Exploring Advanced Euclidean Geometry with GeoGebra
Mathematical Association of America (Verlag)
978-0-88385-784-7 (ISBN)
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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 Poincar 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.
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.
Preface
0. 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
References
Index
About the Author
| Reihe/Serie | Classroom Resource Materials |
|---|---|
| Sprache | englisch |
| Maße | 180 x 254 mm |
| Gewicht | 432 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-88385-784-7 / 0883857847 |
| ISBN-13 | 978-0-88385-784-7 / 9780883857847 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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