Editing Venn diagram (section)

== {{anchor|Symmetric|n}}History ==
[[File:Venn-stainedglass-gonville-caius.jpg|thumb|right|150px|[[Stained-glass]] window with Venn diagram in [[Gonville and Caius College, Cambridge]]]]

Venn diagrams were introduced in 1880 by [[John Venn]] in a paper entitled "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings"<ref name="Venn_2014"/> in the ''Philosophical Magazine and Journal of Science'',<ref name="PM"/> about the different ways to represent [[proposition]]s by diagrams.<ref name="Venn1880_1"/><ref name="Venn1880_2"/><ref name="Sandifer2003"/> The use of these types of diagrams in [[formal logic]], according to [[Frank Ruskey]] and Mark Weston, predates Venn but are "rightly associated" with him as he "comprehensively surveyed and formalized their usage, and was the first to generalize them".<ref name="Ruskey2005"/>

Diagrams of overlapping circles representing unions and intersections were introduced by Catalan philosopher [[Ramon Llull]] (c. 1232–1315/1316) in the 13th century, who used them to illustrate combinations of basic principles.<ref name="Baron_1969" /> [[Gottfried Wilhelm Leibniz]] (1646–1716) produced similar diagrams in the 17th century (though much of this work was unpublished), as did Johann Christian Lange in a work from 1712 describing [[Christian Weise]]'s contributions to logic.<ref name="Leibniz_1690" /><ref name="Baron_1969" /> [[Euler diagram]]s, which are similar to Venn diagrams but don't necessarily contain all possible unions and intersections, were first made prominent by mathematician [[Leonhard Euler]] in the 18th century.<ref group="note" name="NB_1"/><ref name="Venn1881"/><ref name="Gailand_1967"/>

Venn did not use the term "Venn diagram" and referred to the concept as "Eulerian Circles".<ref name="Sandifer2003"/> He became acquainted with Euler diagrams in 1862 and wrote that Venn diagrams did not occur to him "till much later", while attempting to adapt Euler diagrams to [[Boolean logic]].<ref name="Maths Today">{{cite magazine|title=The Venn Behind the Diagram|last=Verburgt|first=Lukas M.|volume=59|issue=2|date=April 2023|pages=53–55|magazine=Mathematics Today|publisher=[[Institute of Mathematics and its Applications]]}}</ref> In the opening sentence of his 1880 article Venn wrote that Euler diagrams were the only diagrammatic representation of logic to gain "any general acceptance".<ref name="Venn1880_1"/><ref name="Venn1880_2"/>

Venn viewed his diagrams as a pedagogical tool, analogous to verification of physical concepts through experiment. As an example of their applications, he noted that a three-set diagram could show the [[syllogism]]: 'All ''A'' is some ''B''. No ''B'' is any ''C''. Hence, no ''A'' is any ''C''.'<ref name="Maths Today"/>

[[Charles L. Dodgson]] (Lewis Carroll) includes "Venn's Method of Diagrams" as well as "Euler's Method of Diagrams" in an "Appendix, Addressed to Teachers" of his book ''Symbolic Logic'' (4th edition published in 1896). The term "Venn diagram" was later used by [[Clarence Irving Lewis]] in 1918, in his book ''A Survey of Symbolic Logic''.<ref name="Ruskey2005"/><ref name="Lewis1918"/>

In the 20th century, Venn diagrams were further developed. [[David Wilson Henderson]] showed, in 1963, that the existence of an ''n''-Venn diagram with ''n''-fold [[rotational symmetry]] implied that ''n'' was a [[prime number]].<ref name="Henderson_1963"/> He also showed that such symmetric Venn diagrams exist when ''n'' is five or seven. In 2002, Peter Hamburger found symmetric Venn diagrams for ''n'' = 11 and in 2003, Griggs, Killian, and Savage showed that symmetric Venn diagrams exist for all other primes. These combined results show that rotationally symmetric Venn diagrams exist, if and only if ''n'' is a prime number.<ref name="Ruskey_2006"/>

Venn diagrams and Euler diagrams were incorporated as part of instruction in set theory, as part of the [[new math]] movement in the 1960s. Since then, they have also been adopted in the curriculum of other fields such as reading.<ref name="Strategies"/>