What do the Pyramids, the Mona Lisa, a daisy, The Milky Way, Beethoven's Fifth Symphony and Game Boy Advanced have in common?

The Fibonacci sequence and the corresponding golden ratio are found widely in nature, as well as in art. The golden ratio has been famed throughout history for its aesthetic properties and it is claimed that the architecture of Ancient Greece was strongly influenced by its use.

Who was Fibonacci?

The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa (Italy), the city with the famous Leaning Tower, about 1175 AD. He was one of the first people to introduce the Hindu-Arabic number system into Europe - the positional system we use today - based on ten digits with its decimal point and a symbol for zero: 1 2 3 4 5 6 7 8 9 . and 0 His book on how to do arithmetic in the decimal system, called Liber abbaci (meaning Book of the Abacus or Book of Calculating) completed in 1202 persuaded many European mathematicians of his day to use this "new" system.

What is the Fibonacci Sequence?

In Fibonacci's book he introduces a problem for his readers to use to practice their arithmetic:-

a pair of rabbits are put in a field and, if rabbits take a month to become mature and then produce a new pair every month after that, how many pairs will there be in twelve months time?

He assumes the rabbits do not escape and none die. The answer involves the series of numbers: 1, 1, 2, 3, 5, 8, 13, 21, ...
but it was the French mathematician Edouard Lucas (1842-1891) who gave the name Fibonacci numbers to this series and found many other important applications of them.

The following three essays written by Year 11 students from St Peters Lutheran College, Indooroopilly, explore Fibonacci sequences and the golden ratio.
Eric Lee, Year 11, 2002
Geoff Martin, Year 11, 2001
Neil Kim, Year 11, 2002