Geometry by Its History
Douban
Alexander Ostermann / Gerhard Wanner
Übersicht
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 19th century.
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.
Inhalt
Front Matter
Pages i-xii
Classical Geometry
Front Matter
Pages 1-2
Thales and Pythagoras
Alexander Ostermann, Gerhard Wanner
Pages 3-26
The Elements of Euclid
Alexander Ostermann, Gerhard Wanner
Pages 27-59
Conic Sections
Alexander Ostermann, Gerhard Wanner
Pages 61-78
Further Results in Euclidean Geometry
Alexander Ostermann, Gerhard Wanner
Pages 79-112
Trigonometry
Alexander Ostermann, Gerhard Wanner
Pages 113-155
Analytic Geometry
Front Matter
Pages 157-158
Descartes’ Geometry
Alexander Ostermann, Gerhard Wanner
Pages 159-184
Cartesian Coordinates
Alexander Ostermann, Gerhard Wanner
Pages 185-240
To be Constructible, or not to be
Alexander Ostermann, Gerhard Wanner
Pages 241-257
Spatial Geometry and Vector Algebra
Alexander Ostermann, Gerhard Wanner
Pages 259-290
Matrices and Linear Mappings
Alexander Ostermann, Gerhard Wanner
Pages 291-317
Projective Geometry
Alexander Ostermann, Gerhard Wanner
Pages 319-344
Solutions to the Exercises
Alexander Ostermann, Gerhard Wanner
Pages 345-401
Back Matter
Pages 403-437