 Archytas was the first person to arrive at a solution to one of the most famous mathematical puzzles in antiquity, the duplication of the cube. The most romantic version of the story, which occurs in many variations and ultimately goes back to Eratosthenes (3rd c. BC), reports that the inhabitants of the Greek island of Delos were beset by a plague and, when they consulted an oracle for advice, were told that, if they doubled the size of a certain altar, which had the form of a cube, the plague would stop (Eutocius, in Archim. sphaer. et cyl. II [III 88.3–96.27 Heiberg/Stamatis]). The simple-minded response to the oracle, which is actually assigned to the Delians in some versions, is to build a second altar identical to the first one and set it on top of the first (Philoponus, In Anal. post., CAG XIII.3, 102.12–22). The resulting altar does indeed have a volume twice that of the first altar, but it is no longer a cube. The next simple-minded response is to assume that, since we want an altar that is double in volume, while still remaining a cube, we should build the new altar with a side that is double the length of the side of the original altar. This approach fails as well. Doubling the side of the altar produces a new altar that is not twice the volume of the original altar but eight times the volume. If the original altar had a side of two, then its volume would be 23 or 8, while an altar built on a side twice as long will have a volume of 43 or 64. What then is the length of the side which will produce a cube with twice the volume of the original cube? The Delians were at a loss and presented their problem to Plato in the Academy. Plato then posed the “Delian Problem,” as it came to be known, to mathematicians associated with the Academy, and no less than three solutions were devised, those of Eudoxus, Menaechmus, and Archytas.