# Proof in a Poem

Inspired by Hannah Hoffman, here’s a poem proof of the irrationality of the square root of 2.

*Suppose that root 2 could be taken to beThe integer a over the integer bWhere a and b have no factor in commonSo nothing divides both the top and the bottom*

*Some algebra that’s quite easy to doGives a ^{2} is equal to b^{2} times 2But if a^{2} is even, so too must be aNow each a in a^{2} has a 2 in our play*

*So a ^{2} in fact has a factor of 4But since this equals 2b^{2} we can say moreThis b^{2} must now have a factor of 2And just as above we know b has one too*

*It appears that we are now able to sayThat 2 divides b and 2 divides aBut common factors were assumed to be noneSo this contradiction shows we are done*

Be sure to check out the excellent efforts of Timothy Gowers and Joel David Hamkins as well.

Here’s the original tweet.

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