Exploring Advanced Euclidean Geometry with GeoGebra

Erscheinungsjahr 2013
ISBN: 978-0-88385-784-7
Verlag: CAMBRIDGE UNIVERSITY PRESS

Buch, Englisch, 186 Seiten, Format (B × H): 183 mm x 263 mm, Gewicht: 428 g

Reihe: Classroom Resource Materials

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.

Autoren/Hrsg.

Venema, Gerard A. (Calvin College

Venema, Gerard A.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Computeralgebra
• Mathematik | Informatik Mathematik Geometrie Euklidische Geometrie

Inhaltsverzeichnis

A quick review of elementary Euclidean geometry; 1. The elements of GeoGebra; 2. The classical triangle centers; 3. Advanced techniques in GeoGebra; 4. Circumscribed, inscribed, and escribed circles; 5. The medial and orthic triangles; 6. Quadrilaterals; 7. The nine-point circle; 8. Ceva's theorem; 9. The theorem of Menelaus; 10. Circles and lines; 11. Applications of the theorem of Menelaus; 12. Additional topics in triangle geometry; 13. Inversions in circles; 14. The Poincaré disk.

Über Autor(innen)

Venema, Gerard A.
Gerard A. Venema is a Professor of Mathematics at Calvin College, Michigan. He is a member of the American Mathematical Society and the Mathematical Association of America. In addition, he served for ten years as an Associate Editor of 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.