## Fibonacci

Fibonacci’s real name was Leonardo Pisano Bogollo. He was born in Pisa, Italy, in 1170. History states that Fibonacci was his nickname which roughly translates as “Son of Bonacci”. His father was a merchant named Guglielmo Bonaccio.

He travelled widely and traded extensively.

Maths was incredibly important to those in the trading industry, and Fibonacci’s passion for numbers was cultivated in his youth. He spent his childhood in North Africa where he studied the Hindu-Arabic arithmetic system and learnt of decimal numbers.

## Liber Abaci

In 1200 he returned to Pisa and used the knowledge he had gained on his

travels to write *Liber Abaci* (published in 1202) which roughly translates as ‘book of calculations’. The book introduced Indian mathematics to the west and shared his knowledge of Arabic numerals which went on to replace the roman numeral system.

The first chapter of the book states:

–

Fibonacci

* *

## Problem with Rabbits

The book demonstrated how a decimal number system could make it easier

to complete calculations. In order to do this Fibonacci included number problems and showed how to solve them.

He posed the problem:

“If two newborn rabbits (one male and one female) are put in

a pen, how many rabbits will be in the pen after one year?”

The problem assumes that:

- A pair of rabbits always produce one male and one female offspring
- A pair of rabbits can reproduce once a month
- Rabbits can reproduce once they are a month old
- Rabbits don’t die within a year!

Using these assumptions, the result can be calculated using the following model:

The sequence of the number of pairs is what is known as the ‘Fibonacci sequence’. It consists of a series of numbers whereby each number is equal to the value of the two numbers before it.

Using this sequence, Fibonacci reached the conclusion that there would be 233 pairs of rabbits in the pen after one year!

## The Golden rectangle

The Fibonacci sequence can be used to create a range of number patterns. The golden rectangle is an example whereby a rectangle’s side lengths are successive Fibonacci numbers. The example below shows the side lengths 34 x 55. The rectangle can be divided into a series of squares which also have lengths that are successive Fibonacci numbers. When an ark is drawn from one corner of each square to the next, they join to form a perfect spiral.

Any two successive Fibonacci numbers have a ratio very close to the golden ratio, which is roughly 1.618034. As the numbers get larger in value, the ratio gets closer. The Golden Ratio is denoted by the Greek letter phi: **φ**.

The Golden Rectangle can be found in many Renaissance art works including the Mona Lisa!

## Fibonacci in Nature and Human Design

The Fibonacci sequence and Golden Rectangle appear surprisingly often both in nature and human designs. In nature, Fibonacci numbers manifest themselves in lots of places from the numbers of petals on a flower to the number of spirals in the seeds of a sunflower. The relationship between the Fibonacci sequence and the arrangement of things in nature is highly efficient as it allows flowers to pack in as many seeds as possible into a small space or branches to grow in such a way that allows leaves to receive equal amounts of sunlight.

Fibonacci numbers have been used in lots of architectural designs including Cornwall’s Eden Project. The building is an environmental and arts education centre, and is composed of geodesic domes that are made up of hexagonal and pentagonal cells. Designed by Jolyon Brewis, the core of the building is based on nature’s architecture and incorporates Fibonacci numbers and phyllotaxis (the arrangement of leaves) in its design. This approach is labelled as ‘Biomimicry’.

## Fibonacci Day

Fibonacci Day is celebrated on 23rd November every year, as it has the digits “1, 1, 2, 3” which are all Fibonacci numbers!

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**Sources:**

http://www-history.mcs.st-andrews.ac.uk/Biographies/Fibonacci.html

https://www.mathsisfun.com/numbers/fibonacci-sequence.html

https://plus.maths.org/content/life-and-numbers-fibonacci

http://www.livescience.com/37470-fibonacci-sequence.html

https://www.youtube.com/watch?v=SjSHVDfXHQ4&t=101s

https://www.youtube.com/watch?v=wTlw7fNcO-0

https://www.youtube.com/watch?v=koFsRrJgioA

http://geometricon.com/10-amazing-examples-of-architecture-inspired-by-mathematics/