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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 wikiPageLength "9269".
- Dandelin_spheres wikiPageOutDegree "31".
- Dandelin_spheres wikiPageRevisionID "702837619".
- Dandelin_spheres wikiPageWikiLink Adolphe_Quetelet.
- Dandelin_spheres wikiPageWikiLink Ancient_Greece.
- Dandelin_spheres wikiPageWikiLink Apex_(geometry).
- Dandelin_spheres wikiPageWikiLink Apollonius_of_Perga.
- Dandelin_spheres wikiPageWikiLink Belgium.
- Dandelin_spheres wikiPageWikiLink Category:Conic_sections.
- Dandelin_spheres wikiPageWikiLink Category:Euclidean_solid_geometry.
- Dandelin_spheres wikiPageWikiLink Category:Spheres.
- Dandelin_spheres wikiPageWikiLink Cone.
- Dandelin_spheres wikiPageWikiLink Conic_section.
- Dandelin_spheres wikiPageWikiLink Cylinder_(geometry).
- Dandelin_spheres wikiPageWikiLink Eccentricity_(mathematics).
- Dandelin_spheres wikiPageWikiLink Ellipse.
- Dandelin_spheres wikiPageWikiLink Focus_(geometry).
- Dandelin_spheres wikiPageWikiLink Geometry.
- Dandelin_spheres wikiPageWikiLink Germinal_Pierre_Dandelin.
- Dandelin_spheres wikiPageWikiLink Hyperbola.
- Dandelin_spheres wikiPageWikiLink Keplers_laws_of_planetary_motion.
- Dandelin_spheres wikiPageWikiLink Locus_(mathematics).
- Dandelin_spheres wikiPageWikiLink Nappe_(disambiguation).
- Dandelin_spheres wikiPageWikiLink Pappus_of_Alexandria.
- Dandelin_spheres wikiPageWikiLink Parabola.
- Dandelin_spheres wikiPageWikiLink Plane_(geometry).
- Dandelin_spheres wikiPageWikiLink Sphere.
- Dandelin_spheres wikiPageWikiLink Tangent.
- Dandelin_spheres wikiPageWikiLink File:Dandelin1.png.
- Dandelin_spheres wikiPageWikiLink File:Dandelin_spheres_and_ellipse.gif.
- Dandelin_spheres wikiPageWikiLinkText "Dandelin spheres".
- Dandelin_spheres id "DandelinSpheres".
- Dandelin_spheres title "Dandelin Spheres".
- Dandelin_spheres wikiPageUsesTemplate Template:Commonscat.
- Dandelin_spheres wikiPageUsesTemplate Template:MathWorld.
- Dandelin_spheres subject Category:Conic_sections.
- Dandelin_spheres subject Category:Euclidean_solid_geometry.
- Dandelin_spheres subject Category:Spheres.
- Dandelin_spheres hypernym Spheres.
- Dandelin_spheres type Food.
- 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 sameAs Q676413.
- Dandelin_spheres sameAs كرات_داندلين.
- Dandelin_spheres sameAs Dandelinsche_Kugel.
- Dandelin_spheres sameAs Esferas_de_Dandelin.
- Dandelin_spheres sameAs Théorème_de_Dandelin.
- Dandelin_spheres sameAs Dandelin-gömb.
- Dandelin_spheres sameAs Sfere_di_Dandelin.
- Dandelin_spheres sameAs 당들랭의_구.
- Dandelin_spheres sameAs Dandelinsfeer.
- Dandelin_spheres sameAs Esferas_de_Dandelin.
- Dandelin_spheres sameAs m.032q78.
- Dandelin_spheres sameAs Шары_Данделена.
- Dandelin_spheres sameAs Кулі_Данделена.
- Dandelin_spheres sameAs Q676413.
- Dandelin_spheres wasDerivedFrom Dandelin_spheres?oldid=702837619.
- Dandelin_spheres depiction Dandelin1.png.
- Dandelin_spheres isPrimaryTopicOf Dandelin_spheres.