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I was just wondering what were the main/important uses of the Fibonacci sequence as well as any other generalized Fibonacci sequences in real life applications.

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    $\begingroup$ Try thinking about a snail shell... $\endgroup$ – VortexYT Mar 6 '17 at 16:19
  • $\begingroup$ @simplest_mathematics: what ?? $\endgroup$ – Yves Daoust Mar 6 '17 at 16:34
  • $\begingroup$ AFAIK, many shelled animal's shells follow a fibbonachi sequence.Search online: $\endgroup$ – VortexYT Mar 6 '17 at 16:37
  • $\begingroup$ Look at this, entitled "15 Uncanny Examples of the Golden Ratio in Nature" $\endgroup$ – lioness99a Mar 6 '17 at 16:38
  • $\begingroup$ And of course you first tried the obvious and the links therein? $\endgroup$ – Did Mar 6 '17 at 16:38
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As far as I know, the Fibonacci sequence have no particular "uses" in real life and they are more relevant in the frame of certain mathematical models.

A particular application I think of is when you know that a function has a single maximum in a given interval. Then it is proven that the optimal sequence of function evaluations to narrow down the maximum is obtained with intervals having a length proportional to the terms of Fibonacci.

But I wouldn't call that real life.

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  • $\begingroup$ See teamnotus.com and download "Final Report Senior Design I". It's about a turbine called Liam F1 Urban Wind Turbine. $\endgroup$ – cgiovanardi Mar 7 '17 at 2:00
  • $\begingroup$ @cgiovanardi: I wonder if the choice of the golden section has any functional justification, other than propagating the folklore. $\endgroup$ – Yves Daoust Mar 7 '17 at 7:46
  • $\begingroup$ @cgiovanardi: where the hell do you see a connection to Fibonacci in these spirals ? $\endgroup$ – Yves Daoust Mar 7 '17 at 15:13
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In computer science, there is a data structure called a Fibonacci Heap that works by storing items in a collection of heaps with degrees that are ascending Fibonacci numbers. Fibonacci heaps have significantly better performance in certain tasks than other similar data structures.

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The number of ways you can climb stairs from 0 to stair N is a fibonacci sequence provided you can climb 1 or 2 stairs at one time. Not real life really but if you want to know :D

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