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Sphere and Cones

Sphere and Cones
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2017-12-09 21:42
Solid GeometryGeometric Construction
This example demonstrates the geometric relationship between a sphere and cones. Key mathematical concepts include solid geometry, specifically spheres and cones. Using GeoGebra commands such as Point, Cube, Intersect, Line, etc., the construction of a sphere and cones, their intersection lines, and surfaces can be observed. Suitable for high school and above students or teachers for teaching and learning solid geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(yAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB_1, edgeBC, edgeCD, edgeAE_1, edgeDH, edgeEH, edgeEF_1, E, edgeBF_1, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE_1, faceBCGF
  5. Intersect(yAxis, xAxis) → I
  6. Point(zAxis) → J
  7. Line(I, J) → f
  8. Intersect(f, faceEFGH) → K
  9. Midpoint(I, K) → L
  10. Sphere(L, K) → b
  11. Pyramid(E, F, B, A, L) → c, faceABFE, edgeEL, edgeFL, edgeBL, edgeAL, faceEFL, faceBFL, faceABL, faceAEL, edgeEF, edgeBF, edgeAB, edgeAE
  12. Intersect(edgeFL, b) → M,
  13. Intersect(edgeEL, b) → N,
  14. Intersect(edgeAL, b) → O,
  15. Intersect(edgeBL, b) → P,
  16. CircleArc(L, M, P) → d
  17. CircleArc(L, M, N) → e
  18. CircleArc(L, N, O) → g
  19. CircleArc(L, P, O) → h
  20. Segment(P, L) → i
  21. Segment(L, M) → j
  22. Segment(M, L) → k
  23. Segment(L, N) → l
  24. Segment(N, L) → m
  25. Segment(L, O) → n
  26. Segment(O, L) → p
  27. Cone(K, L, 4) → o, q, r
  28. Mirror(r, L) → r'
  29. Line(H, E) → s
  30. Line(L, s) → t
  31. Intersect(t, b) → Q, R
  32. Cone(R, L, 4) → u, c_1, v
  33. Cone(Q, L, 4) → w, d_1, a_1
  34. OrthogonalLine(L, t, space) →
  35. OrthogonalLine(L, t, space) →