Miquelian inversive plane
This term is related to: incidence geometry
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This term is related to: inversive geometry
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An inversive plane is said to be 'Miquelian if it satisfies the following. Let be four circles and let the intersection of with (read modulo 4) be the set ( may be equal to ). Then, s are concircular if and only if the s are concircular.
It turns out that an inversive plane is Miquelian if and only if it arises from a non-ruled quadric in a three-dimensional geometry over a commutative field.
Relation with other properties
Finite Geometries by Peter Dembowski, Chapter 6. Inversive planes