Trisecting angles and calculating cube roots was a big problem for Euclid and his cohorts. Discussed by Zsuzsanna Dancso at MSRI.
More links & stuff in full description below ↓↓↓

TRISECT WITH ORIGAMI:    • How to Trisect an Angle with Origami ...  
CIRCLE THE SQUARE:    • Squaring the Circle - Numberphile  
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