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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 wikiPageRevisionID "540920465".
- Circles_of_Apollonius hasPhotoCollection Circles_of_Apollonius.
- Circles_of_Apollonius subject Category:Circles.
- Circles_of_Apollonius type Abstraction100002137.
- Circles_of_Apollonius type Attribute100024264.
- Circles_of_Apollonius type Circle113873502.
- Circles_of_Apollonius type Circles.
- Circles_of_Apollonius type ConicSection113872975.
- Circles_of_Apollonius type Ellipse113878306.
- Circles_of_Apollonius type Figure113862780.
- Circles_of_Apollonius type PlaneFigure113863186.
- Circles_of_Apollonius type Shape100027807.
- 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 label "Okrąg Apoloniusza".
- Circles_of_Apollonius label "アポロニウスの円".
- 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 Q2919145.
- Circles_of_Apollonius sameAs Q2919145.
- Circles_of_Apollonius sameAs Circles_of_Apollonius.
- Circles_of_Apollonius wasDerivedFrom Circles_of_Apollonius?oldid=540920465.
- Circles_of_Apollonius depiction Apollonius_circle_definition_labels.svg.
- Circles_of_Apollonius isPrimaryTopicOf Circles_of_Apollonius.
