The mysteries of Venn diagrams

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Above, a Venn diagram I made visually depicting every combination of Dwarf from the fairy tale. Not included: Snow White.

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The other day I was tying to make some multi-set Venn diagrams with polar symmetry, which it turns out is harder than you’d think and has ties with prime number theory. It’s an obscure but important area of combinatorics. Everybody knows a 3-set one (n=3), and I made a 5-set one with ellipses (pictured to the right). After that, I was stumped. That led me to a great web section maintained by Professors Frank Ruskey and Mark Weston. The Dwarf diagram at the top is based on that work, with Sleepy a little more opaque so you can see the shape. Ruskey and Weston display lots of lovely diagrams, including the elusive n=7 minimum vertex Venn diagram and the remarkable n=11 Venn diagram.

A Survey of Venn Diagrams

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