Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.3 4.3bsd-beta 6/6/85; site ucbvax.BERKELEY.EDU
Path: utzoo!watmath!clyde!burl!ulysses!gamma!epsilon!zeta!sabre!petrus!bellcore!decvax!ittatc!dcdwest!sdcsvax!ucbvax!brahms!weemba
From: weemba@brahms.BERKELEY.EDU (Matthew P. Wiener)
Newsgroups: net.math
Subject: Re: Question came up at a party
Message-ID: <11623@ucbvax.BERKELEY.EDU>
Date: Thu, 30-Jan-86 08:29:54 EST
Article-I.D.: ucbvax.11623
Posted: Thu Jan 30 08:29:54 1986
Date-Received: Sat, 1-Feb-86 06:42:35 EST
References: <532@well.UUCP> <144@linus.UUCP> <2597@sdcrdcf.UUCP> <2731@sjuvax.UUCP>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: weemba@brahms.UUCP (Matthew P. Wiener)
Distribution: net
Organization: University of California, Berkeley
Lines: 20
Keywords: special affine curvature, projective transformations

In article <2731@sjuvax.UUCP> bhuber@sjuvax.UUCP (B. Huber) writes:
>>>> 	Is there a formula which describes *all* conic sections, which

>(Thus the family of conic sections in the plane is five-dimensional, since 
>one can always eleminate one of the real parameters A ... F  by rescaling
>the equation.)
>
>	This is essentially the answer everyone came up with.  It's a good one,
>but suffers on two grounds:  it does not generalize to higher dimensions very
>nicely, and it does not reveal the geometry which inspired the original
>intuition that fundamentally all the conic sections are "the same".  I offer
>two ways to remedy this, one very well-known, the other fairly obscure.
>
>[a fine discussion follows]

B Huber's fine discussion parallels the first chapter of C H Clemens' nice
little book _A Scrapbook of Complex Curve Theory_, published by Plenum Press,
and well worth studying.

ucbvax!brahms!weemba	Matthew P Wiener/UCB Math Dept/Berkeley CA 94720