What is a Venn diagram?
A Venn diagram draws sets as overlapping circles. Each circle holds the things in one set. Where two circles overlap sit the things in both. There is a region for every combination, including the ones that turn out to be empty. Two sets give four regions, counting the outside; three sets give eight.
John Venn published the diagrams in 1880, in the Philosophical Magazine, in a paper called “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings”. He called them Eulerian circles. The name Venn diagram came in 1918, from Clarence Irving Lewis’s book A Survey of Symbolic Logic. Venn’s own figure is in the gallery.
Venn or Euler?
Leonhard Euler drew circles for sets a century earlier, in letters to a German princess written between 1760 and 1762 and published from 1768. An Euler diagram draws only the combinations that occur. If no cat is a dog, the two circles sit apart. A Venn diagram draws every combination and leaves the impossible one empty, so the circles still overlap.
Many diagrams called Venn diagrams have a region missing. Strictly, those are Euler diagrams. VennyD draws each circle and overlap to its number, so a zero overlap keeps two circles apart, and the picture is then an Euler diagram that shows the two groups share nothing.
Why four circles don’t work
Four sets have sixteen combinations. Four circles make at most fourteen regions, however they are placed, so two combinations always have nowhere to go. Venn knew this and drew four sets with ellipses, which can make all sixteen.
That is why this site stops at three circles. Ikigai is the four-circle diagram most people have seen, and its four circles leave two combinations out, so it is not in the gallery. For four sets, draw a table, or two diagrams of three.
Drawn to scale
Most diagrams use equal circles whatever the numbers. An area-proportional Venn diagram sizes each circle and each overlap to its number: a group of 100 is twice the size of a group of 50, and an overlap of 25 covers a quarter of it. Make one, or open one of the famous diagrams and change the numbers.
Sources
- Venn diagram, Wikipedia
- Euler diagram, Wikipedia
- Letters to a German Princess, Wikipedia
- What is a Venn diagram?, Ruskey and Weston