Root 2, You're Being Irrational!

The Discovery

The Pythagorean number system was based on only whole numbers and fractions of whole numbers, called rational numbers. So, when Hippasus geometrically proved (see geometric proof animation) that root 2 couldn’t be written as a fraction of whole numbers (that it was irrational), there was a great uproar. You can learn about the algebraic proof here.

Outrage

Pythagoras couldn’t accept the existence of irrational numbers, because he believed in the absoluteness of numbers. There is speculation that Pythagoras was so upset that he sentenced Hippasus to death by drowning. Another possibility is that the Pythagoreans while sailing were so outraged that they tossed him overboard.

A Revolution

Although they make for good stories, there is no reliable evidence to support that either of these events actually happened. What we do know is that Root 2 is the first known irrational number. It redefined and expanded what math could do and what it could be.