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Topic: Inequality (Read 694 times) |
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ThudnBlunder
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The dewdrop slides into the shining Sea
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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 ->
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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Obob
Senior Riddler
   

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Re: Inequality
« Reply #1 on: Jul 13th, 2008, 2:25pm » |
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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.
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Eigenray
wu::riddles Moderator Uberpuzzler
    

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Re: Inequality
« Reply #2 on: Jul 13th, 2008, 3:02pm » |
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Now, to make this "putnam" worthy, how about showing that |f(t) - pi*t| C t23/73
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