Geometry by Its History (Undergraduate Texts in Mathematics) （2012）

Ostermann, Alexander/ Wanner, Gerhard

Springer-Verlag Berlin and Heidelberg GmbH & Co. K（2014/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 440 p.
• 言語 ENG
• 商品コード 9783642444692
• DDC分類 516.009

Full Description

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.

Contents

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.