A Modern Solution to the Gion Shrine Problem. Issue 2 (15th March 2019)

• Record Type: Journal Article
• Authors: Arias de Reyna, J.; Clark, David; Elkies, Noam D.
• Is Part Of: Mathematics magazine. Volume 92:Issue 2(2019)
• Page Start: 110
• Page End: 122
• Publication Date: 2019-03-15
• Subjects: Primary 01A27 -- Secondary 51M04 -- 11D41; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/0025570X.2019.1557007
• Languages: English
• ISSNs: 0025-570X

Abstract

Summary: We give a new solution to the famous Gion shrine geometry problem from eighteenth-century Japan. Like the classical Japanese solution, ours is given in the form of a degree-ten equation. However, our polynomial has the advantage of being much easier to write down. We also provide some additional analysis, including a discussion of existence and uniqueness. Finally, we prove that the Gion shrine problem has no rational solutions.