Geometry: Our Cultural Heritage

Audun Holme

Springer | 2002 | 410 páginas |  pdf | 8 Mb
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Descrição: This book, aimed at future teachers of mathematics, contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. All too often the geometry which goes into the syllabus for teacher-students presents the material as pedantic and formalistic, suppressing its dynamic character and its role as part of the foundation for our common cultural heritage. The motivation for the book is to open up these aspects of the field. Another motivation is to provide an invitation to mathematics in general. It is an unfortunate fact that today, at a time when mathematics and knowledge of mathematics are more important than ever, phrases like math avoidance and math anxiety are very much in the public vocabulary.

Conteúdos
1. A cultural heritage -- 1. Early beginnings -- 2. The great river civilizations -- 3. Greek and Hellenic geometry -- 4. Geometry in the Hellenistic era -- 5. The geometry of yesterday and today -- 6. Geometry and the real world -- pt. 2. Introduction to geometry -- 7. Axiomatic geometry -- 8. Axiomatic projective geometry -- 9. Models for non-Euclidian geometry -- 10. Making things precise -- 11. Projective space -- 13. Geometry in the affine and the projective plane -- 13. Algebraic curves of higher degrees in the affine plane -- 14. Higher geometry in the projective plane -- 15. Sharpening the sword of algebra -- 16. Constructions with straightedge and compass -- 17. Fractal geometry -- 18. Catastrophe theory.