Areas of Work

Schultz, David, and Serpone, Enrico. Mathematics Teacher, March 2018, 385 - 389 - Delving Deeper: Sangaku Optimization Problems: An Algebraic Approach

During the Edo Period (1603 – 1867), Japan was isolated from the influence of western mathematics.  

Despite this isolation, Japanese mathematics, called Wasan, flourished and a unique approach to present mathematical problems was developed.  

Painted wooden tablets called sangaku were hung on display at Shinto Shrines and Buddhist temples.  Over 900 tablets have been discovered with problems developed from priests, samurai, farmers, and children.  The vast majority of these problems were solved using analytic geometry and algebraic means and the collection as a whole is frequently referred to as Japanese Temple Geometry.  

Within the collection of the sangaku, several optimization problems appear whose answers are included. However, the methods used to obtain those answers are absent. Since the work of Newton and Leibniz was unknown to the Japanese mathematicians of that time, and there is no evidence of the Japanese mathematicians having a formal definition of the derivative, their solution technique(s) to these problems remains unresolved (Fukagawa and Rothman 2008).  

To illustrate a possible non-calculus approach of solution to sangaku optimization problems, we examined two specific examples taken from Shinto Shrines.

Hodgson, Theodore, and Schultz, David. Mathematics Teacher, May 2015, 710 - 15 - Delving Deeper: A Refreshingly Rational Approach to the Center of Mass

The connection between physics and elementary algebra is often absent from most algebra textbooks.

In order to provide students with a real-world example that illustrates that connection, we developed an activity which modeled the center-of-mass point for a draining soda can.

The example provided both mathematics and physics teachers a nice way to connect rational functions to center-of-mass properties utilizing an object familiar to students.