Fibonacci number and nutritional hazards

A really interesting programme is the Melvin Bragg programme on the BBC Radio 4.
He and guests talk about all manner of intelligent topics including mathematics
He sends on request a newsletter which summarises his programme.
The Fibonacci sequence is one of those fascinating games which mathematicians indulge in.
It struck me that the breeding rabbits and the numbers are not dissimilar to the number of unfortunate effects food, it is claimed, can have on the unsuspecting public.
These stick in the text books and like the rabbits never die, only accumulate. The public meanwhile lives longer each century and enjoys food. .
Fibonacci introduced the number sequence through the analogy of breeding rabbits. He based his model on a world where the rabbits could never die or get ill, in other words nothing would stop them constantly reproducing..
Suppose a newborn pair of rabbits (one male and one female) are put in a field. These rabbits take a month to become sexually mature, after which time they produce a new pair of baby rabbits, one male and one female.
These babies will take a month to mature, so although in the third month the mature rabbits can produce yet another pair of baby rabbits, the other pair will only be ready in the fourth month to reproduce. The pattern continues in this fashion and every month there are increasing numbers of rabbits. – 1,1,2,3,5, 8,13_ And so the Fibonacci number sequence emerges from the breeding habits of rabbits.There is a strong interrelationship between the numbers in the Fibonacci sequence. For a start, you get the next Fibonacci number by adding the two previous ones together, so there is already a relationship between them. For example, if you square the first hundred Fibonacci numbers and add them together it is the same result as the hundredth Fibonacci number times the 101st Fibonacci number. It is curious that these connections between the squares of Fibonacci numbers connect with later numbers in the sequence and in fact, there are quite a lot of these weird connections between the numbers. For example, if you have the 100th Fibonacci number and you want to find out the 300th Fibonacci number there is a very simple way to do it. You cube the 100th Fibonacci number, multiply by 5 and then add 3 times the 100th Fibonacci number. This will give the answer to what the 300th Fibonacci number is. There are many formulas linked with the Fibonacci sequence.
Melvyn Bragg Newsletter 30th November 2007

Martin Eastwood
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