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Sphere Central Projection

Sphere Central Projection
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2014-11-07 18:38
VectorSolid GeometryGeometric Construction
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This example demonstrates the shadow of a sphere under central projection. It involves core mathematical concepts like sphere, central projection, vectors, and line segments. Construction highlights include using GeoGebra commands such as Sphere, Midpoint, IntersectConic, Line, Point, OrthogonalPlane, InfiniteCone, and Segment. Suitable for high school students and math enthusiasts learning spatial geometry and projection transformations.

GeoGebra Commands & Parameters

  1. Sphere(M, r) → kug
  2. Midpoint(M, L) → D_1
  3. Sphere(D_1, L) → hk_1
  4. IntersectConic(kug, hk_1) → p
  5. Center(p) → M_1
  6. Line(L, M) → c
  7. Point(p) → P
  8. OrthogonalPlane(M_1, c) → ε
  9. Angle(M, L, P) → α
  10. InfiniteCone(L, M, α) → g
  11. Segment(L, P) → i
  12. IntersectPath(a, g) → h
  13. Intersect(c, a) → M'
  14. IntersectPath(a, ε) → d
  15. Line(M_1, P) → b
  16. Intersect(b, d) → S
  17. Ray(L, P) → e
  18. Intersect(e, h) → P',
  19. Line(M', S) → f
  20. Line(M_1, d) → k
  21. Intersect(k, p) → D, C
  22. Ray(L, C) → l
  23. Ray(L, D) → m
  24. Line(M', d) → n
  25. Intersect(n, l) → C'
  26. Intersect(n, m) → D'
  27. Tangent(C, p) → d_1, e_1
  28. Intersect(e_1, d) → S_2
  29. Ray(S_2, C') → t
  30. Tangent(D, p) → a_1, b_1
  31. Intersect(d, a_1) → S_1
  32. Ray(S_1, D') → c_1
  33. Axes(h) → q, s
  34. OrthogonalPlane(M_1, d) → u
  35. Intersect(d, u) → A
  36. Line(M_1, A) → f_1
  37. Intersect(q, h) → B, E
  38. Line(E, d) → g_1
  39. Line(B, d) → h_1