### Schools Mathematics Grand Challenge

Did You Know ?

Some people take numbers very seriously indeed!

The square root of 2 is an example of an irrational number. This means that you cannot express it as a ratio of two whole numbers or a fraction. An equivalent way of saying this is that there exist no whole numbers a and b for which

a^2 = 2 x b^2.

Thus, it is impossible to find two whole numbers where the square of one of the m is two times the square of the other one.

In ancient Greece, there was a society known as the Pythagoreans who were followers of the philosopher Pythagoras. They believed that everything could be related to mathematics, and also had some strange practices and rules. For instance, it was forbidden to walk over a cross-bar or to eat beans! The Pythagorean school is credited with discovering the ratios behind the musical scale that we still use today, and also with discovering irrational numbers.

Legend has it that a member of the school named Hippasus discovered that the square root of two was irrational while on a boat. When he told his fellow Pythagoreans about this, they were not happy with his discovery as it went against some of their fundamental beliefs, so it is said that they threw poor Hippasus overboard!