Paper sizes maths stuff

So something new I learnt today. The ratio of the long side to the short side of an ISO A[0-9] sheet of paper is \sqrt{2}. Why this is news to me I don’t know as it should be pretty obvious. Since the relationship from size A(n) to size A(n+1) is that the longest side is halved, and keeping the ratio of the long/short sides the same:

 \dfrac{x}{y}=\dfrac{y}{\frac{x}{2}}\\ \dfrac{x}{y}=\dfrac{2y}{x}\\ x^2=2y^2\\ \dfrac{x^2}{y^2}=2\\ \dfrac{x}{y}=\sqrt{2}

Well it’s a nice distraction from all the M208 group theory stuff I’m working through.

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