nearest points

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1 total messages Started by John Manuel Paz Wed, 30 Dec 1992 03:25

#159

Author: John Manuel Paz
Date: Wed, 30 Dec 1992 03:25

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Hi,
	In "Number Theory" Hardy presents a result which shows that the
closest rational approximation to an irrational number is:

	| r - p/q | <= 1/q^2,	r - irrational, 0<p<=q, p, q rational

which is the same thing as saying the closest point of an approximating
lattice to a line is O(1/q^2).  I was wondering if anyone could direct
me to any results concerning circles or any curves with curvature.
Thanks in advance.

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