Euler Circles

An example of Euler circles. Letters indicate, for example, properties: - Living being, - person, - the inanimate thing

The Euler Circle [1] is a geometric scheme with which you can draw relationships between subsets for a visual representation. Invented by Leonard Euler. Used in mathematics, logic, management and other applied areas.

An important special case of Euler circles is the Euler-Venn diagrams , depicting all combinations properties, that is, a finite Boolean algebra. With the Euler – Venn diagram is usually depicted as three circles with centers at the vertices of an equilateral triangle and with the same radius approximately equal to the length of the side of the triangle.

In solving a variety of problems, Leonard Euler used the idea of ​​depicting sets using circles. However, this method was used before the Euler by the outstanding German philosopher and mathematician Gottfried Wilhelm Leibniz. Leibniz used them for geometrical interpretation of logical connections between concepts, but nevertheless preferred to use linear schemes. [2]

An example of obtaining arbitrary Euler circles from Venn diagrams with empty (black) sets

But L. Euler himself developed this method quite thoroughly. The method of Euler circles was also used by the German mathematician Ernst Schroeder in the book Algebra of Logic. Graphic methods reached their peak in the writings of the English logic of John Venn, who set forth them in detail in his book Symbolic Logic, published in London in 1881. Therefore, such schemes are sometimes called Euler-Venn diagrams .

Venn diagram

Venn diagram showing all intersections of Greek, Russian and Latin alphabets (capital letters)

The Venn diagram (as a rule, the common name is the Euler – Venn diagram ) is a schematic depiction of all possible intersections of several (often three) sets.

Venn diagrams depict all combinations properties, that is, a finite Boolean algebra. With the Euler – Venn diagram is usually depicted as three circles with centers at the vertices of an equilateral triangle and with the same radius approximately equal to the length of the side of the triangle.

An example of obtaining arbitrary Euler circles from Venn diagrams with empty (black) sets.

They appeared in the writings of the English logic of John Venn (1834–1923), who set forth them in detail in the book Symbolic Logic, published in London in 1881.