Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
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.