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Convex geometry. --- Geometry, Hyperbolic. --- Differentiable dynamical systems. --- Functions of several complex variables. --- Convex bodies. --- Random walks (Mathematics) --- Géométrie convexe --- Géométrie hyperbolique --- Dynamique différentiable --- Fonctions de plusieurs variables complexes --- Corps convexes --- Promenades aléatoires (Mathématiques)
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Differential geometry. Global analysis --- Ergodentheorie --- Ergodic theory --- Ergodique [Theorie ] --- Measure theory --- Mesure [Théorie de la ] --- Metingen--Theorie
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514.144 --- Projective geometry --- 514.144 Projective geometry
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The third and second centuries BC witnessed, in the Greek world, a scientific and technological explosion. Greek culture had reached great heights in art, literature and philosophy already in the earlier classical era, but it was in the age of Archimedes and Euclid that science as we know it was born, and gave rise to sophisticated technology that would not be seen again until the 18th century. This scientific revolution was also accompanied by great changes and a new kind of awareness in many other fields, including art and medicine. What were the landmarks in the meteoric rise of science 2300 years ago? Why are they so little known today, even among scientists, classicists and historians? How do they relate to the post-1500 science that we are familiar with from school? What led to the end of ancient science? These are the questions that this book discusses, in the belief that the answers bear on choices we face today.
Science --- Science, Ancient. --- Technology --- History --- Science, Ancient --- Ancient science --- Science, Primitive --- History. --- Mathematics. --- Popular works. --- History of Science. --- History of Mathematical Sciences. --- Popular Science, general. --- Math --- Annals --- Auxiliary sciences of history --- Sciences --- Histoire
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This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.
Topology --- Differential geometry. Global analysis --- Geometry, Hyperbolic --- Three-manifolds (Topology) --- Géométrie hyperbolique --- Variétés topologiques à 3 dimensions --- Geometry, Hyperbolic. --- 514.1 --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean --- General geometry --- Three-manifolds (Topology). --- 514.1 General geometry --- Géométrie hyperbolique --- Variétés topologiques à 3 dimensions --- 3-sphere. --- Abelian group. --- Affine space. --- Affine transformation. --- Atlas (topology). --- Automorphism. --- Basis (linear algebra). --- Bounded set (topological vector space). --- Brouwer fixed-point theorem. --- Cartesian coordinate system. --- Characterization (mathematics). --- Compactification (mathematics). --- Conformal map. --- Contact geometry. --- Curvature. --- Cut locus (Riemannian manifold). --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Dimension (vector space). --- Dimension. --- Disk (mathematics). --- Divisor (algebraic geometry). --- Dodecahedron. --- Eigenvalues and eigenvectors. --- Embedding. --- Euclidean space. --- Euler number. --- Exterior (topology). --- Facet (geometry). --- Fiber bundle. --- Foliation. --- Fundamental group. --- Gaussian curvature. --- Geometry. --- Group homomorphism. --- Half-space (geometry). --- Holonomy. --- Homeomorphism. --- Homotopy. --- Horocycle. --- Hyperbolic geometry. --- Hyperbolic manifold. --- Hyperbolic space. --- Hyperboloid model. --- Interior (topology). --- Intersection (set theory). --- Isometry group. --- Isometry. --- Jordan curve theorem. --- Lefschetz fixed-point theorem. --- Lie algebra. --- Lie group. --- Line (geometry). --- Linear map. --- Linearization. --- Manifold. --- Mathematical induction. --- Metric space. --- Moduli space. --- Möbius transformation. --- Norm (mathematics). --- Pair of pants (mathematics). --- Piecewise linear manifold. --- Piecewise linear. --- Poincaré disk model. --- Polyhedron. --- Projection (linear algebra). --- Projection (mathematics). --- Pseudogroup. --- Pullback (category theory). --- Quasi-isometry. --- Quotient space (topology). --- Riemann mapping theorem. --- Riemann surface. --- Riemannian manifold. --- Sheaf (mathematics). --- Sign (mathematics). --- Simplicial complex. --- Simply connected space. --- Special linear group. --- Stokes' theorem. --- Subgroup. --- Subset. --- Tangent space. --- Tangent vector. --- Tetrahedron. --- Theorem. --- Three-dimensional space (mathematics). --- Topological group. --- Topological manifold. --- Topological space. --- Topology. --- Transversal (geometry). --- Two-dimensional space. --- Uniformization theorem. --- Unit sphere. --- Variable (mathematics). --- Vector bundle. --- Vector field. --- Topologie algébrique --- Topologie combinatoire --- Algebraic topology. --- Combinatorial topology. --- Variétés topologiques --- Geometrie --- Theorie des noeuds
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Fysica [Mathematische ] --- Fysica [Wiskundige ] --- Mathematical physics --- Mathematische fysica --- Physical mathematics --- Physics -- Mathematics --- Physics [Mathematical ] --- Physique -- Mathématiques --- Physique -- Méthodes mathématiques --- Physique mathématique --- Physique théorique --- Topologie --- Topology --- Wiskundige fysica --- Topology. --- Mathematical physics. --- 515.163 --- Physics --- 515.163 Topological manifolds. Microbundles. Imbeddings. Immersions --- Topological manifolds. Microbundles. Imbeddings. Immersions --- Mathematics --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Physique mathématique
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Electronic data processing documentation. --- C (Computer program language) --- Electronic data processing documentation --- Computer documentation --- Documentation in electronic data processing --- Documents in electronic data processing --- Electronic data processing --- Computer software --- Records --- Documents --- TeX (Computer file) --- Tau epsilon chi --- TeX (Computer system)
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