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Shadow of a Sphere by Tatsuyoshi Hamada

Shadow of a Sphere by Tatsuyoshi Hamada
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2017-06-23 23:23
TrigonometrySolid GeometryLimitGeometric Construction
This example demonstrates the changing shadow of a sphere under varying light angles. It involves core mathematical concepts like similar triangles, limits, quadrilaterals, curved surfaces, and secants. Construction highlights include commands like Sphere, OrthogonalPlane, IntersectPath, Center, Line, Intersect, Locus, and Polygon from GeoGebra. Suitable for high school and above students studying solid geometry, light projection, and complex geometric constructions.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), 1) → a
  2. OrthogonalPlane(P, n) → b
  3. IntersectPath(b, a) → c
  4. Center(c) → C
  5. Line(C, yAxis) → d
  6. Intersect(d, c) → A, B
  7. Line(A, u) → e
  8. Line(B, u) → f
  9. Intersect(e, xOyPlane) → D
  10. Intersect(f, xOyPlane) → E
  11. Locus(D, h) → loc1
  12. Locus(E, h) → loc2
  13. Polygon(A, B, E, D) → poly1, a_1, b_1, e_1, d_1
  14. IntersectPath(xOyPlane, a) → g