In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury.
Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.
Author(s): Alexander Ostermann, Gerhard Wanner (auth.)
Series: Undergraduate Texts in Mathematics
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2012
Language: English
Pages: 440
Tags: Geometry; Algebraic Geometry; History of Mathematical Sciences
Front Matter....Pages i-xii
Front Matter....Pages 1-2
Thales and Pythagoras....Pages 3-26
The Elements of Euclid....Pages 27-59
Conic Sections....Pages 61-78
Further Results in Euclidean Geometry....Pages 79-112
Trigonometry....Pages 113-155
Front Matter....Pages 157-158
Descartes’ Geometry....Pages 159-184
Cartesian Coordinates....Pages 185-240
To be Constructible, or not to be....Pages 241-257
Spatial Geometry and Vector Algebra....Pages 259-290
Matrices and Linear Mappings....Pages 291-317
Projective Geometry....Pages 319-344
Solutions to the Exercises....Pages 345-401
Back Matter....Pages 403-437
