How
maths influences nature and the representation of beauty
Nature
is beautiful, so many different, unique shapes and patterns.
Such irregular dimensions and variations appear too random to
have any mathematical connection.
Professor
Ian Stewart our mathematical expert says this isn't the case.
The appearance of beauty in nature is strongly influenced by
numbers and our perceptions of beauty are connected to mathematics
too.
Look
carefully and you will notice the seeds are arranged in spiral
patterns. Count
the number of seeds in each spiral and you produce numbers such
as 55 in one direction and 89 in the other direction, or 34
in one direction and 55 in the other. These pairs of number
are known as Fibonacci numbers. Professor
Ian Stewart
explains that these numbers correspond very closely with growth
and design in plants.
"Those numbers are clues to the dynamic process, which is
the way the plant grows" .
All
of the different plants grow in a similar pattern. New parts
of the plant are arranged at the tip of a shoot in a spiral
pattern. If you do the maths on the spiral pattern Fibonacci
numbers fall out.
Nature's
pattern book
How
do you explain the patterns on Angelfish, Tigers or Zebras?
Professor
Ian Stewart suggests that with all the different patterns
that can be found in the animal kingdom there is a kind of hidden
unity.
"It's as if there is a kind of universal pattern book
with a particular kind of mathematical system that generates
all the patterns in the book"
Theory
suggests that the stripes in animals such as Zebras or Tigers
are created by waves of chemicals diffusing through the tissues
of the animals at a very early stage in their development. The
patterns for the adult are pretty much laid down in the embryo.
"If
you study the mathematics of these waves you get the same kind
of patterns of waves. If you look at waves on the ocean they
arrange themselves in parallel rows just like the stripes on
a tiger and mathematically there is a unity in all of these
things."
Pretty
is what changes
What
is it about flowers that we perceive as beautiful?
Ian
Stewart
suggests that evolution may have played a role in our perception
of beauty. People are sensitive to changes in a pattern, we
are intrigued by patterns that don't quite work.
"If
you are going to woo your lady friend you should not give her
absolutely perfect flowers you should give her flowers with
a little bit of character."
The
maths of art
A world without perspective
As
we've grown up in a world where perspective is given, it seems
very odd that someone had to conceive how to portray it.
Tom
Korner
tells us that before the Renaissance there was no perspective
in paintings. People knew that things looked different. In older
paintings things in the distance looked smaller but there was
no consistency.
It was a young Florentine called Brunelleschi who constructed
a painting with a pinhole in it where you held a mirror on
the other side, and viewed through the pinhole, the reflection.
"For
people of that time it was like virtual reality, it was extraordinary,
something that was talked about and talked about"
What
he had done was remarkably simple. You imagine the eye connected
by straight threads to each object and then the painting is
just a plane, a piece of glass cutting those threads and where
each thread passes through the plane you put a spot of paint.
"Leonardo
Da Vinci thought you could not be an artist without being a
mathematician"
The
world's favourite painting
Are
there common elements in paintings that people are attracted
to?
According
to Ian Stewart
worldwide with the exception of the Dutch everybody likes a
landscape with some water and some mountains in the background,
a few trees and a few animals. The belief is that this goes
back to when we lived on the Savannahs and this sort of landscape
was a safe place to be.
