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Symmetry of Two Points in Sphere & Cylinder

Symmetry of Two Points in Sphere & Cylinder
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2019-05-10 13:34
CircleSolid GeometryGeometric Construction
This example demonstrates the symmetry of two points in a sphere and a cylinder. The key mathematical concepts include symmetry, geometric transformations, and the geometry of spheres and cylinders. Construction involves GeoGebra commands such as Point, Sphere, Circle, Intersect, and Cylinder. Suitable for high school or university geometry courses to understand three-dimensional geometric symmetry and spatial figure construction.

GeoGebra Commands & Parameters

  1. Point(xAxis) → STAR
  2. Sphere(STAR, a) → b
  3. Circle(STAR, a) → c
  4. Point(c) → planet
  5. Circle(STAR, d) → e
  6. PointIn(b) → Pointb_1
  7. PointIn(b) → Pointb_2
  8. Point(e) → Pointe
  9. PointIn(b) → Pointb_3
  10. PointIn(b) → Pointb
  11. Circle(zAxis, STAR) → k
  12. Intersect(e, xAxis, 2) → A
  13. Intersect(e, yAxis, 1) → B
  14. Intersect(e, xAxis, 2) → C
  15. Intersect(e, yAxis, 2) → D
  16. Point(zAxis) → E
  17. Point(zAxis) → F
  18. Cylinder(E, F, d) → f, h, p, i
  19. Line(B, zAxis) → j
  20. Line(D, zAxis) → l
  21. Intersect(j, p, 1) → G
  22. Intersect(l, p, 1) → H
  23. Segment(G, planet) → m
  24. Segment(H, planet) → n

AI Drawing Prompt Reference

Draw a figure consisting of two points, one on a sphere and one on a cylinder, with symmetry. The points are connected by lines. Construct the sphere and cylinder first, then place the points, and finally connect them.
The prompt above was compiled from the original drawing commands and is for reference only.