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In geometry, inversive geometry is the study of inversion, ... Examples of inversion of circles A to J with respect to the red circle at O. Circles A to F, which pass ...
Pages in category "Inversive geometry" The following 13 pages are in this category, out of 13 total. This list may not reflect recent changes. ...
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 of each other. If α and β are non-intersecting or tangent, a single circle of antisimilitude exists; if α and β intersect at two points, there are two circles of antisimilitude.
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 with center O and radius k the inverse of a point Q is the point P for which P lies on the ray OQ and OP·OQ = k 2. The inverse of the curve C is then the locus of P as Q runs over C.
A natural setting for problem of Apollonius is inversive geometry. [4] [12] The basic strategy of inversive methods is to transform a given Apollonius problem into another Apollonius problem that is simpler to solve; the solutions to the original problem are found from the solutions of the transformed problem by undoing the transformation ...
In inversive geometry a straight line is considered to be a generalized circle containing the point at infinity; inversion of the plane with respect to a line is a Euclidean reflection. More generally, a Möbius plane is an incidence structure with the same incidence relationships as the classical Möbius plane.
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