Can You Double a Cube?
Build a new cube with exactly twice the volume of the first. Easy?
The Challenge
If the original cube has side 1, its volume is 1. A side of 2 does not work — that makes the volume 8.
The required side is the cube root of 2.
The Delian Problem
Ancient tradition linked this puzzle to Delos, where a cubical altar was supposedly to be doubled. The problem became famous as the Doubling of the Cube.
Archytas’ Solution
Archytas of Tarentum devised an extraordinary geometric solution using the intersection of three three-dimensional surfaces — an early triumph of spatial geometry.
Why It Mattered
With only an unmarked straightedge and compass, the exact construction is impossible. Trying to solve the problem pushed Greek mathematics beyond ordinary plane geometry.
History or Legend?
The Delos-and-oracle story comes from later sources and survives in several versions. The mathematical problem itself was very real.
From Voices of the Past: Origins
Some problems matter because solving them forces us to invent new mathematics.