Methods for Euclidean Geometry

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.

• 1. Early history; 2. Axioms: from Euclid to today; 3. Lines and polygons; 4. Circles; 5. Length and area; 6. Loci; 7. Trigonometry; 8. Coordinatization; 9. Conics; 10. Complex numbers; 11. Vectors; 12. A+ne transformations; 13. Inversions; 14. Coordinate method with software.

Textbooks for school and college geometry that were used until the beginning of the past century were nothing more than variants of parts of Euclid's Elements. Today, such textbooks usually highlight the inadequacy of Euclid's five axioms and replace them by a modern treatment containing expanded sets of axioms; but methods of proofs remain essentially those of Euclid. The book under review does provide in its first chapters, such a modern treatment, but its distinguishing features lie in the last eight chapters where the authors compile tools and methods, taken from the mathematics of the past few centuries, that can be useful in solving geometrical problems. Each of these chapters contains a lucid presentation of the basics of the subject, a set of examples, a set of problems solved at the end of the book, and a set of practice problems. ...Besides being excellent for a first course in Euclidean geometry, this book is also excellent for an upper level course in which students can see, in one basket, the fruits of what they had learned in many different courses. It is also excellent for training beginning students for competitions."" - Mowaffaq Hajja, Zentrallblatt""Methods for Euclidean Geometry is a college geometry textbook with a unique mission. Instead of treating the subject as a distinct unit in the math curriculum, the authors integrate a variety of mathematical disciplines to engage and enlighten the reader...Unlike many textbooks, this one hunts down and proves propositions that are often taken for granted. Take for instance solving systems of equations using the substitution and elimination methods. Rarely do texts help students understand why these methods give the same unique solution. In situations like this the authors prompt students to ask the questions why and how and then help answer them...The content and the thorough explanations should excite and enthuse students. Questions leading to deeper understanding are sprinkled throughout the work...With its treatment of history, unusual proofs and various methods of finding solutions, this text strives to teach the whole picture. Methods for Euclidean Geometry does a wonderful job exploring geometry through fresh new eyes."" - Ruth Doherty, MAA Reviews