fibonacci sequence in nature handout pdf

There’s even a style of poetry inspired by the Fibonacci sequence, known as Fib Poetry. In Mozart’s sonatas, the number of bars of music in the latter section divided by the former is approximately 1.618, the Golden Ratio. is introduced) and the development and recapitulation (where the theme is developed and repeated). A sonata can be divided into two separate sections, known as the exposition (where the theme close Theme A short, distinctive piece of music that is repeated and developed throughout a piece of music. Mozart made use of the Golden Ratio when writing a number of his piano sonatas close Sonata A piece of instrumental music, usually for a solo instrument, or a small group. Indian poets and musicians had already been aware of the Fibonacci sequence for centuries though, having spotted its implications for rhythm and different combinations of long and short beats. Fibonacci explained his findings in a book called Liber Abaci, published in 1202, which had a section devoted to the intriguing sequence which would be named after him hundreds of years later.

There, he learnt how the Hindu-Arabic numerals of 0-9 could be used to complete calculations more easily than the Roman numerals still in use across much of Europe. Born Leonardo Bonacci in 12th-Century Pisa, Italy, the mathematician travelled extensively around North Africa. Listening for the Fibonacci sequence in musicįibonacci didn’t actually discover the sequence himself. The perfect degree of turn needs to be an irrational number, which can’t be easily approximated by a fraction, and the answer is the Golden Ratio. There would be four lines of seeds, but that’s not much better than one when trying to cover a circular area. If the degree of turn was a fraction, like 1/4, that doesn’t help matters much because after four turns the seed pattern would be right back at the start again. The best way of minimising wasted space is for the seeds to grow in spirals, with each seed growing at a slight angle away from the previous one. Now, if it simply grew seeds in a straight line in one direction, that would leave loads of empty space on the flower head.

To be as efficient as possible, its seeds need to be closely packed together without overlapping. Again, this is a number that can be found the natural world. The Golden Ratio is an irrational number, and so cannot be written as a fraction. The larger the numbers, the closer you get to 1.618.

If you take a number in the sequence above 5, and divided it by the previous number, you will get an answer very close to 1.618. This is because of something known as the Golden Ratio, the Golden Section or the Greek letter Phi. The Fibonacci sequence even plays a role in the subtle spirals you can see in the seed head of a sunflower. Bananas have three sections whilst apples have five. If you cut into a piece of fruit, you’re likely to find a Fibonacci number there as well, in how the sections of seeds are arranged. No wonder rare four leaf clovers are seen as lucky! That is of course, until a petal falls off. Irises have three petals whereas wild roses and buttercups have five petals. Most flowers, for example, will have a number of petals which correspond with the Fibonacci sequence.

The mathematical sequence that governs natureįor starters, Fibonacci numbers can be found in the natural world all around us.

Fibonacci sequence in nature handout pdf