The Venn diagram, also known as the set diagram, is a diagram which shows which are the possible logical relations between a collections of sets. The Venn diagram is used in many fields, primary academics, but also statistics, computer science, linguistics, logic, and probability. Every Venn diagram will usually comprise overlapping circles, with the exterior symbolizing elements which are characteristic exclusively to the elements being compared, and the interior of the circle representing the elements of the set, meaning the common characteristics of the elements being compared.
The history of the Venn diagram goes back to 1880, when British logician and philosopher John Venn introduced it in his research paper On the Diagrammatic and Mechanical Representation of Propositions and Reasonings, which was published in the Philosophical Magazine and Journal of Science. With the help of the Venn diagram, he wanted to illustrate the different ways in which propositions can be represented by means of diagrams. At that time, John Venn referred to the Venn diagram as the Eulerian circle, because it resembles Euler diagrams, invented by Leonhard Euler. In 1918, American academic philosopher Clarence Irving Lewis used the term Venn diagram for the first time, in his book A Survey of Symbolic Logic. The Venn diagram was developed later on by D.W. Henderson, which claimed in 1963 that, as an n-Venn diagram with n-fold rotational symmetry existed, then n was prime. He then proved than the Venn diagram can bee symmetric when n is 5 or 7.
In 2002, Peter Hamburger took the symmetry theory to the next level, after showing that the Venn diagram can also be symmetric when n is 11. One year later, Griggs, Sauvage, and Killian demonstrated that Venn diagrams are symmetric for all other prime numbers. They later concluded that the symmetric Venn diagram exists if and only if n is a prime number. Since then, the Venn diagram has greatly increased in popularity, becoming an important part of instruction in set theory, which was part of the new math movement back in the 1960s.