Abstract
The ancient Greek astronomical calculator known as the Antikythera Mechanism has been analyzed using geometrical, calculus, trigonometric and complex variable methods. This analysis demonstrates that the Mechanism modeled the variations in the Moon’s angular velocity as seen from the Earth, to better than 1 part in 200. A major implication of this analysis is that the Antikythera Mechanism of the 2nd century BCE modeled the anomalistic motion of the Moon more accurately than Ptolemy’s account of Hipparchus’s theory of the 2nd century CE. In the present work, mathematics, astronomy, history and methodology of the sciences combine in the study of a unique artifact, preserved for posterity in an ancient ship that sank in the Mediterranean 2100 years ago and recovered by Greek sponge divers at the dawn of the 20th century.