An inversive plane is a class of incidence structure in mathematics.
It may be axiomatised by taking two classes, "points" and "circles" (or "blocks") with the properties
- any three points lie on exactly one circle;
- if P and Q are points and c a circle with P on c and Q not, then there is exactly one circle e containing P and Q and intersecting c only in P;
- there are four points not all on the same circle.
The finite inversive planes are precisely the designs. Such a design is always a Steiner system.
Read more about Inversive Plane: Ovoids, Derived Designs and Extensions
Famous quotes containing the word plane:
“At the moment when a man openly makes known his difference of opinion from a well-known party leader, the whole world thinks that he must be angry with the latter. Sometimes, however, he is just on the point of ceasing to be angry with him. He ventures to put himself on the same plane as his opponent, and is free from the tortures of suppressed envy.”
—Friedrich Nietzsche (1844–1900)