The Unsolved Problem of Two Circles and a Square
Refreshments at 3:30 PM on the 2nd floor
In the early 1800s, mathematician Yamaguchi Kanzan traveled through Japan recording mathematical problems. The focus was on sangaku, which were tablets containing mathematics that were displayed in Buddhist temples and Shinto shrines. These tablets contained problems, and sometimes solutions, that ranged from simple to very difficult. Yamaguchi’s travel diaries lay mostly unnoticed until the 1980s, when large portions were translated into English, resulting in books and a Scientific American article about these “Japanese Temple” problems. Two of the problems presented were so difficult that they remained unsolved, despite being quite easy to state.
One of the problems was solved in 2018. This talk is about the other unsolved problem, and the work of David Krumm and myself on that problem. This year, we completed a proof that this remaining unsolved problem cannot be solved. In other words, there is no closed-form solution. The proof uses techniques ranging from basic geometry through calculus and advanced algebra, and is completed using computational tools in Galois theory that have only recently become available. The talk will be accessible to all students, with a particular focus on geometry plus a little bit of calculus, and then will touch upon the more advanced algebra underlying the completion of the proof.