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- Dandelin_spheres abstract "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 1822. They are named in honor of the Belgian mathematician Germinal Pierre Dandelin, though Adolphe Quetelet is sometimes given partial credit as well. The Dandelin spheres can be used to prove at least two important theorems. Both of those theorems were known for centuries before Dandelin, but he made it easier to prove them.The first theorem is that a closed conic section (i.e. an ellipse) is the locus of points such that the sum of the distances to two fixed points (the foci) is constant. This was known to Ancient Greek mathematicians such as Apollonius of Perga, but the Dandelin spheres facilitate the proof.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. Again, this theorem was known to the Ancient Greeks, such as Pappus of Alexandria, but the Dandelin spheres facilitate the proof.A conic section has one Dandelin sphere for each focus. In particular, an ellipse has two Dandelin spheres, both touching the same nappe of the cone. A hyperbola has two Dandelin spheres, touching opposite nappes of the cone. A parabola has just one Dandelin sphere.".
- Dandelin_spheres thumbnail Dandelin1.png?width=300.
- Dandelin_spheres wikiPageExternalLink Dandelin.html.
- Dandelin_spheres wikiPageExternalLink index.asp.
- Dandelin_spheres wikiPageExternalLink belges.htm.
- Dandelin_spheres wikiPageID "683726".
- Dandelin_spheres wikiPageRevisionID "552286475".
- Dandelin_spheres hasPhotoCollection Dandelin_spheres.
- Dandelin_spheres id "DandelinSpheres".
- Dandelin_spheres title "Dandelin Spheres".
- Dandelin_spheres subject Category:Conic_sections.
- Dandelin_spheres subject Category:Euclidean_solid_geometry.
- Dandelin_spheres subject Category:Spheres.
- Dandelin_spheres type Abstraction100002137.
- Dandelin_spheres type Attribute100024264.
- Dandelin_spheres type ConicSection113872975.
- Dandelin_spheres type ConicSections.
- Dandelin_spheres type Environment113934596.
- Dandelin_spheres type Figure113862780.
- Dandelin_spheres type PlaneFigure113863186.
- Dandelin_spheres type Shape100027807.
- Dandelin_spheres type Situation113927383.
- Dandelin_spheres type Sphere114514039.
- Dandelin_spheres type Spheres.
- Dandelin_spheres type State100024720.
- Dandelin_spheres comment "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 1822.".
- Dandelin_spheres label "Dandelin spheres".
- Dandelin_spheres label "Dandelinsche Kugel".
- Dandelin_spheres label "Dandelinsfeer".
- Dandelin_spheres label "Esferas de Dandelin".
- Dandelin_spheres label "Esferas de Dandelin".
- Dandelin_spheres label "Sfere di Dandelin".
- Dandelin_spheres label "Théorème de Dandelin".
- Dandelin_spheres label "Шары Данделена".
- Dandelin_spheres label "كرات داندلين".
- Dandelin_spheres sameAs Dandelinsche_Kugel.
- Dandelin_spheres sameAs Esferas_de_Dandelin.
- Dandelin_spheres sameAs Théorème_de_Dandelin.
- Dandelin_spheres sameAs Sfere_di_Dandelin.
- Dandelin_spheres sameAs 당드랑의_구.
- Dandelin_spheres sameAs Dandelinsfeer.
- Dandelin_spheres sameAs Esferas_de_Dandelin.
- Dandelin_spheres sameAs m.032q78.
- Dandelin_spheres sameAs Q676413.
- Dandelin_spheres sameAs Q676413.
- Dandelin_spheres sameAs Dandelin_spheres.
- Dandelin_spheres wasDerivedFrom Dandelin_spheres?oldid=552286475.
- Dandelin_spheres depiction Dandelin1.png.
- Dandelin_spheres isPrimaryTopicOf Dandelin_spheres.
