On Mar 1, 7:21=A0pm, Gene Ward Smith <g...@[EMAIL PROTECTED]
> wrote:
> Butch Malahide <fred.gal...@[EMAIL PROTECTED]
> wrote in news:7ce37c6d-9f9b-485e-
> bec7-93f3440a2...@[EMAIL PROTECTED]
>
> >> Euler scores with the generalized Fermat little theorem, the
V-E+F=3D2
> >> theorem, the summation of the reciprocals of the square numbers,
solvin=
g
> >> Pell's equation, the pentagonal number theorem for partitions, the
> >> Konigsberg bridges problem, and the divergence of the sum of the
> >> reciprocals of the primes, for a total of seven.
>
> > One of those seven is not like the others. I'm not sure if Euler
> > actually proved (or even stated) the characterization of "Eulerian"
> > graphs, and I'm too lazy to look it up, but even if he did, it seems
> > to lack the depth and im****tance of the other six. I'm not sure it
> > even belongs on a list of *Euler's* top 100 theorems.
>
> Euler proved the theorem for convex polyhedra. Like many things, it's
> im****tant in good measure because of what it leads to.
Sorry for mumbling. I wasn't talking about V-E+F, I was talking about
the Koenigsberg bridges. The generalization (which I'm not sure Euler
did) is the characterization of Eulerian graphs (graphs having a
circuit that contains all the edges) as connected graphs with no
vertices of odd degree. Which is im****tant and useful, but I don't
think it's in the same league with the others.
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