The Fibonacci Sequence

The Fibonacci sequence is a series of numbers where the next number in the series is found by adding the two previous numbers together. The series starts with 0 and 1, or sometimes with 1 and 1, and goes 0,1,1,2,3,5,8,13,21,34, and so on. The mathematical expression for this sequence is: Fn = Fn-1 + Fn-2.

This series is named after Fibonacci, also known as Leonardo of Pisa and these numbers were first introduced in his Liber abaci in 1202. Fibonacci first noted this sequence when pondering a mathematical problem about rabbit breeding. He started off with a male rabbit and a female rabbit, which would be the first two numbers. Rabbits reach sexual maturity after one month and the gestation period of a rabbit is also one month. The female rabbit gives birth to one male rabbit and one female. This then happens every month and the sequence follows for the number of rabbits. So after three months, we have a pair of sexual mature rabbits and a pair of premature sexual rabbits. After the fourth month, we have two pairs of sexual mature rabbits and a pair of premature sexual rabbits. As you can see, this well keep growing and growing just as the Fibonacci sequence does. There was one issue with Fibonacci’s sequence, and that is that the rabbits do die at some point, and he didn’t include this in his sequence.

Looking at the previous example makes Fibonacci’s sequence look unrealistic, but these numbers do appear in nature. For example, sunflower seeds are arranged in a Fibonacci spiral, keeping the seeds uniformly distributed no matter how large the seed head might be. A Fibonacci spiral is a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. The squares fit perfectly together because of the nature of the sequence, where the next number is equal to the sum of the two before it. Any two successive Fibonacci numbers have a ratio very close to the Golden Ratio, which is roughly 1.618034. The larger the pair of Fibonacci numbers, the closer the approximation. The spiral and resulting rectangle are known as the Golden Rectangle.

Mathematics is all around us, it may not be obvious, but it is most definitely there. We just need to look closely enough to the everyday things that we see around us and admire the beauty and mathematical concepts behind them. This can be applied while teaching mathematics to give the pupils a reason behind the learning of new math concepts which they may see as useless.

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