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An Elegant New(ish) Proof

Tom Apostol’s square root of 2 proof is beautiful

This proof was published in 2000 by Tom Apostol. It just might become your new favourite proof that the square root of 2 is irrational. Here’s how it goes.

Figure 1

You have a right isosceles triangle, ABC (Fig. 1). Suppose sides AC and BC have integer length. Their ratio will be the square root of 2. Suppose further…




Maths is like finger-painting. Messy and beautiful.

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Adam Hrankowski, ADHD

Adam Hrankowski, ADHD

Canadian math guy, experimenting with fiction. Find my new scifi/fantasy serial here:

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