117. Irrational Numbers


Followers of the Greek mathematician Pythagoras held numbers in great reverence and awe. Their chief belief was that “Integers” or the “whole numbers” held the secret of the Universe, concealed in them.

According to them any number can be expressed as a whole number or a ratio of two whole numbers. The numbers less than one, can be put as 49/50 or 91/100 etc. So they were duly shocked, when a strange type of number, which they named as “irrational number”, was discovered.

The length of the diagonal of a square, with unit length as its side, is given as the square root of 2, by Pythagoras Theorem. Try as they might, Pythagoreans could not put it as a ratio of two numbers, completely.

Depending on the accuracy of calculations, the value of the square root of 2 was 14/10 or 141/100 or 1414/1000 etc. It could never be completely revealed as the ratio of two whole numbers.

The same is true of many numbers. Perfect squares like 1, 4, 9, and 16 have their square roots as 1, 2, 3, 4 etc. But all the numbers lying in between these perfect squares, like 2,3,5,6,7,8, 10,11,12,13,14,15 have non-ending square roots, which are irrational numbers.

Pythagoreans were forbidden to reveal this startling discovery, under the pain of death. New and revolutionary discoveries have never been accepted or acclaimed easily.

Whether or not we want to have them, the irrational numbers do exist and we have learnt to live with them.

Visalakshi Ramani

16 Responses to 117. Irrational Numbers

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