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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 |
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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] |
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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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