紹介
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 Poincare 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.
目次
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 Poincare disk.
