A Mathematical Model of Archimedes’ Cattle Problem

Daniel D. FRIESEN
Mike C. PATTERSON
Bob HARMEL
John MARTINEZ

Keywords

Archimedes, Cattle problem, Optimization, Math History

Abstract

This paper sheds light on the complex interrelationships between history and mathematical developments by examining Archimedes' Cattle Problem. With modern computing capacities, what seemed like an almost impossible computational problem in Archimedes day is no longer such a seemingly intractable problem. This paper demonstrates the formulation of Archimedes’ Cattle Problem through an Excel spreadsheet utilizing an Excel add-in optimizing tool. After providing the solution to Archimedes' Cattle Problem, the paper then argues that intractable mathematical solutions of bygone eras become facilitated over time by the use of new instruments. The paper concludes by noting that in certain cases it is difficult to separate the virtues of the instrument from those of the observer. Had modern computing capacity been available in Archimedes day, the solution to his cattle problem would have been readily at hand.