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A4 Paper Puzzle

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I found this neat puzzle in a YouTube video from the brilliant Matt Parker, who does maths standup, and has posted countless highly entertaining and instructive videos. I recommend them to anyone who enjoys recreational mathematics.

Here's the puzzle. We take a sheet of A4 paper, whose sides you can assume have lengths 1 and square root 2. We fold down the top left-hand corner, then fold down the top right-hand corner. What is the length of the red perimeter?

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SXR103 chemistry is fun (2008) :-)

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