Geometry by Its History / by Alexander Ostermann, Gerhard Wanner.

Springer eBooks

Preface -- Part I: Classical Geometry -- Thales and Pythagoras -- The Elements of Euclid -- Conic Sections -- Further Results on Euclidean Geometry -- Trigonometry -- Part II: Analytic Geometry -- Descartes' Geometry -- Cartesian Coordinates -- To be Constructible, or not to be -- Spatial Geometry and Vector Algebra -- Matrices and Linear Mappings -- Projective Geometry -- Solutions to Exercises --  References -- Figure Source and Copyright -- Index.

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.

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