Females usually end up as worker bees but someĪre fed with a special substance called royal jelly which makes them Males are produced by the queen's unfertilised eggs, so male bees only have a mother but no father.Īll the females are produced when the queen has mated with a male and The male bees do no work and are called drone bees. The other females are worker bees who, unlike the queen bee, produce no eggs. In a colony of honeybees there is one special female called the queen. The rabbit problem is obviously very contrived, but the Fibonacci sequence does occur in real populations. Following this through you'll find that after 12 months (or 1 year), there will be 233 pairs of rabbits. Which is simply the rule for generating the Fibonacci numbers: add the last two to get the next. But new pairs are only born to pairs at least 1 month old, so there will be new pairs. The number of pairs in month will be (in this problem, rabbits never die) plus the number of new pairs born. Now imagine that there are pairs of rabbits after months. Yet another new pair, the female born two months ago produced her At the end of the fourth month, the original female has produced.

At the end of the third month, the original female produces a second pair, making 3 pairs in all.

At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits.

At the end of the first month, they mate, but there is still only 1 pair.

How many pairs will there be in one year? Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose a newly-born pair of rabbits, one male, one female, are put in a field. One of the mathematical problems Fibonacci investigated in Liber Abaci was about how fast rabbits could breed in ideal circumstances. However, Fibonacci is better remembered forĪ certain sequence of numbers that appeared as an example in LiberĪ page of Fibonacci's Liber Abaci from the Biblioteca Nazionale di Firenze showing the Fibonacci sequence (in the box on the right).' The problem with rabbits The impact of Fibonacci's book as theīeginning of the spread of decimal numbers was his greatest Mathematical calculations could be done with this new number systemĬompared to the unwieldy Roman numerals. Fibonacci wrote Liber Abaci for these merchants, filled with practical problems and worked examples demonstrating how simply commercial and Merchants had to convert from one to another whenever they traded between these systems. Italy at the time was made up of small independent towns and regions and this led to use of many kinds of weights and money systems. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated.' 'These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. His travels to write Liber Abaci (published in 1202) in which he introduced the Latin-speaking world to the decimal number system. In 1200 he returned to Pisa and used the knowledge he had gained on On business trips to Egypt, Syria, Greece, Sicily and Provence. Moors and travelled widely in Barbary (Algeria), and was later sent Of Bonaccio' – as his surname, and Fibonacci was born.įibonacci (as we'll carry on calling him) spent his childhood in NorthĪfrica where his father was a customs officer.

Misinterpreted part of the title – 'filius Bonacci' meaning 'son (as it was published before printing was invented), they Scholars were studying the hand written copies of Liber Abaci His father was a merchant called Guglielmo Bonaccio and it's because of his father's name that Leonardo Pisano became known as Fibonacci. Leonardo Pisano was born late in the twelfth century in Pisa, Italy: Pisano in Italian indicated that he was from Pisa, in the same way Mancunian indicates that I am from Manchester.

Nature fibonacci sequence