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riddles >> putnam exam (pure math) >> Inequality
(Message started by: ThudanBlunder on Jul 13th, 2008, 9:55am)

Title: Inequality
Post by ThudanBlunder on Jul 13th, 2008, 9:55am
For any real t > o, define f(t) to be the number of pairs of integers (a,b) which satisfy a2 + b2 < t

Evaluate LIM f(t)/t as t -> http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/infty.gif

Title: Re: Inequality
Post by Obob on Jul 13th, 2008, 2:25pm
[hide]For large enough t, f(t) is approximately the area of a circle of radius sqrt(t), i.e. pi * t.  So the limit is pi.[/hide]

Title: Re: Inequality
Post by Eigenray on Jul 13th, 2008, 3:02pm
Now, to make this "putnam" worthy, how about showing that |f(t) - [hide]pi[/hide]*t| http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/le.gif C t23/73  :P



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