Hippasus of Metapontum, ca. 500 B.C., was a Greek philosopher. He was a disciple of Pythagoras. Hippasus is attributed the discovery of the existence of irrational numbers. More specifically, he is credited with the discovery that the square root of 2 is irrational.
It is believed that he proved the existence of irrational numbers at a time when the Pythagorean belief was that whole numbers and their ratios could describe anything that was geometric. Not only that, they didn’t believe there was a need for any other numbers.
Up until Hippasus’ discovery, the Pythagoreans preached that all numbers could be expressed as the ratio of integers. Despite the validity of his discovery, the Pythagoreans initially treated it as a kind of religious heresy and they either exiled or murdered Hippasus. Legend has it that the discovery was made at sea and that Hippasus’ fellow Pythagoreans threw him overboard.
The Pythagoreans were a strict society and all discoveries that happened had to be directly credited to them, not the individual responsible for the discovery. The Pythagoreans were very secretive. They all took oaths to ensure that their discoveries remained with the Pythagorean society. They considered whole numbers to be their rulers and that all quantities could be explained by whole numbers and their ratios. An event would happen that would change the very core of their beliefs. Along came Pythagorean Hippasus who discovered that the diagonal of a square whose side was one unit could not be expressed as a whole number or a ratio. Hence, the Pythagorean Theorem which crushed their original beliefs. Thus, they certainly didn’t want Hippasus’ discovery to be revealed and shatter their pride and core beliefs.
In mathematics, an irrational number is any real number that is not a rational number — that is, it is a number which cannot be expressed as a fraction m/n, where m and n are integers, with n not equal to zero. It can be deduced that they also cannot be represented as terminating or repeating decimals.
Pi is a famous irrational number. People have calculated Pi to over one million decimal places and still there is no pattern. 3.1415926535897932384626433832795 (and more …)
The number e (Euler’s Number) is another famous irrational number. People have also calculated e to lots of decimal places without any pattern showing. 2.7182818284590452353602874713527 (and more …)
The square root of 2, also known as Pythagoras’ constant (ironic huh), is 1.41421356237309504880168872420969807856967187537694807317667973799 (and more …)
