How to double a cube?

We continue reading the Russian adventurous math books by  Vladimir Levshin (1904-1984) – see an older post about it – and Simon is often excited about the challenges discussed. This time however, he first thought that something was impossible (and the Russian book said that, too), but our amazing favourite Murderous Math thought otherwise! It was one of the three oldest “unresolved” problems in the world, about how to double a cube (and let it remain a cube), which basically boils down to “how to draw the cube root of 2”:

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Some more unrelated notes that Simon made recently, while listening to the Russian adventurous math book:

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