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

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- Thread starter aeterminator1
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- #1

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

- #2

matt grime

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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

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How is bread different from music?

That made my day!

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In the movie

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...

- #5

matt grime

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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.

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Could you make that more precise? :)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)

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- #8

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My wife knitted me a Fibonacci scarf the other day. You can view it http://bp0.blogger.com/_wmbmRX6H5EA...PauTY/s1600-h/2007-03-04-fibonacci-scarf.jpg".

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- #9

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please give a simple explanation

- #10

matt grime

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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]

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- #11

matt grime

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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.

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