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.
An enquiry-based introduction to Euclidean geometry that uses the geometry program GeoGebra to explore many advanced results in the subject.
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.
… 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
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