From: "Iain Davidson" Subject: Re: QR with Stokes theorem? Date: Sat, 18 Mar 2000 14:15:52 -0000 Newsgroups: sci.math Summary: [missing] John R Ramsden wrote in message news:38d359ce.4081311@news.demon.co.uk... > Richard Cudney wrote: > > > > I believe I once saw a reference in this newsgroup to a proof of > > quadratic reciprocity using stokes theorem. If anyone has a reference to > > this, or to anything remotely like this, I would be very appreciative. > > I think it was me who mentioned this a couple of months ago, while trying > to argue that QR might not be as remote from physical theories as certain > people (Pertti L) like to think. Unfortunately the statement was based on > a distant recollection and may not be accurate. However, there is no doubt > that some well-known result in number theory can be proved fairly directly > by using Stokes' Theorem or Green's Theorem. But I can't remember which. > Sorry to spread possible half-truths and inaccuracies. On Page 56 of Rose's "A course in Number Theory", he states "Other proofs (of QR) use results from algebra, geometry, permutation theory and even fluid dynamics - there is one (Lewy, 1946, Waves on Beaches, Bull. Am. Math. Soc., 52, 737-75) which begins by considering the wave equation on a beach with constant angle (pi)p/2q. Bachmann P. (1968 Niedere Zahlentheorie, Chelsea, NewYork) has given a detailled analysis of all proofs known before 1910, see also LeVeque (1974, Reviews of Number Theory (1940 -72), A14 and R40, American Mathematical Society, Providence, RI) and Guy "Unsolved Problems" Maybe it is just coincidence, but Stokes is a name linked with fluid dynamics, Stokes' law etc. .