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wu :: forums    riddles    putnam exam (pure math) (Moderators: Grimbal, SMQ, towr, Eigenray, william wu, Icarus)    Inequality « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Inequality  (Read 691 times) ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Inequality   « on: Jul 13th, 2008, 9:55am » Quote Modify 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 -> IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Obob Senior Riddler     Gender: Posts: 489 Re: Inequality   « Reply #1 on: Jul 13th, 2008, 2:25pm » Quote Modify 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. IP Logged Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Inequality   « Reply #2 on: Jul 13th, 2008, 3:02pm » Quote Modify Now, to make this "putnam" worthy, how about showing that |f(t) - pi*t| C t23/73   IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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