StudentShare solutions

# Fibonacci numbers and the golden section - Article Example

## Extract of sample Fibonacci numbers and the golden section

Recall that an integer is prime if it has no proper divisors. Some Fibonacci numbers are prime, for example 514229, but it is still unknown whether there exist infinitely many prime Fibonacci numbers. The problem of finding prime numbers with many digits is crucial for the
find a very large prime number, you are able to write a secret code that is reasonably safe (this principle is the basis of the Public Key Cryptography, nowadays used by banks and governments all over the world).
Suggested readings. We suggest, as a first reading, the following website: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html. It is well written, in elementary terms, contains a number of illustrations and it explains clearly some applications of Fibonacci numbers to natural sciences. It contains also several links to other websites on the same topic. We suggest to follow the link "Fibonacci numbers in nature": there, you will find applications to family trees of rabbits, cows, geometry, flowers, and vegetables! It is a short, fascinating walk in the real world seen through the mathematicians' eyes.
As a further, more technical reading, one can read the material contained in the website: http://en.wikipedia.org/wiki/Fibonacci_number. ...
It is well written, in elementary terms, contains a number of illustrations and it explains clearly some applications of Fibonacci numbers to natural sciences. It contains also several links to other websites on the same topic. We suggest to follow the link "Fibonacci numbers in nature": there, you will find applications to family trees of rabbits, cows, geometry, flowers, and vegetables! It is a short, fascinating walk in the real world seen through the mathematicians' eyes.
At the bottom of the page there are suggestions on the paths to follow to explore further the site.
As a further, more technical reading, one can read the material contained in the website: http://en.wikipedia.org/wiki/Fibonacci_number. Part of this site is probably too advanced for a non-specialist, but most of its content is certainly accessible.
These readings can be the opportunity to learn a little, but very useful, piece of mathematics: the difference equations. A difference equation is a function whose value at n is
defined linearly by the value at n-1 and n-2, as in the case of Fibonacci numbers. For such functions, there exist always a closed formula, that is, a formula giving the value at n only as a function of n, with no knowledge of the values at n-1 and n-2. The method is explained at the beginning of http://en.wikipedia.org/wiki/Recurrence_relation.
In the bibliography, we suggest some elementary books for a further reading.
To conclude, I think that this suggested reading is accessible to everybody, it doesn't require any special knowledge in mathematics and it has sufficiently many practical applications in arts and science, to be a fascinating and intriguing subject.

BIBLIOGRAPHY

## Summary

Why are these numbers interesting First of all, they show up in many practical problems, especially in biological contexts, such as the branching in trees, genealogy trees and the production and shape of fruits. But they are also related to the so-called 'golden section': given a segment [a,b], to find its golden section means to find a number x on that segment such that
Author : fred32
Save Your Time for More Important Things
Let us write or edit the article on your topic
"Fibonacci numbers and the golden section"
with a personal 20% discount.
Grab the best paper

### Check these samples - they also fit your topic

Prescription for success in an associate degree nursing program
This paper critically analyzes the article, “Prescription for success in an associate degree nursing program” by the author Tanya L. Rogers, which highlights the aforementioned issue and explores the factors underlying success of students enrolled in an entry level nursing program.
6 pages (1500 words) Article
The Ancient World
Also in Catullus Poems, we find a number of very beautiful poems that portray the love of beauty and excellence by the Romans. Also, in Thucydides’, History of the Peloponnesian war (1.1-23, 2.34-46), we find descriptions of magnificent works of Art by the Romans.
4 pages (1000 words) Article
Training and Development Article
The second kind of training adheres to preparing the employee for promotions and other such activities. Therefore, training and development processes may either be diagnostic or based on future role play. In this case, the kinds of training followed by an organization may be categorized into on the job and off the job training methods.
12 pages (3000 words) Article
Small Scale Experimental Machine
Its designers, Frederic Williams, Tom Kilburn and Geoff Tootill, who worked at the Electrical Engineering department of the University, developed the machine as a test-bed for Williams Tube - one of the created at that time computer memories, and did not mean the Baby to become a prototype of the contemporary computer (Enticknap, 1998).
5 pages (1250 words) Article
US Immigration/ 3 articles
It can be seen what effect the law has had on the school attendance by the affected groups especially the Hispanics. The other article expresses some of the measures that have been put in place by the various
3 pages (750 words) Article
Journal article review
f mostly students from minority and disadvantageous social group, was able to convey the probability concept by using basic statements, which described events of their daily lives. Children were able to distinguish differences of those statements describing which events are
2 pages (500 words) Article
Module 6 DQ1 and 2
Such preventive measures as security guards, passkeys and identification tags, locked equipment, and keeping an eye out for unauthorized people are all facets of physical security. Technical
2 pages (500 words) Article
Discussions questions
ive worth or importance and implies excellence based on desirability or usefulness and is represented as a magnitude or quantity best defined from customer’s perspective as a benefit received from the offer versus the sacrifices to obtain it. Value is created when product and
2 pages (500 words) Article
Write a criteria section for a feasibility study
the above criteria was due to different dynamics of concern in renovation of such facilities like bathroom with different kinds of emphasis put into it. There are a number of criteria that were evaluated and filtered to form the basis for our criteria of renovating the
2 pages (500 words) Article
Discussion 1: The Methods Section Week 7 722
The Human chorionic gonadotropin strips were used as the detection target in the study. A complementary metal-oxide semiconductor sensor was used to identify the colors of the control line and test
1 pages (250 words) Article
Hire a pro to write