Golden ratio

:This article is about the mathematical ratio. For the Aristotelian concept of "golden mean" see Nicomachean Ethics.

A startlingly quick proof of irrationality

The relation

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:rac{a}{b} = rac{b}{a-b}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

gives a startlingly quick proof that this number is irrational: If a/b is a fraction in lowest terms, then b/(a − b) is in even lower terms — a contradiction.

Related Topics:
Irrational - Lowest terms

~ ~ ~ ~ ~ ~ ~ ~ ~ ~