Mathematics and philology: An example from wasan

Abstract

Fukagawa and Rothman introduced a difficult wasan problem concerning an ellipse inscribed in a right triangle from an old travel diary. Like the famous Gion Shrine problem, it does not specify numerical data but asks only for an equation of a particular kind; moreover, modern solutions of the problem entail polynomial equations of degree greater than four. One may therefore wonder whether the problem was recorded correctly. A careful examination of the primary text suggests that problem may have been written in haste, and that the original problem may have been more tractable mathematically.