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Exploring Advanced Euclidean Geometry with GeoGebra

Gerard A. Venema


The geometry we study in school was mostly discovered in ancient times and was systematized by the Greek mathematician Euclid of Alexandria in around 300 BC. The subject of Euclidean geometry has continued to expand in the years since Euclid did his work. Many beautiful and amazing new discoveries that build on the geometry of Euclid have been made by a variety of people. In this book, easy-to-use dynamic geometry software is employed to explore some of those newer results. The reader is guided to discover the theorems, to develop a deep understanding of them, and to come to appreciate them for their elegance and beauty as well as for their utility.

Exploring Advanced Euclidean Geometry with GeoGebra 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 standalone introduction to advanced topics in Euclidean geometry.

Electronic ISBN:  9781614441113

Preface

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Exploring Advanced Euclidean Geometry with GeoGebra $23.00

 

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