ESFERAS DE DANDELIN PDF

In geometry , the Dandelin spheres are one or two spheres that are tangent both to a plane and to a cone that intersects the plane. The intersection of the cone and the plane is a conic section , and the point at which either sphere touches the plane is a focus of the conic section, so the Dandelin spheres are also sometimes called focal spheres. The Dandelin spheres were discovered in The Dandelin spheres can be used to give elegant modern proofs of two classical theorems known to Apollonius of Perga. The first theorem is that a closed conic section i. The second theorem is that for any conic section, the distance from a fixed point the focus is proportional to the distance from a fixed line the directrix , the constant of proportionality being called the eccentricity.

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Conic sections via Mathoverflow. It's particularly nice because it explains the foci geometrically, as well as the focus-directrix property with some more work. Conic Section. Maths Paper. Geometry Activities. Surface Area. Mechanical Engineering. Sacred Geometry. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane which is parallel to another plane which is tangential to the conical surface. A third description is algebraic.

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Esferas de Dandelin

Conic sections via Mathoverflow. It's particularly nice because it explains the foci geometrically, as well as the focus-directrix property with some more work. Conic Section. Maths Paper. Geometry Activities. Surface Area. Mechanical Engineering.

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