One century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have included detailed sections on what is known as well as outlining problems that remain to be solved. There are sections on classical geometries, methods for constructing non-classical geometries and classifications and characterizations of geometries. This work is related to a host of other fields including approximation, convexity, differential geometry topology and many more. This book will appeal to students, researchers and lecturers working in geometry or any one of the many associated areas outlined above.
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Editorial Reviews
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"This book mainly concerns geometries with point sets that form some sort of surface (e.g. a plane, a sphere, a torus, a cylinder) and line sets of a general nature that validate certain standard sets of incidence axioms.... Altogether well designed, quite suitable for browsing, and accessible to undergraduates, this book will form a vital supplement to courses in the foundations of geometry. General readers; lower-division undergraduates through faculty." Choice
"...a carefully written introduction to the subject of topological geometries on surfaces, with many illustrations, motivations, and examples." Mathematical Reviews
"...a carefully written introduction to the subject of topological geometries on surfaces, with many illustrations, motivations, and examples." Mathematical Reviews
Book Description
One century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have include detailed secions on what is known as well as outlining problems that remain to be solved. The authors add interest by giving connections to a host of other areas of maths. This book will appeal to students, researchers and lecturers working in geometry or any one of the many associated areas.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
In this book of geometry will usually consists of a nonempty point set and nonempty line set, where a line is a subset of the point set containing at least three points and every point is contained in at least three lines. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
flat projective plane, flat linear spaces, nonparallel points, derived affine plane, topological oval, flat circle planes, geometry whose point set, unisolvent sets, bundle involution, abstract oval, antiregular quadrangle, coordinatizing function, maximal group dimension, nontrivial parallelism, skew parabola, biaffine plane, piecewise projective homeomorphisms, continuous lineations, topological arc, inner involution, outer involutions, central automorphisms, finite covering group, involutory homeomorphism, pseudoline arrangement Key Phrases - Capitalized Phrases (CAPs): (learn more)
Equals Classical, Open Problems, Brouwer's Theorem, Characterizations of the Classical Plane, The Space of Circles, Affine Pasted Planes, Characterization of Semi-classical Planes, High Degree of Transitivity, The Space of Flags, Topological Characterization, Topology Circle Space, Triodes Form Neighbourhood Basis New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
In this book of geometry will usually consists of a nonempty point set and nonempty line set, where a line is a subset of the point set containing at least three points and every point is contained in at least three lines. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
flat projective plane, flat linear spaces, nonparallel points, derived affine plane, topological oval, flat circle planes, geometry whose point set, unisolvent sets, bundle involution, abstract oval, antiregular quadrangle, coordinatizing function, maximal group dimension, nontrivial parallelism, skew parabola, biaffine plane, piecewise projective homeomorphisms, continuous lineations, topological arc, inner involution, outer involutions, central automorphisms, finite covering group, involutory homeomorphism, pseudoline arrangement Key Phrases - Capitalized Phrases (CAPs): (learn more)
Equals Classical, Open Problems, Brouwer's Theorem, Characterizations of the Classical Plane, The Space of Circles, Affine Pasted Planes, Characterization of Semi-classical Planes, High Degree of Transitivity, The Space of Flags, Topological Characterization, Topology Circle Space, Triodes Form Neighbourhood Basis New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 20
books:
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11
books
cite this book:
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- Handbook of Incidence Geometry: Buildings and Foundations by F. Buekenhout in Front Matter, and Back Matter
- Projective planes (Graduate texts in mathematics) by D. R Hughes on page 53, and Back Matter
- Graph Theory (Cambridge Mathematical Library) by W. T. Tutte in Front Matter (1), and Front Matter (2)
- Special Functions (Encyclopedia of Mathematics and its Applications) by George E. Andrews in Front Matter
- Dimension Theory (Princeton Mathematical Ser.; Vol 4) by Witold Hurewicz in Back Matter
See all 20 books this book cites
- Basic Hypergeometric Series (Encyclopedia of Mathematics and its Applications) by George Gasper in Front Matter
- Large Deviations and Metastability (Encyclopedia of Mathematics and its Applications) by Enzo Olivieri in Front Matter
- Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications) by Alexei Kushner in Front Matter
- The Mountain Pass Theorem: Variants, Generalizations and Some Applications (Encyclopedia of Mathematics and its Applications) by Youssef Jabri in Front Matter
- Topics in Algebraic Graph Theory (Encyclopedia of Mathematics and its Applications) (v. 1) by Lowell W. Beineke in Front Matter
See all 11 books citing this book
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