Perspectives on Projective Geometry

1 Pappos's Theorem: Nine Proofs and Three Variations.- 2 Projective Planes.- 3 Homogeneous Coordinates.- 4 Lines and Cross-Ratios.- 5 Calculating with Points on Lines.- 6 Determinants.- 7 More on Bracket Algebra.- 8 Quadrilateral Sets and Liftings.- 9 Conics and Their Duals.- 10 Conics and Perspectivity.- 11 Calculating with Conics.- 12 Projective $d$-space.- 13 Diagram Techniques.- 14 Working with diagrams.- 15 Configurations, Theorems, and Bracket Expressions.- 16 Complex Numbers: A Primer.- 17 The Complex Projective Line.- 18 Euclidean Geometry.- 19 Euclidean Structures from a Projective Perspective.- 20 Cayley-Klein Geometries.- 21 Measurements and Transformations.- 22 Cayley-Klein Geometries at Work.- 23 Circles and Cycles.- 24 Non-Euclidean Geometry: A Historical Interlude.- 25 Hyperbolic Geometry.- 26 Selected Topics in Hyperbolic Geometry.- 27 What We Did Not Touch.- References.- Index.

Full Professor for Geometry and Visualization at Technical University Munich. Research in combinatorial, computational and dynamic geometry, automated geometric theorem proving and visualization. Author of the dynamic geometry program Cinderella and of the interactive visualization portal Mathe-Vital. Cinderella was awarded the Multimedia Innovation Award, the European Academic Software Award and the Deutsche Bildungssoftwarepreis. Mathe-Vital won the renowned MedidaPrix in 2008.

From the reviews:

Choice - Oustanding Academic Title in 2012

"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. ... Summing Up: Highly recommended. Upper-division undergraduates and faculty." (R. L. Pour, Choice, Vol. 49 (5), January, 2012)

"This lovely book offers an introduction to the key ideas of projective geometry ... . The book is written in a leisurely way that will make it accessible to undergraduate students with a basic knowledge of algebra. ... There is no doubt that the author went to great lengths to write clearly and to make his book as user friendly as possible, as the well chosen illustrations, several per page, many in colour, testify." (S. C. Coutinho, SIGACT News, January, 2014)

"The author, known for the co-development of the interactive geometry software Cinderella, here presents a thorough introduction to real and complex, mostly plane geometry. ... Because of the detailed explanations ... and the very readable style the book can be recommended warmly even to undergraduates as well as to computer scientists and physicists." (G. Teschl, Monatshefte für Mathematik, Vol. 166 (2), May, 2012)

"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."