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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 and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied.
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.
circle inversion examples: Image title: Examples of inversion of circles A to J with respect to the red circle at O by CMG Lee. Circles A to F which pass through O map to straight lines. Circles G to J which do not map to other circles. The reference circle and line L map to themselves. Circles intersect their inverses, if any, on the reference ...
Moser's worm problem (also known as mother worm's blanket problem) is an unsolved problem in geometry formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem asks for the region of smallest area that can accommodate every plane curve of length 1.
The inversive distance has been used to define the concept of an inversive-distance circle packing: a collection of circles such that a specified subset of pairs of circles (corresponding to the edges of a planar graph) have a given inversive distance with respect to each other.
Learn to edit; Community portal; Recent changes ... Download as PDF; Printable version; In other projects ... Pages in category "Inversive geometry" The following 13 ...
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