Matches in DBpedia 2016-04 for { ?s ?p "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."@en }
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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.".