C.C. MacDuffee Award

2001 – Clayton W. Dodge

On August 4, 2001, at the annual meeting of Pi Mu Epsilon in Madison, Wisconsin, the C. C. MacDuffee Award for Distinguished Service was presented to Clayton W. Dodge, Professor Emeritus of Mathematics at the University of Maine. The location of this presentation was of historic significance, because Cyrus C. MacDuffee, seventh president of Pi Mu Epsilon, was Professor at the University of Wisconsin. The award, established in 1966, honors the memory of this superb teacher and algebraist, whose dedication and service profoundly influenced our society. Previous award recipients are J. Sutherland Frame, Richard V. Andree, John S. Gold, Francis Regan, J. C. Eaves, Houston Karnes, Richard Good, Milton D. Cox, and Eileen L. Poiani.

Professor Clayton Dodge was an active student at Miss Blakeslee’s Kindergarten in Malden, Massachusetts, and his later education was “all downhill from there.” In 1949, he graduated from Browne and Nichols School in Cambridge, Massachusetts, spent a semester at Harvard and eventually graduated from the University of Maine in 1956, majoring in mathematics with minors in electrical engineering and psychology.

He labored to teach arithmetic, algebra, and science for a whole six months at Brecksville Junior-Senior High School in Ohio and joyfully returned to teach at the University of Maine as an instructor of mathematics. In 1960 he received a master’s degree in mathematics under Howard Eves, who inspired him to work in geometry and problems. He did graduate work in mathematics at Brown University in 1960-1961.

For two years in the early 1960’s, he assisted Howard Eves in editing the Elementary Problems Department of the American Mathematical Monthly. Later, he served on the University of Maine Problems Group for the seven years that it edited that department. In 1981 he assumed the editorship of the Problem Department of the Pi Mu Epsilon Journal.

With the current issue, Clayton Dodge has completed a remarkable 20 years as Problems Editor of this Journal. Starting with problem #462, (Spring 1980, Volume7 No2) problem proposals were sent to Clayton Dodge, while Leon Bankoff was still problems editor. Transition from Leon Bankoff to Clayton Dodge took place over the period of a year. With the spring 1982 issue his apprenticeship had ended. All problem proposals and solutions were received, handled with care, formulated, polished, checked and corrected by Clayton Dodge, until problem #1006, which was the last problem whose solution was to be sent to the by now so familiar address. The Fall 2000 issue was the start of a new transition. More than half of all the problems published thus far in this Journal have gone through the hands of Clayton Dodge.

He has written five published textbooks, two others that were duplicated for use in his classes and has written several articles primarily on pedagogy, geometry, and calculators. A strong advocate of the use of calculators and computers by students, he wrote text material and taught several courses in their use, emphasizing the understanding of their workings so as to maximize their usefulness and make their results meaningful, see for example [1]. When color came to computers, because there was a great lack of appropriate software, he wrote software for graphing functinos in both 2 and 3 dimensions, for demonstrating basic concepts of the calculus, and for grade books, software that gained wide acceptance during the DOS years.

Since retirement he has helped build houses for the local chapter of Habitat for Humanity and he serves on its board of directors. He sings in a choir and an oratorio society, and he has taken up the sport of scuba diving in warm tropical waters. He dabbles in stained glass and enjoys working around the house.

For a mathematical project, he is editing notes for a book on the arbelos, writeen by the late Victor Thebault of France and the late Leon Bankoff of Los Angelos, for 60 years a practicing dentist and PMEJ problems editor from 1968 to 1981. The arbelos is the figure formed as follows. Draw two mutually tangent circles, external to one another and not necessarily the same size. Surround these circles by another cricle just tangent to them both. These circles all share a common diatmetral line. Cut the figure along this line and throw away one half, including the line. The figure that remains, looking like a bent two-tined fork, is the arbelos, also known as the shoemaker’s knife. It may also be described as a triangle whose sides are semicircles and whose angles are all zero degrees.

We hope that after the transition to the new problems editors is complete, Clayton Dodge will quickly complete his arbelos task, the impatient reader may enjoy a preview in [2].


[1] Clayton W. Dodge, Square roots and calculators, PME Journal, Vol. 11, No. 2, pp 69-74, 2000.

[2] Clayton W. Dodge, Thomas Shoch, Peter Y. Woo, Paul Yiu, Those ubiquitous Archimedian circles, Mathematics Magazine, 72, No. 3, pp 202-213, 1999.