How come that pi (π) extends its decimal numbers infinitely?

Question

Is there any explanation behind this?

In: Mathematics

Answer 1

Unfortunately there isn’t a “simple” proof that pi is irrational (ie it has infinite non-repeating decimals), in fact it’s such a hard problem that despite pi being studied since ancient Greece we only proved it was irrational in 1760.

A lot of the proofs involve sin and cos (remember your trigonometry class), which stop working properly if there was a way to write pi as a/b (ie if pi was a rational number).