Exploring Advanced Euclidean Geometry with GeoGebra

Classroom Resource Materials

by Gerard A. Venema

This book provides an enquiry-based introduction to advanced Euclidean geometry. It utilises the dynamic geometry program GeoGebra to explore many of the most interesting theorems in the subject. Topics covered include triangle centres, inscribed, circumscribed and escribed circles, medial and orthic triangles, the nine-point circle, the theorems of Ceva and Menelaus, and many applications. 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 or as a stand-alone introduction to advanced topics in Euclidean geometry. The exposition consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. The ideas are first explored at the computer and then assembled into a proof of the result under investigation, allowing readers to experience the joy of discovery and develop a deeper appreciation for the subject.

Genres: Mathematics

186 pages, Hardcover

First published May 31, 2013

Reviews

[Charles · Rating 5 out of 5]

Geometry is such a visual subject that it cannot be learned without the creation of understandable diagrams. In the classrooms of past years, this meant a writing utensil on either a chalk or whiteboard, a process that was not easy for those of use that are challenged by simple drawings. The combination of this text and the ability to use a free package that can be used to illustrate the examples is a powerful tool for teaching Euclidean geometry.
The speed with which the geometry can be taught as well as the level of student retention will both be increased by using this book as a text in combination with Geogebra. Since not much has changed in the area of advanced Euclidean algebra in a long time, the content is fairly standard. Although I was very impressed with the last chapter where the Poincaré disk is used to demonstrate hyperbolic geometry. There is a misplaced notion among many that non-Euclidean geometry is hard when in fact there are very understandable ways to introduce it. This shows a logical and effective way to demonstrate hyperbolic geometry.
Utilizing the dynamic and visual advantages of Geogebra, the math teacher can delve far deeper into the subject matter than was possible before. Since the text is very clear as a standalone tool, the combination will make the teaching of geometry far more efficient than it has been in the past.

This book was made available for free for review purposes and this review appears on Amazon.