Exploring Advanced Euclidean Geometry with GeoGebra (Classroom Resource Materials) - Hardcover

Venema, Gerard A.

Hardcover

ISBN 10: 0883857847 ISBN 13: 9780883857847

Publisher: American Mathematical Society, 2013

Synopsis

This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincaré disk model for hyperbolic geometry.

The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry. The text consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. First the ideas are explored at the computer and then those ideas are assembled into a proof of the result under investigation. The goals are for the reader to experience the joy of discovering geometric relationships, to develop a deeper understanding of geometry, and to encourage an appreciation for the beauty of Euclidean geometry.

About this title

Book Description

An enquiry-based introduction to advanced Euclidean geometry using the dynamic geometry program GeoGebra that is ideal for both the computer lab and the classroom. The exposition consists mostly of exercises (with hints) that guide students as they explore some of the most interesting results in the subject.

About the Author

Gerard Venema earned an A.B. in mathematics from Calvin College and a Ph.D. from the University of Utah. After completing his education he spent two years in a postdoctoral position at the University of Texas at Austin and another two years as a Member of the Institute for Advanced Study in Princeton, NJ. He then returned to his alma mater, Calvin College, and has been a faculty member there ever since. While on the Calvin College faculty he has also held visiting faculty positions at the University of Tennessee, the University of Michigan, and Michigan State University. He spent two years as a Program Director in the Division of Mathematical Sciences at the National Science Foundation.

Venema is a member of the American Mathematical Society and the Mathematical Association of America. He served for ten years as an Associate Editor of the American Mathematical Monthly and currently sits on the editorial board of MAA FOCUS. Venema has served the Michigan Section of the MAA as chair and is the 2013 recipient of the section s distinguished service award. He currently holds the position of MAA Associate Secretary and is a member of the Association s Board of Governors.

Venema is the author of two other books. One is an undergraduate textbook, Foundations of Geometry, published by Pearson Education, Inc., which is now in its second edition. The other is a research monograph coauthored by Robert J. Daverman. It is titled Embeddings in Manifolds and was published by the American Mathematical Society as volume 106 in its Graduate Studies in Mathematics series. In addition to these books, Venema is author of over 30 research articles in geometric topology.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2013
• ISBN 10: 0883857847
• ISBN 13: 9780883857847
• Binding: Hardcover
• Language: English
• Number of pages: 186