Geometry by Its History

2012
ISBN: 978-3-642-44469-2
Verlag: Springer

Buch, Englisch, 440 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 680 g

Reihe: Readings in Mathematics

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 19century.

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Wanner, Gerhard

Ostermann, Alexander

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Geometrie Euklidische Geometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

Alexander Ostermann has published numerous research articles as well as several books with Springer. He is a professor in the Department of Mathematics at the University of Innsbruck, Austria.

Gerhard Wanner is the former President of Section VII of the Swiss Academy of Natural Sciences, former Head of Department of Mathematics at the University of Geneva, and former President of the Swiss Mathematical Society. He is the author of several books with Springer, including Analysis by its History, written together with Ernst Hairer.