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Intersection of a Cone and a Tetrahedron

Intersection of a Cone and a Tetrahedron
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2017-04-11 14:07
FunctionTrigonometrySolid GeometryGeometric Construction
This example demonstrates the intersection of a cone and a tetrahedron, involving core mathematical concepts like cones, intersections, sine functions, polynomial functions, planes, complex numbers, and cubes. It is constructed using GeoGebra commands such as Circle, OrthogonalLine, Point, Cone, Segment, Distance, Midpoint, Tetrahedron, Intersect, and Locus. Suitable for high school solid geometry teaching and introductory mathematical modeling.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. OrthogonalLine(A, xOyPlane) → f
  3. Point(f) → D
  4. Cone(c, Distance[A, D]) → b, d, e
  5. Point(c) → F
  6. Segment(D, F) → g
  7. Distance(A, B) → j
  8. Midpoint(A, B) → E
  9. Point(Circle[Midpoint[C, G], (Distance[C, G] * sqrt(3) / 2), Segment[C, G]]) → I
  10. Tetrahedron(C, G, I) → a, J, arestaIJ, arestaGJ, caraCGI, caraCIJ, caraCGJ, caraGIJ, arestaCI, arestaCG, arestaGI, arestaCJ
  11. Intersect(g, caraCGI) → K
  12. Intersect(g, caraCGJ) → L
  13. Intersect(g, caraCIJ) → M
  14. Intersect(g, caraGIJ) → N
  15. Locus(K, F) → LlocGeomètric1
  16. Locus(L, F) → LlocGeomètric2
  17. Locus(M, F) → LlocGeomètric3
  18. Locus(N, F) → LlocGeomètric4