Monday, April 22, 2013

Perspectives on Projective Geometry by Richter-Gebert


Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry PDF Download Ebook. J├╝rgen Richter-Gebert offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms.

The major theme that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists.

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

The author covers most of the traditional topics in real projective geometry, and extends the concepts through complex projective geometry. He provides the reader with concise proofs, clear and insightful presentations, and a coherent development of the topic. Richter-Gebert presents algebraic, visual, and diagrammatic approaches to unify the subject, while his fresh writing style make for a very readable text. Additionally, the student and teacher will enjoy the quotations introducing each section.

The author describes his work as ‘a guided tour through real and complex geometry’, and these words explain perfectly the aim of the book. The prerequisites for reading the book are just the basics of linear algebra (in terms of coordinates), so that the book seems accessible to a wide audience ranging from mathematicians to computer scientists and physicists.

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