what is the history of it and how is it different from maclaurin and taylor series
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.
That made my day!
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. 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...
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.
Could you make that more precise? :)
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.
My wife knitted me a Fibonacci scarf the other day. You can view it here.
please give a simple explanation
Yes. But you could equally well do a google search and save me the bother.
Or looke here
Of what? The difference between Fibonnacci series and power series?
Here is the Fibonnacci sequence
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.
Separate names with a comma.