Delian Problem

Diagram showing how Archytas solved the Delian problem, evidence of how advanced Pythagorean mathematics and geometry had become in little more than one century (after Pythagoras' death)

There can be no doubt that as a scholar Archytas lived by the great insight that set the pythagoreans apart from other ancient thinkers: that numbers and number relationships were the key to vast knowledge about the universe. Archytas was a rigorous mathematician who solved an infamous problem in Greek mathematics known as the Delian problem, or doubling a cube, that is, creating a new cube twice the volume of the first. Archytas' solution was sophisticated, requiring new geometry using three dimensions - "solid" geometry - and involving the idea of movement. ~ page 121 (The Music of Pythagoras)

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