From: utzoo!decvax!harpo!seismo!hao!cires!nbires!ut-ngp!utastro!bill
Newsgroups: net.math
Title: Re: re: Math riddle
Article-I.D.: utastro.334
Posted: Fri May  6 17:09:15 1983
Received: Tue May 17 20:27:23 1983
References: ihuxf.368 utastro.333

I forgot to mention in my previous submission, that the L[infinity]
norm of the vector (x,y) is just max(|x|,|y|).  So the formula

	max(|x|,|y|) = k

also gives a square.  If you are interested, the L[1] norm and
L[infinity] norms are, like the L[2] norm, very useful for curve
fitting problems.  L[2] is Least Squares; L[infinity] is Chebyshev
fitting (minimize the maximum error); finally, L[1] is related to the
median (and is very resistant to bad data points).  See

	Branham, Richard L., "Alternatives to Least Squares",
		Astronomical Journal *87*, 928-937 (1982)

for a very illuminating discussion.