Sphere and Quadrilateral Comprehensive Exercise

Sphere and Quadrilateral Comprehensive Exercise
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2017-05-06 17:21
This example demonstrates the geometric relationships between a sphere and quadrilaterals in space, along with the distribution of integer points. Core concepts include sphere construction, vector operations, analytical geometry, orthogonal planes and lines, and path tracing. Constructed using GeoGebra commands such as Sphere, Vector, Line, Intersect, OrthogonalPlane, OrthogonalLine, IntersectPath, Point, and Segment. Suitable for high school and above students for learning solid geometry, analytical geometry, and combinatorics.

GeoGebra Commands & Parameters

  1. Sphere(Ω, sqrt(3)) → a
  2. Vector((2, 5, -1)) → u
  3. Line(A, u) → D
  4. Intersect(D, a) → B, C
  5. Line(Ω, I) → f
  6. OrthogonalPlane(I, f) → b
  7. OrthogonalLine(Ω, c) → g
  8. Intersect(g, c) → E
  9. IntersectPath(c, a) → d
  10. Point(d) → F
  11. Segment(F, E) → h
  12. Segment(E, Ω) → i
  13. IntersectPath(c, b) → j