Dandelin Spheres

The inner and outer Spheres Tangent internally to a Cone and also to a Planeintersecting the Cone are called Dandelin spheres.

The Spheres can be used to show that the intersection of the Plane with the Cone is anEllipse. Let be a Plane intersecting a right circular Cone with vertex in the curve . Call the Spheres Tangent to the Cone and the Plane and , and theCircles on which the Spheres are Tangent to the Cone and . Picka line along the Cone which intersects at , at , and at . Call the points on thePlane where the Circles are Tangent and . Because intersecting tangents have thesame length,

References

Honsberger, R. ``Kepler's Conics.'' Ch. 9 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., p. 170, 1979.

Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp. 40-44, 1991.

Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 80-81, 1990.

Ogilvy, C. S. Excursions in Mathematics. New York: Dover, pp. 68-69, 1994.

• Stellated Truncated Hexahedron
• Stellation
• Stem-and-Leaf Diagram
• Step
• Step Function
• Step Polynomial
• Steradian
• Stereogram
• Stereographic Projection
• Stereology
• Stern-Brocot Tree
• Stevedore's Knot
• Stewart's Theorem
• Stickelberger Relation
• Stick Number
• Stiefel Manifold
• Stiefel-Whitney Class
• Stiefel-Whitney Number
• Stieltjes Constants
• Stieltjes Integral
• Stieltjes' Theorem
• Stieltjes-Wigert Polynomial
• Stirling Cycle Number
• Stirling Number of the First Kind
• Stirling Number of the Second Kind