Miquelian inversive plane

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This term is related to: incidence geometry
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This term is related to: inversive geometry
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Template:Inversive plane property

Definition

An inversive plane is said to be 'Miquelian if it satisfies the following. Let C_1, C_2, C_3, C_4 be four circles and let the intersection of C_i with C_{i+1} (read modulo 4) be the set \{ a_i,b_i \} (a_i may be equal to b_i). Then, a_is are concircular if and only if the b_is 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

Weaker properties

References

Finite Geometries by Peter Dembowski, Chapter 6. Inversive planes