## Mysteries of the equilateral triangle

In a new twist on the love triangle – Dr. Brian McCartin is in love WITH the triangle, the equilateral triangle to be specific. He has written of his love in a new book.

A process for wrapping chocolates, the detection of gravitational waves, cartography and voting theory are all related mathematically – through their “uncle” the equilateral triangle, according to Dr. Brian McCartin, professor of Applied Mathematics at Kettering University and author of the new book “Mysteries of the Equilateral Triangle (Hikari Ltd., 2010).

In his preface McCartin calls Mysteries of the Equilateral Triangle (or MOTET, an homage to his love of music), “my collection of equilateral triangular arcana.” The book is an examination of the history of the equilateral triangle from ancient Greece to the modern United States, including five religious traditions, and showing how it can be found in everything from art and alchemy to vegetables and television programs.

The book was written while McCartin was on sabbatical leave in 2010.

As a mathematician he, of course, explores the equilateral triangle’s mathematical properties, then looks at its place in Applied Mathematics where it is used in pursuits as diverse as electrocardiography and the wrapping of chocolates.

McCartin goes on to write about the equilateral triangle in Recreational Mathematics, Olympiad-caliber problems, providing biographical sketches of mathematicians and a look at the manifestation of the equilateral triangle in the world around us, both natural and man-made.

“Human beings . . . tend to take for granted some of their greatest discoveries (witness the wheel, fire, language, music . . . )” he writes. “In Mathematics, the once flourishing topic of Triangle Geometry has turned fallow and fallen out of vogue (although Phil Davis offers us hope that it may be resuscitated

by The Computer [70]). A regrettable casualty of this general decline in prominence has been the Equilateral Triangle,” he concludes.

“Yet,” he argues, “the facts remain that Mathematics resides at the very core of human civilization, Geometry lies at the structural heart of Mathematics and the Equilateral Triangle provides one of the marble pillars of Geometry.

Dr. Phil Davis, professor Emeritus of Applied Mathematics at Brown University, reviewed the book in SIAM News (January/February 2012, p. 5), the newsletter of the Society for Industrial and Applied Mathematics.

Davis, like McCartin a Chauvenet Prize winner, categorized McCartin as a “contributor of a substantial addition to the literature of triangle geometry.” And observed that McCartin “has fallen in love with the equilateral triangle,” and declaring that "everything you might want to know or teach about equilateral triangles is here, and then some."

In November 2011 McCartin gave a presentation on the book to Kettering’s B-section Kappa Mu Epsilon National Mathematics Honor Society students. The video of his presentation can be found at http://www.youtube.com/watch?v=teqyejsnryw

Mysteries of the Equilateral Triangle has been included in the American Mathematical Society's elite Book List, highlighting books that have mathematical themes and are aimed at a broad audience potentially including mathematicians, students, and the general public. The electronic version of the book is available free for download at the publisher's web site: http://www.m-hikari.com/mccartin-2.pdf

Originally from Providence, R.I., McCartin received his bachelor's and master's degrees from the University of Rhode Island and his doctoral degree in Applied Mathematics from the Courant Institute of Mathematical Sciences at New York University. He is past-vice president of the Great Lakes Section of the Society for Industrial and Applied Mathematics, and winner of the Kettering 2000 Outstanding Researcher Award and 2001 Outstanding Teacher Award. He was named an honorary member of the Kettering University Robots Honors Society in 2001 by his students and is the founder of Kettering's chapter of Kappa Mu Epsilon National Mathematics Honor Society. In 2004, the Michigan Section of the Mathematical Association of America presented him with their Award for Distinguished University Teaching. McCartin is a Fellow of the Electromagnetics Academy and has served on the Editorial Board of the international journal Applied Mathematical Sciences (AMS). He received the prestigious Chauvenet Prize for Mathematical Expository Writing in 2010.

Written by Dawn Hibbard

810.762.9865

dhibbard@kettering.edu