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Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry
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. This book 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. One of the major themes 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. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
- GenresMathematicsGeometry
593 pages, Hardcover
First published January 1, 2011
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Displaying 1 of 1 review
October 12, 2018
Thrilling! Inspiring! It's been months since I read such a concise and elegant geometry book as this one. Despite just a few chapters I've been through, I enjoyed every theorem and proof the author exhibited to me. It is natural, intuitive and interesting.
I remember when I took part in mathematics Olympics contest in high school, The most painful problem for me is plane geometry. Many points, lines, circles join and meet together in some unreasonable way and suddenly a mysterious statement fell down and it was incredible true. Usually I didn't even know where to start constructing the proof. Then only thing I could think was how lucky those contest makers were to find out another geometry "coincidence". Plane geometry leaves me a deep impression of unprovable but amazing thing. That feeling last so long until I touched projective geometry, which makes it so intuitive and incredible easy.
The book begins with nine proofs of the celebrated Pappus' theorem in projective geometry, accompanied with many figures. Each proof suggests one distinct thought, which will be explained in later chapters in detail.
Here I list some inspiring sections so far: joins and meets, determinant, Plucker coordinate, bracket algebra and diagram techniques
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To be continued
I remember when I took part in mathematics Olympics contest in high school, The most painful problem for me is plane geometry. Many points, lines, circles join and meet together in some unreasonable way and suddenly a mysterious statement fell down and it was incredible true. Usually I didn't even know where to start constructing the proof. Then only thing I could think was how lucky those contest makers were to find out another geometry "coincidence". Plane geometry leaves me a deep impression of unprovable but amazing thing. That feeling last so long until I touched projective geometry, which makes it so intuitive and incredible easy.
The book begins with nine proofs of the celebrated Pappus' theorem in projective geometry, accompanied with many figures. Each proof suggests one distinct thought, which will be explained in later chapters in detail.
Here I list some inspiring sections so far: joins and meets, determinant, Plucker coordinate, bracket algebra and diagram techniques
---
To be continued
Displaying 1 of 1 review