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Euler diagram

Contributor(s): Matthew Haughn

An Euler diagram (pronounced OY-ler diagram) is a graphic depiction commonly used to illustrate the relationships between sets or groups; the diagrams are usually drawn with circles or ovals, although they can also use other shapes.

Inclusion is represented by the overlapping of circles – called Eulerian circles -- representing the sets and and subsets. Exclusion is represented by non-overlapping circles. Euler diagrams typically include colors that are blended in areas where the circles overlap. Generally, the size of the circles is not significant but only adjusted to allow for more space for subsets.

Euler diagrams are closely related to Venn diagrams and depending on the sets in question, can look identical. However, in Venn diagrams, overlapped circles don't necessarily indicate a commonality between sets, just a possible logical relationship, unless their labels are in the intersecting circle.

See a simple example, below, of how the relationship between the sets of animals and minerals and the subset of four legs could be depicted in Venn and Euler diagrams:

 Venn Diagram Euler diagram

Euler diagrams, Eulerian circles and Euler’s constant are named for Swiss mathematician Leonhard Euler (1707–1783). Both Venn and Euler diagrams were adopted for teaching set theory as part of the new math movement of the 1960s.

This was last updated in July 2015

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