This article is about a family of circles sharing a radical axis, and the corresponding family of orthogonal circles. For other circles associated with Apollonius of Perga, see circles of Apollonius.
Some Apollonian circles. Every blue circle intersects every red circle at a right angle. Every red circle passes through the two points C, D, and every blue circle separates the two points.
In geometry, Apollonian circles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa. These circles form the basis for bipolar coordinates. They were discovered by Apollonius of Perga, a renowned Greek geometer.
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In geometry, Apolloniancircles are two families (pencils) of circles such that every circle in the first family intersects every circle in the second...
In mathematics, an Apollonian gasket or Apollonian net is a fractal generated by starting with a triple of circles, each tangent to the other two, and...
Apollonian circle is the basis of the Apollonius pursuit problem. It is a particular case of the first family described in #2. The Apolloniancircles are two...
complex plane maps Ford circles to other Ford circles. Ford circles are a sub-set of the circles in the Apollonian gasket generated by the lines y = 0 {\displaystyle...
coordinates are a two-dimensional orthogonal coordinate system based on the Apolloniancircles. Confusingly, the same term is also sometimes used for two-center...
The Apollonian and the Dionysian are philosophical and literary concepts represented by a duality between the figures of Apollo and Dionysus from Greek...
generalised circles are actually circles: a generalised circle is either a (true) circle or a line. The tangent line through a point P on the circle is perpendicular...
Bryson of Heraclea argued that, since larger and smaller circles both exist, there must be a circle of equal area; this principle can be seen as a form of...
on the ground that the isodynamic points are related to the three Apolloniancircles associated with a triangle. The solution of the Apollonius problem...
the three given things are circles. In the 16th century, Vieta presented this problem (sometimes known as the Apollonian Problem) to Adrianus Romanus...
previously-drawn circles. The fractal collection of circles produced in this way is called an Apollonian gasket. If the process of producing an Apollonian gasket...
leads up to a geometric precursor of the law of cosines. Book 3 focuses on circles, while the 4th discusses regular polygons, especially the pentagon. Book...
orthogonal to the circle of ideal points bounding the disk. Orthogonality Radical axis Power center (geometry) Apolloniancircles Bipolar coordinates...
plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262...
points determine a circle in Euclidean geometry and two distinct points determine a pencil of circles such as the Apolloniancircles. These results seem...
the circumcircle. From that, we know that the circumcircle is an Apolloniancircle with foci M, D. So AS is the bisector of angle ∠DAM, and we have achieved...
and each circle is surrounded by six other circles. For circles of diameter D and hexagons of side length D, the hexagon area and the circle area are...
circle Problem of Apollonius Concepts and definitions Angle Central Inscribed Axiomatic system Axiom Chord Circles of Apollonius Apolloniancircles Apollonian...
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency:...
100–170 AD) was of a very advanced level and rarely mastered outside a small circle. Examples of applied mathematics around this time include the construction...
dynamics and has worked extensively on counting and equidistribution for Apolloniancircle packings, Sierpinski carpets and Schottky dances. She is currently...
methods. Cassini oval Confocal conic sections Trajectory Apolloniancircles, pairs of families of circles that are all orthogonal to each other A. Jeffrey: Advanced...
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