Fibonacci series

  • #1

Main Question or Discussion Point

what is the history of it and how is it different from maclaurin and taylor series
 

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
9,395
3
One is a sequence of integers, the other is an approximation of a function by a power series. How is bread different from music?

As I pointed out to yet another poster: JFGI. Inserting the words fibonnacci and sequence into a google search will give you a whole plethora of information - far more than anyone here could ever (be bothered to) write down.
 
  • #3
JasonRox
Homework Helper
Gold Member
2,314
3
  • #4
haha... or look up the breadfish, perhaps? :tongue:

In the movie Pi, the main guy gives a brief explanation on the fibonacci series to another character, explaining how it also relates to the golden ratio etc. And yes, as a movie, it's bound to have flaws in the accuracy of the actual maths presented. One of the equations written is apparently slightly erroneous, and I quote from imdb:

Max writes the golden ratio as (a/b) = (a/a+b). It should be a/b = (a+b)/a, if, by definition, a>b.


But hey, it may just be a more interesting approach in understanding this stuff than by laborously filtering through the googolplex. Pretty standard approach, heh. :wink: You can also get films, music--various symphonies-- set to the golden ratio. Amazing. Oh, the Parthenon too, but hey, that was one of many achievements set by the Greeks. Those Greeks... :rolleyes:
 
  • #5
matt grime
Science Advisor
Homework Helper
9,395
3
Oh, the Parthenon too, but hey, that was one of many achievements set by the Greeks. Those Greeks... :rolleyes:
There is no evidence to support the assertion that phi, the golden ratio, is important in greek architecture, or anywhere else, for non-mathematical reasons. Indeed, there are many elegant rebuttals of all the abuses of phi that exist. It does occur in nature for very good and well understood reasons (it has the 'slowest' converging rational approximation, in a sense that can be made precise), but none that supports any suggestion that is aesthetically pleasing.

The reason it 'occurs' in the parthenon is becuase some people choose to measure some ratios from some not well chosen positions. There are many rations one can write down from the parthenon that are not phi, but those are all conveniently ignored.
 
Last edited:
  • #6
53
0
It does occur in nature for very good and well understood reasons (it has the 'slowest' converging rational approximation, in a sense that can be made precise)
Could you make that more precise? :)
 
  • #7
14
0
The book The Golden Section: Nature's Greatest Secret by Scot Olsen is all about the subject. It is a very light read. You could probally finish it one afternoon at a bookstore.
 
  • #9
please give a simple explanation
 
  • #10
matt grime
Science Advisor
Homework Helper
9,395
3
Could you make that more precise? :)
Yes. But you could equally well do a google search and save me the bother.

Or looke here

http://www.maa.org/devlin/devlin_06_04.html [Broken]
 
Last edited by a moderator:
  • #11
matt grime
Science Advisor
Homework Helper
9,395
3
please give a simple explanation
Of what? The difference between Fibonnacci series and power series?

Here is the Fibonnacci sequence

1,1,2,3,5,8,13,21,34,55,....

if x(n) is the n'th term it satisfies the rule x(n)=x(n-1)+x(n-2), and x(1)=x(2)=1.

A Taylor seres looks like this:

sin(x)=x-x^3/3! +x^5/5! - .....


I don't see that there is anything that needs to be said to explain that they are different.
 
Last edited:

Related Threads on Fibonacci series

  • Last Post
Replies
3
Views
651
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
9
Views
4K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
8K
  • Last Post
Replies
5
Views
700
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
8
Views
17K
  • Last Post
Replies
9
Views
2K
Top