Classroom Note: Finding the Center of a Circular Starting Line in an Ancient Greek Stadium

Two methods for finding the center and radius of a circular starting line of a racetrack in an ancient Greek stadium are presented and compared. The first is a method employed by the archaeologists who surveyed the starting line and the second is a least-squares method leading to a maximum-likelihood circle. We show that the first method yields a circle whose radius is somewhat longer than the radius determined by the least-squares method and propose reasons for this difference. A knowledge of the center and radius of the starting line is useful for determining units of length and angle used by the ancient Greeks, in addition to providing information on how ancient racetracks were laid out.