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 Poincare 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.
Industry Reviews
... If you want to teach a course that conveys the joy of mathematical thinking to students, consider leading your students on a journey through Venema's book. The theorems are classics and Venema's presentation allows the reader to experience the discovery of insights, which make them all the more meaningful and memorable. An Inquiry Based Learning course based on Venema's book would be a perfect experience for any mathematics major, particularly, a person who might teach geometry later. Exploring Advanced Euclidean Geometry with GeoGebra is also a perfect book for individual or small group study. Students, teachers, or anyone who enjoys geometrical beauty can take their time and savor the many wonderful theorems that this book contains. Whether used in a classroom setting or for individual instruction, every reader of Gerard Venema's Exploring Advanced Euclidean Geometry with GeoGebra is in for a feast of delectable geometry."" - Michael Starbird ""Exploring Advanced Euclidean Geometry with GeoGebra is written for an inquiry-based approach, with lots of exercises and just enough narrative and historical commentary to hold it all together. ... There is also much value to be mined as a supplement to other Euclidean geometry texts. ... This book would work as a sourcebook for directed study and as such is worth consideration for many academic libraries. Inquiry-minded instructors should absolutely give this some attention. Working through these exercises feels very much like the process of doing mathematics, which is about the most one can ask of a book like this. The engaged student will learn much about learning as well as geometry."" - Bill Wood, MAA Reviews
