MathPlotAI Logo MathPlotAI

Movable Dandelin Spheres

Movable Dandelin Spheres
Loading the math board and drawing, please wait…
2015-08-12 10:51
TrigonometrySolid GeometryGeometric Construction
In collections intersection: surface-surface, curve-curve
This example demonstrates the application of Dandelin spheres in conic sections, visually illustrating the relationship between a cone's cross-section and the spheres through dynamic adjustments. Key mathematical concepts include conic sections, Dandelin sphere theorem, and geometric proofs. Construction highlights involve GeoGebra commands/objects like Point, Cylinder, Plane, etc., as detailed in the summary. Suitable for high school solid geometry education to intuitively understand properties of conic sections and the application of the Dandelin sphere theorem.

GeoGebra Commands & Parameters

  1. Point(zAxis) → B
  2. Point(zAxis) → A
  3. Cylinder(A, B, 2) → a, c, d, b
  4. Point(zAxis) → C
  5. Point(zAxis) → D
  6. PointIn(b) → E
  7. PointIn(b) → F
  8. PointIn(b) → G
  9. Plane(E, F, G) → e
  10. IntersectPath(e, a) → f
  11. Sphere(C, 2) → g
  12. Sphere(D, 2) → h
  13. Vector(C, B) → u
  14. Circle(C, 2, u) → k
  15. Intersect(zAxis, e) → H
  16. Point(f) → I
  17. Line(I, H) → i
  18. Intersect(i, f, 1) → J
  19. OrthogonalLine(H, i, f) → j
  20. Intersect(j, f, 1) → K
  21. Intersect(j, f, 2) → L
  22. Circle(L, Distance[I, H], f) → p
  23. Intersect(i, p) → M, N
  24. Circle(D, 2, u) → q
  25. Point(f) → O
  26. Segment(N, O) → l
  27. OrthogonalLine(O, d) → m
  28. Intersect(m, k) → P,
  29. Segment(O, P) → n
  30. Segment(M, O) → r
  31. Intersect(m, q) → Q,
  32. Segment(O, Q) → s