Date on Honors Thesis



Mathematics / Applied Math

Examining Committee Member

Dr. Elizabeth A. Donovan, Advisor

Examining Committee Member

Dr. Robert Donnelly, Committee Member

Examining Committee Member

Dr. Mary Williams, Committee Member


When the country of Japan was closed from the rest of the world from 1603 until
1867 during the Edo period, the field of mathematics developed in a different way
from how it developed in the rest of the world. One way we see this development
is through the sangaku, the thousands of geometric problems hung in various Shinto and Buddhist temples throughout the country. Written on wooden tablets by people from numerous walks of life, all these problems hold true within Euclidean geometry. During the 1800s, while Japan was still closed, non-Euclidean geometries began to develop across the globe, so the isolated nation was entirely unaware of these new systems. Thus, we will explore the sangaku in two of the other well-known systems, namely the neutral and hyperbolic geometric systems. Specifically, we will highlight how these traditionally-solved problems change under the varying definitions of line parallelism.