I like the Johnson solids. 92 solids + prisms + antiprisms. ----- Original Message ----- From: "Gareth McCaughan" <gareth.mccaughan@pobox.com> To: <math-fun@mailman.xmission.com> Sent: Tuesday, October 14, 2008 6:34 PM Subject: Re: [math-fun] what's the best way of finding n unknown integersfrom their sums taken k at a time
On Tuesday 14 October 2008, Dan Asimov wrote:
This is so cool! I love results like this, where a simply stated problem has a straightforward answer, except for some small and/or strange set. ... I am interested to hear of mathematical results that have a small and strange set of exceptions.
A few I can think of are these: ... Other such examples are solicited.
Classification of finite simple groups. (A few nice "obvious" families, plus the sporadic ones.)
I'm not convinced by your examples of the form "Such-and-such a ring always has non-unique factorization, except for these cases"; this seems a bit like Mike Stay's joke example "all even numbers are composite, except 2". I mean, surely the real story for k(sqrt(d)), for instance, is that the class number function -> oo as d -> oo, so obviously it's only 1 for a finite number of cases.
-- g
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