Perspectives on Projective Geometry A Guided Tour Through Real and Complex Geometry /

• Κύριος συγγραφέας: Richter-Gebert, Jürgen (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Θέματα: Mathematics.; Algebra.; Algorithms.; Visualization.; Geometry.; Convex geometry.; Discrete geometry.; General Algebraic Systems.; Convex and Discrete 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 of...

Πίνακας περιεχομένων:

• 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.