

The First Simple Symmetric 11-Venn Diagram found - Rickasaurus
http://webhome.cs.uvic.ca/~ruskey/Publications/Venn11/Venn11.html

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showerst
If you were to 'color' these like a four color map problem, are they all
trivially colorable with just two colors? It looks that way from the pictures,
but I lack the math intuition to prove it.

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shasta
Yes, the intersection of a number of curves defining regions is color-able
with two colors: any point covered by an odd number of regions is black and
any point covered by an even number of regions is white (i.e. a checkerboard
pattern). Works as long as the boundary intersections are transverse. The
proof is simply that if you cross a boundary, you must be decreasing or
increasing the region count by one, changing the parity.

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akent
Are there any practical uses for this?

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jaredhansen
Yes, in the way that there are practical uses for a fair amount of mathematics
in general:

[http://mathoverflow.net/questions/10334/what-practical-
appli...](http://mathoverflow.net/questions/10334/what-practical-applications-
does-set-theory-have)

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aik
There are practical uses for much math but in very many cases it's only
practical in extremely specialized fields/cases. Meaning, in most cases very
impractical if speaking strictly in terms of practicalities. Yet, it's widely
taught, widely misunderstood, and so widely hated. The idea has become
humorous to me -- math, a natural pervasive wonder of our universe, hated by
many. Very impressive feat.

On this topic this book is great: A Mathematician's Lament by Paul Lockhart.
It opened my eyes to the concept of viewing much of math not in terms of
something strictly practical, but rather in broader terms, ie. natural art and
beauty with very practical applications mixed in here and there. Just as one
person enjoys painting, another enjoys dabbling in mathematics taking pleasure
from the elegance.

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ordinary
The essay that preceded the book is also food for thought. It's freely
available online: <http://www.maa.org/devlin/LockhartsLament.pdf>

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nuclear_eclipse
That doesn't look very "simple".

~~~
Pinckney
"A simple Venn diagram is one in which no more than two curves intersect at a
common point."

[http://www.combinatorics.org/files/Surveys/ds5/VennWhatEJC.h...](http://www.combinatorics.org/files/Surveys/ds5/VennWhatEJC.html)

