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Pyramid Inside Sphere

Pyramid Inside Sphere
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2019-05-10 03:11
TrigonometrySolid GeometryGeometric Construction
This example demonstrates the geometric construction of a pyramid completely inscribed within a sphere. It involves core mathematical concepts such as solid geometry, geometric construction, and the relationship between spheres and polyhedra. Key GeoGebra commands and objects used include Point, Sphere, Polygon, and Pyramid. Suitable for high school and above students to learn about spatial geometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → STAR
  2. Sphere(STAR, R_s) → a
  3. Circle(STAR, R_s, xOyPlane) → c
  4. Point(c) → planet
  5. PointIn(a) → A
  6. PointIn(a) → C
  7. Point(Circle[C, Distance[A, C], Segment[A, C]]) → E
  8. Polygon(C, E, 4, xOyPlane) → poly1, f, g, h, i, B, D
  9. OrthogonalLine(STAR, xOyPlane) → j
  10. OrthogonalLine(STAR, xOyPlane) → k
  11. Pyramid(poly1, STAR) → b, faceCESTAR, faceBESTAR, faceBDSTAR, faceCDSTAR, edgeCSTAR, edgeESTAR, edgeBSTAR, edgeDSTAR
  12. Point(Circle[Midpoint[C, R_s], (Distance[C, R_s] * sqrt(3) / 2), Segment[C, R_s]]) → F
  13. Tetrahedron(C, R_s, F) → d, G, edgeFG, edge3, face1, faceCFG, face2, face3, edgeCF, edge1, edge2, edgeCG
  14. Segment(C, planet) → n
  15. Point(h) → H
  16. Segment(H, planet) → p
  17. Segment(R_s, planet) → q
  18. Segment(E, planet) → r