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Maximum Cone

Maximum Cone
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2017-08-10 23:01
TrigonometryCoordinate GeometrySolid GeometryOptimizationGeometric Construction
This example demonstrates the dynamic construction of a cone to show the maximum volume phenomenon. Key math concepts include the cone volume formula, analytical geometry, triangle properties, ellipses, and reflection. Construction highlights involve commands/objects like Circle, Point, Angle, Segment, Polygon, CircumcircleArc, Sector, CircleArc, Surface, Textfield, and Locus in GeoGebra. Suitable for high school and above students to understand solid geometry optimization problems and dynamic geometry software applications.

GeoGebra Commands & Parameters

  1. Circle(O, 1) → c
  2. Point(c) → B
  3. Angle(A, O, B) → α
  4. Segment(O, P) → a
  5. Segment(V, C) → b
  6. Segment(V, O) → g
  7. Segment(O, C) → i
  8. Polygon(O, C, V) → poly1, v, o, c_1
  9. Circle(zAxis, C) → p
  10. CircumcircleArc(D, E, C) → q
  11. Sector(c, A, B) → d
  12. CircleArc(O, A, B) → k
  13. Surface((u * cos(v)), (u * sin(v)), f(u), u, 0, rr, v, 0, β) → S
  14. Segment(O, A) → j
  15. Textfield(sl) → InputBox1
  16. Circle(O, r) → s
  17. Locus(Q, B) → loc1