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Sections of a Sphere by Steve Phelps

Sections of a Sphere by Steve Phelps
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2019-04-22 04:27
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the sections of a sphere. It involves solid geometry and coordinate geometry. Using GeoGebra commands such as Sphere and IntersectPath, various sections of the sphere can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sphere((0, n, 0), 5) → a
  2. IntersectPath(y = -4, a) → c
  3. IntersectPath(y = -3.5, a) → d
  4. IntersectPath(y = -3, a) → e
  5. IntersectPath(y = -2, a) → f
  6. IntersectPath(y = -1, a) → g
  7. IntersectPath(y = 0, a) → h
  8. IntersectPath(y = 1, a) → k
  9. IntersectPath(y = 2, a) → p
  10. IntersectPath(y = 3, a) → q
  11. IntersectPath(y = 4, a) → r
  12. IntersectPath(y = -2.5, a) → s
  13. IntersectPath(y = -1.5, a) → t
  14. IntersectPath(y = -0.5, a) → c_1
  15. IntersectPath(y = 0.5, a) → d_1
  16. IntersectPath(y = 1.5, a) → e_1
  17. IntersectPath(y = 2.5, a) → f_1
  18. IntersectPath(y = 3.5, a) → g_1
  19. IntersectPath(y = 4.5, a) → h_1
  20. IntersectPath(y = -4.5, a) → k_1
  21. Sequence(Polygon[(-6, w, -6), (6, w, -6), (6, w, 6), (-6, w, 6)], w, -6, 6) → l1
  22. IntersectPath(y = -5.5, a) → p_1
  23. IntersectPath(y = -6, a) → q_1
  24. IntersectPath(y = -5, a) → r_1
  25. IntersectPath(y = 5.5, a) → s_1
  26. IntersectPath(y = 5, a) → t_1
  27. IntersectPath(y = 6, a) → c_2

AI Drawing Prompt Reference

Draw a sphere and show its intersections with multiple horizontal planes at different heights, creating a series of circular cross-sections. Add two vertical squares on the left and right sides of the sphere, with their bases touching the bottom and top of the sphere.
The prompt above was compiled from the original drawing commands and is for reference only.