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Frustum of a Cone - Animation Demo

Frustum of a Cone - Animation Demo
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2016-11-08 07:47
Solid GeometryGeometric Construction
This example demonstrates the formation of a frustum of a cone through animation. It involves core mathematical concepts such as the cone, ellipse, power functions, and geometric transformations. Construction highlights include the use of GeoGebra commands and objects like Intersect, Point, Segment, Polygon, Circle, OrthogonalLine, Rotate, Line, Tangent, and CircleArc. Suitable for high school and above students to learn about the properties of frustums and related geometric principles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O_1
  2. Point(yAxis) → A
  3. Segment(O_1, A) → R
  4. Point(zAxis) → S
  5. Polygon(O_1, A, S) → BigCone, R_v, s_v, H_v
  6. Circle(S_p, s_v, xOyPlane) → c
  7. OrthogonalLine(S_p, xAxis, xOyPlane) → f
  8. Intersect(f, c, 1) → C
  9. Intersect(f, xAxis) → J
  10. Segment(C, J) → n
  11. Segment(O_1, J) → m
  12. Segment(A, S) → s_V
  13. Segment(S, O_1) → H_Z
  14. Rotate(BigCone, α, zAxis) → RotationBigCone
  15. Point(zAxis) → O_2
  16. Line(O_2, yAxis) → i
  17. Intersect(i, s_V) → B
  18. Segment(O_2, B) → r
  19. Polygon(O_2, B, S) → SmallCone, r_M, s_m, H_M
  20. Polygon(O_1, A, B, O_2) → Frustum, R_z, s_z, r_z, H_z
  21. Rotate(SmallCone, α, zAxis) → RotationSmallCone
  22. Rotate(Frustum, α, zAxis) → RotationFrustum
  23. Rotate(A, α, zAxis) → A'
  24. Rotate(B, α, zAxis) → B'
  25. Segment(O_1, A') → R'
  26. Circle(S_p, s_m, xOyPlane) → d
  27. Circle(O_1, A) → e
  28. Tangent(C, c) → g,
  29. CircleArc(O_1, A, A', xOyPlane) → lukAA'
  30. Segment(A'_1, S_p) → OpisOmotac
  31. Intersect(OpisOmotac, c) → D, A'_p
  32. Intersect(OpisOmotac, d) → F, B'_p
  33. Segment(A'_p, B'_p) → h