This book 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. It is geared towards the needs of future mathematics teachers. One of my goals for this book is to open up for the dynamic character of geometry as such, and to extend an invitation to geometry as a gateway to mathematics in general. It is unfortunate that today, at a time when mathematics is more important than ever, phrases like math avoidance and math anxiety are very much in the public vocabulary. Making a serious effort to heal these ills is an essential task. Thus the book also aims at an informed public, interested in making a new beginning in math For the 2nd edition, some of the historical material has been expanded and numerous illustrations have been added, as has a chapter on polyhedra and tessellations and their symmetries. A large number of exercises with some suggestions for solutions is also included. A very readable short history of geometry No prerequisites required Easy to understand by beginners New edition with large number of exercises with some suggestions for solutions INDICE: Part I A Cultural Heritage: 1 Early Beginnings.- 2 The Great RiverCivilizations.- 3 Greek and Hellenic Geometry.- 4 Geometry in the HellenisticEra.- 5 Arabic Mathematics and Geometry.- 6 The Geometry of Yesterday and Today.- 7 Geometry and the Real World.- Part II Introduction to Geometry: 8 Axiomatic Geometry.- 9 Axiomatic Projective Geometry.- 10 Models for Non-Euclidean Geometry.- 11 Making Things Precise.- 12 Projective Space.- 13 Geometry in theAffine and the Projective Plane.- 14 Algebraic Curves of Higher Degrees in the Affine Plane R2.- 15 Higher Geometry in the Projective Plane.- 16 Sharpeningthe Sword of Algebra.- 17 Constructions with Straightedge and Compass.- 18 Fractal Geometry.- 19 Catastrophe Theory.- 20 General Polyhedra and Tesselations, and their Groups of Symmetry.- 21 Hints and Solutions to some of the Excercises.- References.- Index
- ISBN: 978-3-642-14440-0
- Editorial: Springer
- Encuadernacion: Cartoné
- Fecha Publicación: 01/09/2010
- Nº Volúmenes: 1
- Idioma: Inglés