tag:blogger.com,1999:blog-3722233.post2710934609148478273..comments2021-11-30T15:06:41.716-06:00Comments on Computational Complexity: How important are the Fib numbers in math? in Nature? In History of Math books?Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-3722233.post-14053786157613968912012-01-20T08:54:34.581-06:002012-01-20T08:54:34.581-06:00I think the official statement to be made against ...I think the official statement to be made against the author in these times is "citation needed".Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-65456778819939596622012-01-19T22:44:09.518-06:002012-01-19T22:44:09.518-06:00In my experience, the Fibonacci numbers are an inc...In my experience, the Fibonacci numbers are an incredibly valuable tool in mathematics. I can say with near certainty that the most important application of Fibonacci numbers is as a toy. There are any number of compelling results about them which become a gateway for learning induction, modular arithmetic, and a passion for the beauty of mathematics. I would think that countless mathematicians were set on that path with the help of Fibonacci numbers, thus leading to countless interesting theorems having nothing to do with them.<br /><br />There seem to be other interesting applications listed above, but none are as important as the role of attraction.Andy Parrishhttps://www.blogger.com/profile/12252029594014518238noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-84467880962884247842012-01-18T23:07:53.780-06:002012-01-18T23:07:53.780-06:00Yet further to Jeffrey Shallit's comment, Fibo...Yet further to Jeffrey Shallit's comment, Fibonacci numbers are also the worst case in Huffman coding. They also turn out to be "harmonics" in many algorithms, to the extent that if you're graphing the performance of certain algorithms for problems of various size, Fibonacci numbers are often outliers. (That, or powers of two.)<br /><br />As well as Fibonacci heaps, we have Fibonacci codes and a bunch of other constructions which rely on Fibonacci numbers.<br /><br />So at the very least, Fibonacci numbers are a useful design and analysis tool in disparate areas of computer science.Pseudonymnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-38062850495829816202012-01-18T04:22:12.572-06:002012-01-18T04:22:12.572-06:00I think you meant Matijasevic.I think you meant Matijasevic.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-40752292192490216582012-01-17T23:36:13.836-06:002012-01-17T23:36:13.836-06:001) In the above examples do you really need FIB
(1...1) In the above examples do you really need FIB<br />(1,1,2,3,5,8,...) or would any sequence satisfying<br />a(n)=a(n-1)+a(n-2),perhaps with diff initial conditions, suffice.<br /><br />2) If you Google <br /><br />Matijasec Hilbert<br /><br />the first hit you get is... This blog. I am sure that the way I<br />spelled it is not an alternative spelling but is just plain wrong.<br />(Will fix later.)GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-111849946147924542012-01-17T23:00:26.641-06:002012-01-17T23:00:26.641-06:00In my opinion, one of the biggest contributions Fi...In my opinion, one of the biggest contributions Fibonacci numbers make to math (that isn't too obscure) is a contribution which doesn't get **anywhere near** as much attention as it deserves. Namely, they contribute a neat application example to matrix diagonalization (an otherwise dry subject which the Fibonacci example really breathes life into). What on Earth am I talking about? Once you know how to diagonalize matrices, it becomes routine to derive the formula for the nth Fibonacci number, a formula which is otherwise somewhat mystical-seeming. (For details see: http://mathproofs.blogspot.com/2005/04/nth-term-of-fibonacci-sequence.html )<br /><br />Is Matijasec some weird alternate spelling? I've seen Matiyasevich spelled several different ways but never THAT way...Sam Alexanderhttp://www.math.osu.edu/~alexander/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-42749163087784012102012-01-17T15:10:51.672-06:002012-01-17T15:10:51.672-06:00In Computer Science we have Fibonacci Heaps.In Computer Science we have Fibonacci Heaps.Clyde Kruskalnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-18220731219731203562012-01-17T09:40:25.212-06:002012-01-17T09:40:25.212-06:00Related to last Shallit's comment: Fibonacci w...Related to last Shallit's comment: Fibonacci words are often used as worst-case examples in stringology. Altough this does not mean that we could not live without them.Matthias GallĂ©http://www.cs.famaf.unc.edu.ar/~galle/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-26439870829691183442012-01-17T09:12:36.322-06:002012-01-17T09:12:36.322-06:00How about the role of the Fibonacci numbers as the...How about the role of the Fibonacci numbers as the worst-case of Euclid's algorithm for the GCD? That seems pretty fundamental.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.com