**Drawing the Cube Root of 2 with Plato – TOM ROCKS MATHS**
https://tomrocksmaths.com/2022/05/17/drawing-the-cube-root-of-2-with-plato/

May 17, 2022 · To demonstrate the ratio PBPA (as shown in the diagram below) is the cube root of 2, we first assume PA to be of unit length 1 and call the length PB = x. Our task is then to show x = 2 1/3. Let AR = k, then PR = CR = 1 + x – k (since the total length of one side is 1 + x). In triangle APR, Pythagoras’ Theorem tells us PR 2 = AR 2 + AP 2.

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