Ranging from kindergarten mathematics to the fringe of research
this informal article paints the big picture of number in a non
technical way suitable for primary teachers and older students.
Published November 2004,November 2004,December 2004,December 2011,February 2011.
It's a stormy day on the sea off the coast of Greece. The date
is around 520 BC. Fighting for his life, a man is heaved over the
side of a boat and dropped into the open water to die. His name is
Hippasus of Metapontum. His crime? Telling the world a mathematical
secret. The secret of the dangerous ratio.
The murder of Hippasus is a matter of legend, but the secret was
real, and certainly dangerous enough to the beliefs of those who
knew about it.
It was a secret owned by the school of Pythagoras. These early
Greek mathematicians (Pythagoras himself was born around 569 BC )
were obsessed with the significance of whole numbers and their
ratios. The Pythagorean's motto, carved above the entrance of the
school, was "All is number".
The inner circle of the school, the mathematikoi, believed that
the universe was built around the whole numbers. Each number from
one to ten was given a very special significance. Odd numbers were
thought to be male and even numbers female. Yet there was one
number that the Pythagoreans found terrifying, the number that
might have cost Hippasus his life for revealing its existence to
The name Pythagoras these days is best remembered for a
geometrical theorem, the one that tells us how to calculate the
lengths of the sides of a right angled triangle, and it is from
this theorem that the dangerous ratio emerges.
Imagine a simple square shape, each side 1 unit in length. How
long is the square's diagonal?