a total of 13 beats grouped in 3’s and 2’s. For example “A fly and a flea in a flue Were imprisoned so what could they do? Said the fly, Let us flee, let us fly said the flea so they fled through a flaw in the flue. It’s easy to see the first 2 and last line have 3 beats, and the middle two have 2 beats for a total of 13 beats in five lines. The Mathematics of Fibonacci Numbers: To the casual observer, Fibonacci numbers may appear to be nothing more than random numbers. Some are odd, and some are even, some are prime, some are composite, and the distances between them vary. But the intuitive or informed eye will note the sequence I have described in so many contexts in this speech; each Fibonacci number is the sum of the previous two numbers beginning with one. The simplest of all numbers is of course 1. By following it with another 1, I can generate an infinite sequence of numbers. Any two adjacent numbers create the next number by addition. The mathematical properties of Fibonacci numbers are fascinating and extensive. The following are just a few of the vast number of examples. No two consecutive Fibonacci numbers have any common factors. Twice any Fibonacci number minus the next Fibonacci number equals the second number preceding the original one. The product of any two alternating Fibonacci numbers differs from the square of the middle number by 1. If Fibonacci numbers are squared and the adjacent squares are added together, a sequence of alternate Fibonacci numbers emerges. The difference of the squares of alternate Fibonacci numbers is always a Fibonacci number. For any four consecutive Fibonacci numbers, the difference of the squares of the middle two numbers equals the product of the smallest and largest numbers. The diagonals of Pascal’s triangles add up to Fibonacci numbers. Any Fibonacci number of a prime term is prime. This concludes my studies on the Fibonacci series, Thank You for your time...
