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Cone Cross Section Exploration

Cone Cross Section Exploration
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2016-01-12 20:32
TrigonometryCoordinate GeometrySolid GeometryCalculusGeometric Construction
In collections Cross Sections
This example demonstrates the investigation of various cross sections of a cone and their geometric properties. Key math concepts include cones, conic sections, 2D vectors, triangles, differential calculus, reflections, and trigonometric functions. The construction utilizes GeoGebra commands such as Intersect, Point, Cone, PointIn, Circle, If, and IntersectPath, with objects like sliders (n, m, l), points (E, D, C, I, F, B, etc.), and text elements. It is suitable for high school students and math enthusiasts studying solid geometry, coordinate geometry, and calculus.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → E
  2. Point(zAxis) → D
  3. Cone(E, D, 2) → a, e, f
  4. PointIn(f) → C
  5. PointIn(f) → B
  6. PointIn(f) → A
  7. Circle(E, 2, zAxis) → g
  8. If(l ≟ 0, Plane[A, B, C], If[l ≟ 1, Plane[F, G, H], Plane[I, J, K]]) → d
  9. IntersectPath(d, a) → h
  10. IntersectPath(d, a) → k