Discovery: The Delian Problem

Around 430 BCE it is reported that a typhoid epidemic carried off about a quarter of the population of Athens in ancient Greece. When the gods were asked what could be done to halt this raging epidemic, they apparently replied that the altar in the Temple of Apollo in Delios would have to be doubled in size. After several attempts to double the size of the cube-shaped altar including placing an identical cube alongside it (causing the altar to lose its cube shape) and building a cubic altar with its edges double the length of the original edges (increasing the volume by a factor of eight), the gods were still not happy. If the length of an edge of the old altar was one unit, then the length of the edge of the new altar would have to be the cube root of 2 units; hence, the mathematicians were called in. In this Discovery article, the author presents the Delian Problem and suggests teachers ask their students to solve the problem using logic rather than calculators.