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- Circles_of_Apollonius abstract "The circle of Apollonius is any of several types of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for example, counterparts on the surface of a sphere can be defined through stereographic projection.The main uses of this term are fivefold: Apollonius showed that a circle can be defined as the set of points in a plane that have a specified ratio of distances to two fixed points known as foci. This circle of Apollonius is the basis of the Apollonius pursuit problem. The Apollonian circles are two families of mutually orthogonal circles. The first family consists of the circles with all possible distance ratios to two fixed foci, whereas the second family consists of all possible circles that pass through both foci. These circles form the basis of bipolar coordinates. Apollonius' problem is to construct circles that are simultaneously tangent to three specified circles. The solutions to this problem are sometimes called the \"circles of Apollonius\". The Apollonian gasket—one of the first fractals ever described—is a set of mutually tangent circles, formed by solving Apollonius' problem iteratively. The isodynamic points and Lemoine line of a triangle can be solved using three circles, each of which passes through one vertex of the triangle and maintains a constant ratio of distances to the other two.".
- Circles_of_Apollonius thumbnail Apollonius_circle_definition_labels.svg?width=300.
- Circles_of_Apollonius wikiPageID "2932144".
- Circles_of_Apollonius wikiPageLength "9899".
- Circles_of_Apollonius wikiPageOutDegree "50".
- Circles_of_Apollonius wikiPageRevisionID "666145095".
- Circles_of_Apollonius wikiPageWikiLink Ancient_Greece.
- Circles_of_Apollonius wikiPageWikiLink Apollonian_circles.
- Circles_of_Apollonius wikiPageWikiLink Apollonian_gasket.
- Circles_of_Apollonius wikiPageWikiLink Apollonius_of_Perga.
- Circles_of_Apollonius wikiPageWikiLink Apollonius_point.
- Circles_of_Apollonius wikiPageWikiLink Arc_length.
- Circles_of_Apollonius wikiPageWikiLink Bipolar_coordinates.
- Circles_of_Apollonius wikiPageWikiLink C._Stanley_Ogilvy.
- Circles_of_Apollonius wikiPageWikiLink Category:Circles.
- Circles_of_Apollonius wikiPageWikiLink Circle.
- Circles_of_Apollonius wikiPageWikiLink Circles_of_Apollonius.
- Circles_of_Apollonius wikiPageWikiLink Circumscribed_circle.
- Circles_of_Apollonius wikiPageWikiLink Curve.
- Circles_of_Apollonius wikiPageWikiLink Euclidean_geometry.
- Circles_of_Apollonius wikiPageWikiLink File:Apollonian_gasket.svg.
- Circles_of_Apollonius wikiPageWikiLink Focus_(geometry).
- Circles_of_Apollonius wikiPageWikiLink Fractal.
- Circles_of_Apollonius wikiPageWikiLink Gottfried_Wilhelm_Leibniz.
- Circles_of_Apollonius wikiPageWikiLink Hausdorff_dimension.
- Circles_of_Apollonius wikiPageWikiLink Inversive_geometry.
- Circles_of_Apollonius wikiPageWikiLink Isodynamic_point.
- Circles_of_Apollonius wikiPageWikiLink Kleinian_group.
- Circles_of_Apollonius wikiPageWikiLink List_of_geometers.
- Circles_of_Apollonius wikiPageWikiLink Orthogonality.
- Circles_of_Apollonius wikiPageWikiLink Plane_(geometry).
- Circles_of_Apollonius wikiPageWikiLink Problem_of_Apollonius.
- Circles_of_Apollonius wikiPageWikiLink Radical_axis.
- Circles_of_Apollonius wikiPageWikiLink Right_angle.
- Circles_of_Apollonius wikiPageWikiLink Sierpinski_triangle.
- Circles_of_Apollonius wikiPageWikiLink Stereographic_projection.
- Circles_of_Apollonius wikiPageWikiLink Tangent.
- Circles_of_Apollonius wikiPageWikiLink Triangle.
- Circles_of_Apollonius wikiPageWikiLink Wikt:interstice.
- Circles_of_Apollonius wikiPageWikiLink File:Apollonian_circles.svg.
- Circles_of_Apollonius wikiPageWikiLink File:Apollonius8ColorMultiplyV2.svg.
- Circles_of_Apollonius wikiPageWikiLink File:Apollonius_circle_definition_labels.svg.
- Circles_of_Apollonius wikiPageWikiLinkText "Circle of Apollonius".
- Circles_of_Apollonius wikiPageWikiLinkText "Circles of Apollonius".
- Circles_of_Apollonius wikiPageWikiLinkText "Circles_of_Apollonius#Apollonius_pursuit_problem".
- Circles_of_Apollonius wikiPageWikiLinkText "Lemoine line".
- Circles_of_Apollonius wikiPageWikiLinkText "circle of Apollonius".
- Circles_of_Apollonius wikiPageWikiLinkText "circles of Apollonius".
- Circles_of_Apollonius wikiPageWikiLinkText "other types of circles".
- Circles_of_Apollonius wikiPageUsesTemplate Template:Clear.
- Circles_of_Apollonius wikiPageUsesTemplate Template:Commons_category.
- Circles_of_Apollonius wikiPageUsesTemplate Template:Main.
- Circles_of_Apollonius wikiPageUsesTemplate Template:Redirect3.
- Circles_of_Apollonius wikiPageUsesTemplate Template:Reflist.
- Circles_of_Apollonius wikiPageUsesTemplate Template:Sfrac.
- Circles_of_Apollonius subject Category:Circles.
- Circles_of_Apollonius type Redirect.
- Circles_of_Apollonius comment "The circle of Apollonius is any of several types of circles associated with Apollonius of Perga, a renowned Greek geometer.".
- Circles_of_Apollonius label "Circles of Apollonius".
- Circles_of_Apollonius sameAs Q20781897.
- Circles_of_Apollonius sameAs Círculo_de_Apolonio.
- Circles_of_Apollonius sameAs アポロニウスの円.
- Circles_of_Apollonius sameAs Okrąg_Apoloniusza.
- Circles_of_Apollonius sameAs m.08dhd3.
- Circles_of_Apollonius sameAs Đường_tròn_của_Apollonius.
- Circles_of_Apollonius sameAs Q20781897.
- Circles_of_Apollonius wasDerivedFrom Circles_of_Apollonius?oldid=666145095.
- Circles_of_Apollonius depiction Apollonius_circle_definition_labels.svg.
- Circles_of_Apollonius isPrimaryTopicOf Circles_of_Apollonius.