In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines...

by composition of reflections, it is a special case of inversive geometry. Inversive geometry itself can be performed with the larger system known as...

their higher-dimensional analogs such as higher finite inversive geometries. Finite geometries may be constructed via linear algebra, starting from vector...

then D is the inverse of B with respect to the circle (O,k) with center O and radius k. Thus, by the properties of inversive geometry, since the figure...

Geometry of Complex Numbers is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geometry, and non-Euclidean...

metric space is the hyperbolic plane. In terms of the models of hyperbolic geometry, this model is frequently designated the Poincaré half-plane model. Mathematicians...

In inversive geometry, the inversive distance is a way of measuring the "distance" between two circles, regardless of whether the circles cross each other...

geometry Information geometry Integral geometry Inversive geometry Inversive ring geometry Klein geometry Lie sphere geometry Non-Euclidean geometry Noncommutative...

flat models are the spaces of inversive geometry. For pseudo-Euclidean of metric signature (p, q), the model flat geometry is defined analogously as the...

Congruence (geometry) Hamming distance (string or sequence similarity) Helmert transformation Homoeoid (shell of concentric, similar ellipsoids) Inversive geometry...

published a paper about the inversion transformation, which leads to inversive geometry. His reputation as a mathematician was established by 1834 and an...

Morley, Inversive Geometry". Bull. Amer. Math. Soc. 40 (5): 374–375. doi:10.1090/s0002-9904-1934-05848-8. Henry Forder (1934) Review:Inversive Geometry, The...

ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry. Several notations for the inverse trigonometric...

In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following...

theory Inversive geometry the study of invariants preserved by a type of transformation known as inversion Inversive plane geometry inversive geometry that...

and vice-versa. However, generalized circles are fundamental to inversive geometry, in which circles and lines are considered indistinguishable, the...

Circle and the Sphere is a mathematics book on circles, spheres, and inversive geometry. It was written by Julian Coolidge, and published by the Clarendon...

also considered as a kind of generalized circles, for instance in inversive geometry, then an orthogonal pair of lines or line and circle are orthogonal...

inappropriate for lower grades. Thus inversive geometry, a larger study than grade school transformation geometry, is usually reserved for college students...

hyperbolic planes, elliptic planes two-dimensional spherical geometry. Plane curve Inversive geometry Geometrography This disambiguation page lists mathematics...

quadrilateral sides to cross. The Apollonius quadrilaterals are important in inversive geometry, because the property of being an Apollonius quadrilateral is preserved...

short descriptions of redirect targets Inversive distance – Concept in inversive geometry Inversive geometry – Study of angle-preserving transformations...

case of a parabola if the parabola resides on a tangent plane. In inversive geometry, a line is a degenerate case of a circle, with infinite radius. Two...

constructed Riemannian geometry, of which elliptic geometry is a particular case. Another example concerns inversive geometry as advanced by Ludwig Immanuel...

{v\cdot a-c}{a\cdot a}}a.} Additive inverse Coordinate rotations and reflections Householder transformation Inversive geometry Plane of rotation Reflection mapping...

inversive plane because it is closed under inversion with respect to any generalized circle, and thus a natural setting for planar inversive geometry...

{\displaystyle z} as a variable are illustrated in Frank Morley's book Inversive Geometry (1933), written with his son Frank Vigor Morley. The other planar...

Firstly, n-dimensional hyperbolic geometry, n-dimensional de Sitter space and (n−1)-dimensional inversive geometry all have isomorphic automorphism groups...

In inversive geometry, the circle of antisimilitude (also known as mid-circle) of two circles, α and β, is a reference circle for which α and β are inverses...

In inversive geometry, an inverse curve of a given curve C is the result of applying an inverse operation to C. Specifically, with respect to a fixed circle...