dupcubfin.mws Duplication of the Cube : Darrell Mattingly, Cateryn Kiernan Origin of the Problem Proof that NO Platoic Solution Exists for the "Delian" Problem "Non-Platoic" Solutions Rule and Collapsable Compass Solution Description Geometric Representation Archytas of Tarentum's Solution The most interesting and complex of the solutions to the "Delian" Problem is the solution developed by Archytas of Tarentum. His solution, however, lies in a geometric proof, contrary to what Plato felt Athenians should avoid. Archytas developed a solution using three geometric figures and their intersects. Archytas used a right cone, a cylinder, and a torus, all placed on the same coordinate system, and claimed that the intersection of these figures gave the length of the desired duplicated cube, 2^(1/3)*a;, where a; is the length of the side of the orginal cube. To illustrate his method to solve the "Delian" problem, we will first decide on the a;. For this illustration, a; is 1. Next, we need the three formulas, Archytas used. They are: Exercises