * sin(zAngRot)) + (((sin(β) * cos(v)))^(3) * cos(zAngRot)))), ((1.5 * r) * ((((-((cos(β) * cos(v)))^(3)) * cos(zAngRot)) * sin(zAngInc)) + ((((sin(β) * cos(v)))^(3) * sin(zAngRot)) * sin(zAngInc)) + ((sin(v))^(3) * cos(zAngInc)))), v, v1, v2) → a1
  34. Sequence(CurveCartesian[((1.5 * r) * ((((cos(u) * cos(v)))^(3) * sin(zAngRot)) + (((sin(u) * cos(v)))^(3) * cos(zAngRot)))), ((1.5 * r) * ((((-((cos(u) * cos(v)))^(3)) * cos(zAngRot)) * sin(zAngInc)) + ((((sin(u) * cos(v)))^(3) * sin(zAngRot)) * sin(zAngInc)) + ((sin(v))^(3) * cos(zAngInc)))), v, v1, v2], u, u1, u2, (2 * paso)) → list2
  35. Sequence(CurveCartesian[((1.5 * r) * ((((cos(u) * cos(v)))^(3) * sin(zAngRot)) + (((sin(u) * cos(v)))^(3) * cos(zAngRot)))), ((1.5 * r) * ((((-((cos(u) * cos(v)))^(3)) * cos(zAngRot)) * sin(zAngInc)) + ((((sin(u) * cos(v)))^(3) * sin(zAngRot)) * sin(zAngInc)) + ((sin(v))^(3) * cos(zAngInc)))), u, u1, u2], v, v1, v2, paso) → list1

AI 绘图提示语参考

绘制一个双曲八面体，展示其由多个双曲多边形构成的面。首先画出两条线段，然后在线段上创建点。接着，利用正交线构造圆，并在圆上生成椭圆。通过椭圆与正交线的交点，进一步绘制线段和曲线，最终形成双曲八面体的复杂结构，体现双曲几何中的关键概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。