Butch Malahide <fred.galvin@[EMAIL PROTECTED]
> wrote in news:7ce37c6d-9f9b-485e-
bec7-93f3440a2177@[EMAIL PROTECTED]
>> Euler scores with the generalized Fermat little theorem, the V-E+F=2
>> theorem, the summation of the reciprocals of the square numbers,
solving
>> 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.
> Gauss scores with the
>> fundamental theorem of algebra, quadratic reciprocity, and the
independenc
> e
>> of the parallel postulate, for a total of three.
>
> Did Gauss prove the independence of the parallel postulate? I thought
> I read somewhere that that was done (model for non-Euclidean geometry)
> later and by some less notorious mathematician. On the other hand,
> shouldn't constructible polygons be on the list? Like you said, it's
> not canonical.
I would certainly say myself that the theorem is due to Beltrami, who gave
a clear proof of it. In fact I did say this in the Wikipedia article on
Beltrami, which proves I'm right.
But it's not my list.
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