Partitioning Pythagorean Triangles Using Pythagorean Angles

Summary

Inside any Pythagorean right triangle, it is possible to find a point M so that drawing segments from M to each vertex of the triangle yields angles whose sines and cosines are all rational. This article describes an algorithm that generates an infinite number of such points.

Additional information

Notes on contributors

Carl Swenson

Carl Swenson ([email protected]) is an emeritus Professor of Mathematics at Seattle University. He is a co-author of two popular textbooks, Precalculus: Functions Modeling Change and Algebra: Form and Function. In addition, he writes training manuals for graphing calculators. He likes to hang out in a cabin on Bainbridge Island and read books by the fire. He also enjoys opera, Shakespeare, and gadgets.

André Yandl

André Yandl ([email protected]) is an emeritus Professor at Seattle University, where he taught from 1956 to 2011. He earned B.S., M.A., and Ph.D. degrees from the University of Washington. He has published six mathematics textbooks and several research articles, has served on C.U.P.M., and been a consultant at the Marathwada University, Aurangabad, India. His research was in the theory of proximate fixed points. Later in his career he worked on problems he could share with students and colleagues. His interests, outside of mathematics, are spending time with his family, speaking French, and playing table tennis. He coached the Saudi Arabian table tennis team in the summer of 1976.