The Gion Shrine Problem: A Solution in Geometry

Abstract: Eighteenth century Japan was a time of isolation and peace, where education and the arts blossomed. Originally posted before 1749 by an unknown author, the sangaku (mathematical tablet) that became known as the Gion Shrine problem, has puzzled people from all walks of life for more than two centuries. Although solutions have been suggested, some of them require mathematics not known in Japan at the time the Gion Shrine problem was written. The problem is still considered unsolved. Using the geometry of Edo Period Japan, the paper's solution is immersed in the culture of that time frame. As identified in this paper, the problem's author deeply understood both the challenge, and inherent beauty, presented by simplicity.