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EXPLORING ADVANCED EUCLIDEAN GEOMETRY WITH GEOGEBRA

EXPLORING ADVANCED EUCLIDEAN GEOMETRY WITH GEOGEBRA

EXPLORING ADVANCED EUCLIDEAN GEOMETRY WITH GEOGEBRA

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Exploring Advanced Euclidean Geometry with GeoGebra
by Gerard A. Venema

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 is in for a feast of delectable geometry. --Michael Starbird

This book is worth any geometry teacher's attention. The problem sequences show the author has thought much, and not just about how to guide the reader to theorem discovery. -Bill Wood, MAA Reviews

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.

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  • Author: Gerard A. Venema
  • ISBN: 978-0-88385-784-7
  • 129 pp.
  • 2013
  • Hardbound
  • Classroom Resource Materials
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