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Sphere Cross Section Similarity

Sphere Cross Section Similarity
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2020-01-27 01:19
VectorSolid GeometryGeometric Construction
This example demonstrates the cross-section of a sphere in detail, showing the similarity of cross-section shapes at different angles. The core mathematical concepts involved include solid geometry, derivatives, and vectors. The construction utilizes GeoGebra commands such as Circle, Sphere, OrthogonalLine, Point, Vector, Plane, IntersectPath, Intersect, Segment, and Polygon. It is suitable for high school and above, ideal for teaching and exploring solid geometry and calculus.

GeoGebra Commands & Parameters

  1. Circle(O, 3, zAxis) → c
  2. Sphere(O, 3) → a_2
  3. OrthogonalLine(B, xOyPlane) → b
  4. Point(b) → C
  5. Vector(B, C) → u
  6. Plane(C, xOyPlane) → d
  7. IntersectPath(d, a_2) → e
  8. Point(e) → D
  9. Intersect(zAxis, d) → E
  10. Segment(D, E) → a
  11. Segment(D, O) → r
  12. Segment(O, E) → h
  13. Polygon(O, E, D) → poly1, h_2, a_1, e_1