A thorough guide to Euclidean geometry with a unique emphasis and methodology, for use as an undergraduate textbook.
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Owen Byers studied for his BA (1989) in Mathematics, with secondary education certification, at Messiah College, Grantham, PA. He then went on to gain both his MS (1991) and Ph.D. (1996) in Mathematics from the University of Delaware. He previously taught for three years at Northwestern College, Orange City, IA. Currently he is Professor of Mathematics at Eastern Mennonite University, where he has been for 12 years. He is a member of MAA and ACMS.
Felix Lazebnik gained his MS from Kiev State University in 1975 before moving to the University of Pennsylvania in 1987 for his Ph.D. in Mathematics. He has taught mathematics for 35 years at various levels, including four years in a high school. Since 1987, he has been with the Department of Mathematical Sciences at the University of Delaware. As a Professor of Mathematics there, he teaches mathematics and does research with graduate and undergraduate students. He served for five years as the Managing Editor of The Electronic Journal of Combinatorics and is a member of their editorial board. He is a member of the AMS, MAA, and the ICA.
Deirdre Smeltzer received her BA (1987) in Mathematics from Eastern Mennonite University, Harrisonburg, VA. She then gained her MS (1989) and Ph.D. (1994) in Mathematics from the University of Virginia. Previously, she taught four years at the University of St Thomas, St Paul, MN. For the past eleven years she has been a Professor of Mathematics and the chair of the Mathematical Sciences department at Eastern Mennonite University. She is a member of MAA (and former officer of MD-DC-VA section) and ACMS.
Methods for Euclidean Geometry explores one of the oldest and most beautiful of mathematical subjects. The book begins with a thorough presentation of classical solution methods for plane geometry problems, but its distinguishing feature is the subsequent collection of methods which have appeared since 1600. For example, the coordinate method, which is a central part of the book, has been part of mathematics for four centuries. However, it has rarely served as a tool that students consider using when faced with geometry problems. The same holds true regarding the use of trigonometry, vectors, complex numbers, and transformations. The book presents each of these as self-contained topics, providing examples of their applications to geometry problems. Both strengths and weaknesses of various methods, as well as the ranges of their effective applications, are discussed. Importance is placed on the problems and their solutions. The book contains numerous problems of varying difficulty; over a third of its contents are devoted to problem statements, hints, and complete solutions. The book can be used as a textbook for geometry courses; as a source book for geometry and other mathematics courses; for capstone, problem-solving, and enrichment courses; and for independent study courses.
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