On the construction of venn diagrams

Abstract

Venn constructed diagrams of up to five simply connected regions that overlapped each other once in each possible way of overlapping. Although Venn did not prove that his diagrams were constructible for more than five simply connected regions — in fact, he preferred to have a doubly connected region in his 5-class diagram — he summarized his method of construction with an intuitive argument: “But for merely theoretical purposes the rule of formulation would be very simple. It would merely be to begin by drawing any closed figure, and then proceed to draw others, subject to the one condition that each is to intersect once and once only all the existing subdivisions produced by those which had gone before.” The method of construction given below leads to a simple topological proof that Venn diagrams can be constructed for any number of simply connected regions.