Can you identify the mathematicians?
First or two articles about Fibonacci, written for students.
Second of two articles about Fibonacci, written for students.
Published February 2011.
The idea of representing places and spaces is very important in
mathematics. It is important to us all if we don't want to keep
losing things - especially ourselves as we move from one place to
another. Many famous mathematicians have spent time working on
problems that involve moving and mapping things. Some of them have
come up with ideas that have helped us find our way around the
world, others have designed intriguing puzzles based on moving
Descartes was one of those people. Descartes was a French
mathematician, philosopher, and anatomist who lived from 1596 to
1650. He contributed to many modern ideas, mainly those associated
with science and the scientific method. He developed a design for
an improved telescope and mapped the pathway of nerves from the eye
to the optical centre in the brain and traced the path of pain
receptors from limbs to the brain.
One of the things that Rene Descartes is most famous for is
The Cartesian Coordinate
System that is named after him. It is interesting how Descartes
came to develop Cartesian coordinates. He was lying on his bed
watching a fly!
Slowly, it came to him that he would be able to accurately
describe the fly's position at any time by just three numbers. He
had to use three numbers because the room was three-dimensional.
The three numbers would describe the fly's position in relation to
where it was to the floor and two adjacent walls. Today this is
known as the x,y,z
coordinate system. Most modern cities are laid out in Cartesian
fashion, tell a stranger to go three blocks down the Main Street
and then turn right on Jackson Avenue and go along 10 blocks and
you are actually using Cartesian coordinates. If you have been lost
in an old town, or even in new developments, you will understand
how useful The Cartesian Coordinate System is. The system is used
by the military and rescue services as well as air traffic
controllers and map makers to accurately describe where to find
people and places.
As a mathematician Descartes was credited with developing the
system that still serves as the foundation for graphing some 350
years after his death.
If you ever play `battleships' then you are using cartesian
coordinates. To set up the grid people often use a system of
letters and numbers. This way you can describe a particular point
on the grid. For instance X here is at (C,2). To make sure people
communicate information in the same way, we have a system for
giving the location of a point. We give the horizonal information
first followed by the vertical. You will find a grid like this as
the board in
the Criss Cross Quiz game .
This is also the same system used for constructing graphs. Rene
Descartes' coordinates are the foundation for graphing. Most graphs
use a grid with only numbers to show positions. In the lower left
corner is a point called the origin, this is the beginning of the
graph and it is at the point located at (0,0). The bottom line of
the graph and the line at the left hand side of the graph are known
as the x and y axes (plural of axis). The x axis runs horizontally,
the y axis vertically, and locations within the graph are described
using (x,y) pairs. It's easy to remember the order that you name
the points because x comes before y in the alaphabet. Other graphs
show specific information along the x and y axes depending on what
the graph is trying to convey.
More than 350 years after his death, Rene Descartes' system of
describing the position or location of things is still very
important in many different ways.
Another mathematician who was interested in problems concerning
motion and maps was Leonard
Euler who lived in the 1700's in Switerland and then later
in Russia. He is remembered today for his work in a new branch of
Topologists are mathematicians who study problems and puzzles
about geometrical structures. Topology sometimes gets called
'rubber sheet geometry' - because topologists study the properties
of shapes that stay the same when the shapes are stretched or
They don't ask questions such as, How big is it? They are much
more interested in answering unusual questions like; Are there any
holes in it? Are all the parts connected together? Can the whole
thing be separated into smaller parts? One example of what
topologists might be interested in is a network - like a network of
train lines that cross each other and have certain points where the
lines come together and then separate. If you made a plan of a rail
network on a rubber sheet and stretched it or squashed it up, while
the map might look funny, it does not change the plan of the
So, if topologists were using the map of the London Underground
network they wouldn't be investigating how far it is from Kings
Cross to Paddington, or even the direction you are travelling in.
They would probably be looking to see if the underground lines
connect up and how many different ways you can travel to the same
station without passing through the same place twice.
Euler worked on and created problems about networks. He designed
a very famous problem based on a town, a river and a network of
bridges. You can read about it