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Square root of two has an exciting and some would say, history.

Like with every crime, and it seems that the crime has been committed in the name of , it is good to start from the beginning.

Pythagoreans believed that the whole universe is based on numbers. However they also knew about the Pythagoras' theorem (no wonder). So one day, they sat in front of their great school, drawing Pythagorean triangles in the sand with a stick, when one of them thought this: what if you choose a triangle whose two sides are equal to 1?

This is how their diagram probably looked:

Then you get, according to the theorem,

And you also get

Then they thought about this number for a while - and tried to get to the end of it, but the wouldn't have it! The decimals were not invented for some centuries later so what do you think confused the Pythagoreans? It was something to do with the irrational numbers...

Eventually Euclid, some centuries later, proved that the is an irrational number!

According to a legend, this number, and its irrationality, became a terrible secret of the Pythagoreans. If all the world was built upon the numbers what happened if they could not be described by other numbers? Unfortunately, so the legend goes on, one of the Pythagoreans at just about that time wanted to split from the group and start his own school of geometry. And he did... but he also told people about the terrible secret of the Pythagoreans. His name was Hippasus - but not for long... Soon after he divulged the great secret of the sect, Hippasus had an accident and drowned at sea. The purpose of the story being - nothing apart from you learning about the irrational numbers and knowing one of the oldest legends in mathematics!

 

 
   

Find more about Pythagoras and Pythagoreans.

There are some other famous numbers to be seen on these pages...

See more about Greek geometry.

 

 

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