University of Leicester Botanic Garden
Fibonacci Pavements
The Friends of the University of Leicester Botanic Garden are celebrating the 25th anniversary of
their founding this year. To commemorate the anniversary, two new pavements have been
constructed in the Botanic Garden. They are based on the Fibonacci series, a set of numbers named
after a 12th century Italian mathematician who discovered them while considering how rabbit
populations might increase in number. Fibonacci (ca1170-1250, from Pisa) played an important role
in reviving ancient mathematics and his book, Liber abaci, introduced the Hindu-Arabic placevalued decimal system and the use of Arabic numerals into Europe. He is most famous, however,
for his series which we get by starting with two 1s and then adding the last two numbers together to
make the next. So we have ...
1
1
2
3
5
8
13
21
... and so on
This may seem to have little to do with plants and botanic gardens, but actually this series is the
basis for various spiral patterns that are common in nature and in plants in particular. Plants show
Fibonacci spirals, e.g. in the arrangement of leaves around a stem and of flowers in a flower head
and of scales on a pine cone. The spiral arrangement represents a very efficient way of packing
individual growing points (meristems) into the small area of a shoot tip. With leaves, it also means
that successive leaves do not hide the ones below to any great extent, thus allowing them to capture
light more efficiently.
In addition, if you divide one number by the next you get an answer that approximates to 0.618…
This is the Golden Ratio, a proportion widespread in nature, from the dimensions of the DNA
molecule itself, to the relative sizes of various parts of the human body. The ratio also frequently
appears in works of art, architecture, music and even the dimensions of credit cards and chocolate
bars!
The two pavements in the Botanic Garden represent a snail shell and a pine cone. In addition there
is a small hopscotch pavement, engraved in the stones of which are the first twelve Fibonacci
numbers. The pavements will form an important component of the mathematics activity offered to
schools by the Garden’s education programme.
UNVEILING CEREMONY 28th JULY
The pavements will be unveiled by the Vice-Chancellor on Thursday, 28th July at 6 for 6.30pm.
Contact: Dr Richard Gornall (Director of the Botanic Garden) 0116-252-3394 or 0116-271-2933 or
email him at:- [email protected]
Explanation of spirals
Starting with a square of side 1 we
then add the other Fibonacci
numbers in the sequence as squares
moving in a clockwise direction.
Each new square has a side which
is equal to the sum of the sides of
the previous two squares. The spiral
is obtained by drawing in each
square a quarter circle using the
side of the square as radius. This
sounds complicated but the
illustration to the right should help.
For more information about Fibonacci and his numbers, see:
http://www.mcs.surrey.ac.uk/Personal/R.Knott
The nature of the leaf arrangement in plants is called phyllotaxis. Starting with one leaf, try
counting the number of times you go around the stem before reaching a leaf directly above the one
you started with. Both the number of turns and the number of leaves encountered on the way are
Fibonacci numbers. For example, on an oak you will make two turns and meet five leaves.
If you divide any number in the series by the preceding number the result will be closer and closer
to 1.61804 as the numbers increase in value. This number is called the Golden Ratio and is
important in music, art and architecture.