Breeding Like Rabbits

Eight hundred years ago an Italian mathematician named Fibonacci posed the following problem:

There are 2 new-born rabbits in a field (one male, one female). After a month they can breed, so at the end of the second month another pair of rabbits are born, who themselves can breed after a month and so on. The rabbits never die and each month they are able to breed they do so and produce a new pair of rabbits (one male, one female). Fibonacci's question was how many rabbits there are at the end of the each month. - To start with, there is just 1 pair. - A month later, there is still 1. - Next month they have bred, so there are 2. - Then there are 3 as they breed again. - Now the first two pairs breed so there are 5. - And so on.

The sequence of numbers goes like this:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,.

They are known as the Fibonacci numbers. Each number in the sequence is the sum of the previous two numbers.

Believe it or not, for a theoretical problem posed like this, these numbers come up all over the place in real life: - The branches of trees, the stems on plants and the fruitlets on pineapples all form patterns based on them - Musical instruments are tuned using them. - The number of ancestors a bee has in each generation - A rough conversion from miles to kilometres is moving up the sequence (For examples, 55 miles is approximately 89 kilometers) - The formation of hurricanes and spiral galaxies - Dividing one by the one before it gives you an approximation to the golden ratio - which is the ratio the human body is built in.

It's amazing that solving a little maths puzzle unlocks so many different areas of the world.