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wu :: forums    riddles    medium (Moderators: ThudnBlunder, Eigenray, towr, SMQ, Icarus, Grimbal, william wu)    Triangle and Fib « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Triangle and Fib  (Read 2591 times) Christine Full Member     Posts: 159 Triangle and Fib   « on: Mar 5th, 2013, 3:24pm » Quote Modify Can you explain why there are no triangles of any kind with sides the fibonacci numbers (being different)?   IP Logged peoplepower Junior Member     Posts: 63 Re: Triangle and Fib   « Reply #1 on: Mar 5th, 2013, 4:41pm » Quote Modify The problem is that your longest side will necessarily be too long for the triangle to not degenerate.   Say you have side lengths Fk,Fm,Fn with k<m<n. Then Fk+Fm <= Fm-1+Fm <= Fn. IP Logged Christine Full Member     Posts: 159 Re: Triangle and Fib   « Reply #2 on: Mar 11th, 2013, 1:18pm » Quote Modify I see. Thanks IP Logged Christine Full Member     Posts: 159 Re: Triangle and Fib   « Reply #3 on: Apr 4th, 2013, 12:22pm » Quote Modify Can you find all integer solutions to   a^2 + b^2 + c^2 + d^2 = e^2 where a, b, c, d, e are fibonacci numbers   a^2 + b^2 + c^2 + d^2 + e^2 = f^2 where a, b, c, d, e, f are fibonacci numbers   IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Triangle and Fib   « Reply #4 on: Apr 4th, 2013, 1:01pm » Quote Modify Do they need to be different and/or non-zero? (Just to rule out the trivial case where you pick all but one on the left-hand side 0.) IP Logged Wikipedia, Google, Mathworld, Integer sequence DB Christine Full Member     Posts: 159 Re: Triangle and Fib   « Reply #5 on: Apr 4th, 2013, 1:19pm » Quote Modify on Apr 4th, 2013, 1:01pm, towr wrote: Do they need to be different and/or non-zero? (Just to rule out the trivial case where you pick all but one on the left-hand side 0.)   Let's ignore the trivial cases.   IP Logged pex Uberpuzzler     Gender: Posts: 880 Re: Triangle and Fib   « Reply #6 on: Apr 4th, 2013, 1:34pm » Quote Modify For the sum of four squares, there's of course 12 + 12 + 12 + 12 = 22.   For sums of five squares, small solutions are 22 + 22 + 22 + 22 + 32 = 52, and 12 + 22 + 32 + 52 + 52 = 82.   There are no other solutions with all numbers positive within the first 38 Fibonacci numbers. (I don't really feel like searching for something with high enough precision to check higher numbers.) It might well be that there are no further solutions... anyone? 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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