Welcome to this page of essential maths' reading!  Here you will find a proof of the irrationality of the number pi.

The number pi is defined as the ratio of the circumference of any circle to its diameter.  Its value is approximately 3.14.  That it is irrational means that it cannot be expressed as the ratio of two integers and that in turn means that it cannot be expressed as a finite or repeating decimal; its expansion must be infinitely long with no repeating pattern.

To prove that pi is irrational.... read on!

We do it by assuming the contrary, ie that pi is rational, and then show that this leads to a contradiction