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Intersection of a Cone and a Cube

Intersection of a Cone and a Cube
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2017-04-10 00:14
Coordinate GeometrySolid GeometryGeometric Construction
In collections intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve
This example demonstrates the intersection lines of a cone and a cube. Key mathematical concepts include solid geometry, distance, and midpoint. Using GeoGebra commands such as Circle, OrthogonalLine, Cone, Cube, and Intersect, the changing intersection lines can be observed. Suitable for high school geometry learners and teachers.

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, caraHIML, caraJKLM, arestaCI, arestaCG, arestaGH, arestaHI, arestaCJ, arestaIM, arestaJM, arestaJK, J, arestaGK, arestaKL, arestaHL, arestaLM, K, L, M, caraCGHI, caraCIMJ, caraCGKJ, caraGHLK
  11. Intersect(g, caraJKLM) → N
  12. Intersect(g, caraHIML) → O
  13. Intersect(g, caraGHLK) → P
  14. Intersect(g, caraCIMJ) → Q
  15. Intersect(g, caraCGKJ) → S
  16. Intersect(g, caraCGHI) → T
  17. Locus(N, F) → LlocGeomètric1
  18. Locus(O, F) → LlocGeomètric2
  19. Locus(P, F) → LlocGeomètric3
  20. Locus(Q, F) → LlocGeomètric4
  21. Locus(S, F) → LlocGeomètric5
  22. Locus(T, F) → LlocGeomètric6