Venn Diagram

The simplest Venn diagram consists of three symmetrically placed mutually intersecting Circles. It is used in Logic theory to represent collections of sets. The region of intersection of the three Circles $A\cap B\cap C$, in the special case of the center of each being located at the intersection of the other two, is called a Reuleaux Triangle.

In general, an order $n$ Venn diagram is a collection of $n$ simple closed curves in the Plane such that

1. The curves partition the Plane into $2^n$ connected regions, and

2. Each Subset $S$ of $\{1, 2, \ldots, n\}$ corresponds to a unique region formed by the intersection of the interiors of the curves in $S$ (Ruskey).

See also Circle, Flower of Life, Lens, Magic Circles, Reuleaux Triangle, Seed of Life

References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 255-256, 1989.

Ruskey, F. ``A Survey of Venn Diagrams.'' Elec. J. Combin. 4, DS#5, 1997. http://www.combinatorics.org/Surveys/ds5/VennEJC.html.

Ruskey, F. ``Venn Diagrams.'' http://sue.csc.uvic.ca/~cos/inf/comb/SubsetInfo.html#Venn.