# Venn Diagrams with Four Ellipses

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To create a four-set Venn diagram, the plane must be divided into 16 non-overlapping regions. The regions (except for the empty set) must be simply connected. The four regions have been marked 1, 2, 3, 4, enclosed in four different colored ellipses. Drag each label to define its proper region. The table at the bottom shows which regions have been labeled correctly.

Contributed by: Izidor Hafner (June 2019)

Open content licensed under CC BY-NC-SA

## Details

Four-set diagram with ellipses was found by Venn [4, p. 43].

[1] F. Ruskey and M. Weston, "A Survey of Venn Diagrams," *The Electronic Journal of Combinatorics*, DS#5, 2005. www.combinatorics.org/files/Surveys/ds5/VennEJC.html.

[2] B. Grünbaum, "The Search for Symmetric Venn Diagrams," *Geombinatorics*, 8(4), 1999 pp. 104–109. (Jun 7, 2019) sites.math.washington.edu/~grunbaum/SymmetricVennDiagrams.pdf.

[3] Wikipedia. "Branko Grünbaum." (Jun 7, 2019) en.wikipedia.org/wiki/Branko_Gr%C3%BCnbaum.

[4] M. Gardner, *Logic Machines, Diagrams and Boolean Algebra*, New York: Dover Publications, 1968.

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