*Thanks to Pythagoras, we know that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides. Trouble is, he also discovered that if those sides are each one unit long, the length of the hypotenuse cannot be expressed by whole numbers, not even in the form of a fraction, however complicated. What’s more, its decimal value doesn’t include recurring sequences, and doesn’t ever terminate. That’s because the square root of two is an *irrational* number.*

1.41421356237309504880168872420969807 856967187537694807317667973799...

You can’t write down my value

However hard you try,

Or convert me to a fraction –

I’m *irrational*, that’s why.

*In 2023, my ex-college friend from the 1960’s, Peter Wooding, felt it should be rebuked for such bragging (Note: ‘ab’ = by, with or from; ‘surd’ = an irrational root):*

(It really is a nonsense:

To put it in a word,

A never-ending sequence?

I think that word’s ‘ab-surd’.)