# Miquelian inversive plane

From Groupprops

This term is related to: incidence geometry

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This term is related to: inversive geometry

View other terms related to inversive geometry | View facts related to inversive geometry

Template:Inversive plane property

## Definition

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

### Weaker properties

## References

*Finite Geometries* by Peter Dembowski, *Chapter 6. Inversive planes*