Fibonacci numbers and the golden section Article

Fibonacci numbers and the golden section - Article ExampleRecall that an integer is crown 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 thefind 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 childlike terms, contains a number of illustrations and it explains clearly some applications of Fibonacci numbers to natural sciences. It contains also several plug intos to other websites on the same topic. We suggest to follow the link Fibonacci numbers in nature there, you will find a pplications 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 good-looking 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 doesnt require any special knowledge in mathematics and it has sufficiently many practical applications in arts and science, to be a fascinating and intriguing subject. BIBLIOGRA PHY1 Dunlap, R. The Golden Ratio and