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:
“Even though I had let them choose their own socks since babyhood, I was only beginning to learn to trust their adult judgment.. . . I had a sensation very much like the moment in an airplane when you realize that even if you stop holding the plane up by gripping the arms of your seat until your knuckles show white, the plane will stay up by itself. . . . To detach myself from my children . . . I had to achieve a condition which might be called loving objectivity.”
—Anonymous Parent of Adult Children. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)