History of Fibonacci Series & Difference from Maclaurin & Taylor

  • Thread starter aeterminator1
  • Start date
  • Tags
    Series
In summary: The Fibonacci sequence is a sequence of integers following a specific rule, whereas a Taylor series is an approximation of a function using a power series. They have different purposes and uses in mathematics.
  • #1
what is the history of it and how is it different from maclaurin and taylor series
 
Mathematics news on Phys.org
  • #2
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
matt grime said:
How is bread different from music?

That made my day!
 
  • #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
CellarDoor said:
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
matt grime said:
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
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
Eighty said:
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
aeterminator1 said:
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:

What is the history of the Fibonacci series?

The Fibonacci series is named after Leonardo Fibonacci, an Italian mathematician who popularized the sequence in his book "Liber Abaci" in the 12th century. However, the sequence was actually discovered by Indian mathematicians centuries before Fibonacci.

What is the difference between Fibonacci series and Maclaurin series?

The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding numbers, starting with 0 and 1. The Maclaurin series, on the other hand, is a mathematical series used to approximate a function by adding up an infinite number of terms. While the Fibonacci series is a specific sequence of numbers, the Maclaurin series is a general concept used in calculus.

What is the relationship between the Fibonacci series and the golden ratio?

The golden ratio is a mathematical constant that is approximately equal to 1.618. It is often found in nature and has been used in architecture and art. The ratio between consecutive numbers in the Fibonacci series approximates the golden ratio as the sequence progresses, which is why the series is often associated with it.

How is the Fibonacci series used in mathematics and other fields?

The Fibonacci series has various applications in mathematics, such as in number theory, geometry, and calculus. It is also used in computer science, finance, and biology. In finance, the series is used in the Fibonacci retracement, a technical analysis tool for predicting potential market trends.

What is the relationship between the Fibonacci series and the Taylor series?

The Taylor series is a mathematical series used to represent a function as an infinite sum of terms. The Maclaurin series is a special case of the Taylor series, where the function is centered at 0. While the Fibonacci series is a specific sequence of numbers, it can be represented by a Taylor series with specific coefficients. However, the two series serve different purposes in mathematics and have different applications.

Suggested for: History of Fibonacci Series & Difference from Maclaurin & Taylor

Replies
3
Views
435
Replies
2
Views
2K
Replies
7
Views
1K
Replies
1
Views
938
Replies
11
Views
1K
Replies
33
Views
2K
Replies
2
Views
706
Replies
23
Views
2K
Back
Top