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Intersection of Cone and Cube

Intersection of Cone and Cube
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2017-05-04 15:43
Solid GeometryGeometric Construction
This example demonstrates the cross-section formed by the intersection of a cone and a cube. Key mathematical concepts include solid geometry and geometric construction. Using GeoGebra commands such as Circle, Cone, Cube, and Intersect, the cross-section can be constructed. Suitable for high school mathematics education and students learning solid geometry.

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[G, Distance[C, G], Segment[C, G]]) → H
  10. Cube(C, G, H) → a, I, FlaecheHIML, FlaecheJKLM, KanteCI, KanteCG, KanteGH, KanteHI, KanteCJ, KanteIM, KanteJM, KanteJK, J, KanteGK, KanteKL, KanteHL, KanteLM, K, L, M, FlaecheCGHI, FlaecheCIMJ, FlaecheCGKJ, FlaecheGHLK
  11. Intersect(g, FlaecheJKLM) → N
  12. Intersect(g, FlaecheHIML) → O
  13. Intersect(g, FlaecheGHLK) → P
  14. Intersect(g, FlaecheCIMJ) → Q
  15. Intersect(g, FlaecheCGKJ) → S
  16. Intersect(g, FlaecheCGHI) → T
  17. Locus(N, F) → Ortslinie1
  18. Locus(O, F) → Ortslinie2
  19. Locus(P, F) → Ortslinie3
  20. Locus(Q, F) → Ortslinie4
  21. Locus(S, F) → Ortslinie5
  22. Locus(T, F) → Ortslinie6