A Venn diagram is a graphical illustration of the relationship between various sets of data. Most famously, it includes two sets, represented by two overlapping circles, although these diagrams can also be made with three circles, or a series of complex shapes to represent more than three sets of data. Venn diagrams are widely used in a branch of mathematics known as set theory, and they often appear in classroom exercises which are designed to get students to think about the relationships between things.
The Venn diagram was developed by John Venn, an English mathematician who lived between 1834-1923. His famous diagram was invented in 1881, and it is actually commemorated in the form of a stained glass window at his former college. By graphically showing how sets of data related to each other, Venn greatly clarified the field of set theory. Later mathematicians tweaked with the form of the diagram, but the basic system remains the same, and in wide use around the world.
A classic Venn diagram includes two sets, such as a list of all of the doctors in a town and all of the residents of a particular neighborhood. Each set is represented by a circle, and where the circles overlap, a region which includes members of both sets is created. In this case, the region would include all of the residents of a particular neighborhood who are also doctors. A third set can be added to the diagram, such as a list of all of the people in the town who have dogs.
When three circles are included in a Venn diagram, several areas of overlap are formed. In the case of the example above, we could see which doctors have dogs, which doctors live in a particular neighborhood, and which residents of that particular neighborhood have dogs. In the very middle of the diagram, where all three circles overlap, we would have a list of dog-owning doctors in the neighborhood.
The Venn diagram is very helpful for categorizing things and laying out information in a way which makes it easier to grasp. Many people like to use it for problem solving, as many world problems can be untangled with its assistance. When more sets of data are involved in a Venn diagram, a number of convoluted shapes must be created to make the desired areas of overlap, which can result in some truly astonishing illustrations of data.