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  3. Analytic Projective Geometry
  • Cited by 1
Publisher:
Cambridge University Press
Online publication date:
October 2023
Print publication year:
2023
Online ISBN:
9781009260626
DOI:
https://doi.org/10.1017/9781009260626
Subjects:
Mathematics, Computer Science, Computer Graphics, Image Processing and Robotics, Geometry and Topology
Information

Book description

Projective geometry is the geometry of vision, and this book introduces students to this beautiful subject from an analytic perspective, emphasising its close relationship with linear algebra and the central role of symmetry. Starting with elementary and familiar geometry over real numbers, readers will soon build upon that knowledge via geometric pathways and journey on to deep and interesting corners of the subject. Through a projective approach to geometry, readers will discover connections between seemingly distant (and ancient) results in Euclidean geometry. By mixing recent results from the past 100 years with the history of the field, this text is one of the most comprehensive surveys of the subject and an invaluable reference for undergraduate and beginning graduate students learning classic geometry, as well as young researchers in computer graphics. Students will also appreciate the worked examples and diagrams throughout.

Reviews

‘This book provides a lively and lovely perspective on real projective spaces, combining art, history, groups and elegant proofs.’

William M. Kantor

‘This book is a celebration of the projective viewpoint of geometry. It gradually introduces the reader to the subject, and the arguments are presented in a way that highlights the power of projective thinking in geometry. The reader surprisingly discovers not only that Euclidean and related theorems can be realized as derivatives of projective results, but there are also unnoticed connections between results from ancient times. The treatise also contains a large number of exercises and is dotted with worked examples, which help the reader to appreciate and deeply understand the arguments they refer to. In my opinion this is a book that will definitely change the way we look at the Euclidean and projective analytic geometry.’

Alessandro Siciliano - Università degli Studi della Basilicata

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