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The Geometry of the SphereThe Geometry of the Sphere
by John C. Polking - Rice University , 2000
We are interested here in the geometry of an ordinary sphere. In plane geometry we study points, lines, triangles, polygons, etc. On the sphere there are no straight lines. Therefore it is natural to use great circles as replacements for lines.
(1119 views)

An Introduction to GeometryAn Introduction to Geometry
by Wong Yan Loi - National University of Singapore , 2009
Contents: A Brief History of Greek Mathematics; Basic Results in Book I of the Elements; Triangles; Quadrilaterals; Concurrence; Collinearity; Circles; Using Coordinates; Inversive Geometry; Models and Basic Results of Hyperbolic Geometry.
(1521 views)

Topics in Coarse GeometryTopics in Coarse Geometry
by John Roe - Penn State University , 2002
Our goal is to understand by way of examples some of the structure 'at infinity' that can be carried by a metric (or, more generally, a 'coarse') space. The connection between coarse geometry and operator algebras will be mentioned.
(1906 views)

Quadratic Forms and Their ApplicationsQuadratic Forms and Their Applications
by Andrew Ranicki, et al. - American Mathematical Society , 2000
This volume includes papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed.
(2709 views)

Tilings and PatternsTilings and Patterns
by E O Harriss - Mathematicians.org.uk , 2008
Contents: Background Material (Euclidean Space, Delone Sets, Z-modules and lattices); Tilings of the plane (Periodic, Aperiodic, Penrose Tilings, Substitution Rules and Tiling, Matching Rules); Symbolic and Geometric tilings of the line.
(3096 views)

Topics in GeometryTopics in Geometry
by John O'Connor - University of St Andrews , 2003
Contents: Foundations; Linear groups; Isometries of Rn; Isometries of the line; Isometries of the plane; Isometries in 3 dimensions; Symmetry groups in the plane; Platonic solids; Finite symmetry groups of R3; Full finite symmetry groups in R3; etc.
(4313 views)

Geometry, Topology and PhysicsGeometry, Topology and Physics
by Maximilian Kreuzer - Technische Universitat Wien , 2010
From the table of contents: Topology (Homotopy, Manifolds, Surfaces, Homology, Intersection numbers and the mapping class group); Differentiable manifolds; Riemannian geometry; Vector bundles; Lie algebras and representations; Complex manifolds.
(5842 views)

Geometry and Group TheoryGeometry and Group Theory
by Christopher Pope - Texas A&M University , 2008
Lecture notes on Geometry and Group Theory. In this course, we develop the basic notions of Manifolds and Geometry, with applications in physics, and also we develop the basic notions of the theory of Lie Groups, and their applications in physics.
(7173 views)

Origami and Geometric ConstructionsOrigami and Geometric Constructions
by Robert J. Lang , 2003
Origami is the art of folding sheets of paper into interesting and beautiful shapes. In this text the author presents a variety of techniques for origami geometric constructions. The field has surprising connections to other branches of mathematics.
(4411 views)

An Elementary Course in Synthetic Projective GeometryAn Elementary Course in Synthetic Projective Geometry
by Derrick Norman Lehmer - Project Gutenberg , 2005
The book gives, in a simple way, the essentials of synthetic projective geometry. Enough examples have been provided to give the student a clear grasp of the theory. The student should have a thorough grounding in ordinary elementary geometry.
(3668 views)

Categorical GeometryCategorical Geometry
by Zhaohua Luo , 1998
This is a book on the general theory of analytic categories. From the table of contents: Introduction; Analytic Categories; Analytic Topologies; Analytic Geometries; Coherent Analytic Categories; Coherent Analytic Geometries; and more.
(3683 views)

Flavors of GeometryFlavors of Geometry
by Silvio Levy - Cambridge University Press , 1997
This book collects accessible lectures on four geometrically flavored fields of mathematics that have experienced great development in recent years: hyperbolic geometry, dynamics in several complex variables, convex geometry, and volume estimation.
(5067 views)

Convex Geometric AnalysisConvex Geometric Analysis
by Keith Ball, Vitali Milman - Cambridge University Press , 1998
Convex bodies are at once simple and amazingly rich in structure. This collection involves researchers in classical convex geometry, geometric functional analysis, computational geometry, and related areas of harmonic analysis.
(4305 views)

The Radon TransformThe Radon Transform
by Sigurdur Helgason - Birkhauser Boston , 1999
The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications.
(5132 views)

Geometry and TopologyGeometry and Topology
by Christopher Cooper - Macquarie University , 2008
The geometry part of the text includes an introductory course on projective geometry and some chapters on symmetry. The topology part consists of geometric and combinatorial topology and includes material on the classification of surfaces, and more.
(7572 views)

Combinatorial and Computational GeometryCombinatorial and Computational Geometry
by J. E. Goodman, J. Pach, E. Welzl - Cambridge University Press , 2007
This volume includes articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension.
(5465 views)

Fundamentals of GeometryFundamentals of Geometry
by Oleg A. Belyaev - Moscow State University , 2007
A continually updated book devoted to rigorous axiomatic exposition of the basic concepts of geometry. Self-contained comprehensive treatment with detailed proofs should make this book both accessible and useful to a wide audience of geometry lovers.
(10351 views)

Fractal GeometryFractal Geometry
by Michael Frame, Benoit Mandelbrot, Nial Neger - Yale University , 2009
This is an introduction to fractal geometry for students without especially strong mathematical preparation, or any particular interest in science. Each of the topics contains examples of fractals in the arts, humanities, or social sciences.
(8543 views)

Topics in Finite Geometry: Ovals, Ovoids and Generalized QuadranglesTopics in Finite Geometry: Ovals, Ovoids and Generalized Quadrangles
by S. E. Payne - University of Colorado Denver , 2007
The present book grew out of notes written for a course by the same name taught by the author during in 2005. Only some basic abstract algebra, linear algebra, and mathematical maturity are the prerequisites for reading this book.
(5039 views)

Projective GeometryProjective Geometry
by Nigel Hitchin , 2003
The techniques of projective geometry provide the technical underpinning for perspective drawing and in particular for the modern version of the Renaissance artist, who produces the computer graphics we see every day on the web.
(6636 views)

Geometric Theorems and Arithmetic FunctionsGeometric Theorems and Arithmetic Functions
by Jozsef Sandor - American Research Press , 2002
Contents: on Smarandache's Podaire theorem, Diophantine equation, the least common multiple of the first positive integers, limits related to prime numbers, a generalized bisector theorem, values of arithmetical functions and factorials, and more.
(7963 views)