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Fairs --- Hyperboloid --- Torus (Geometry)

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Working at the threshold of the Modern Age, Vladimir G. uchov (Shukhov) is regarded as one of the world′s most outstanding and versatile engineers. Some of his fascinating and technically sophisticated structures, always so delicately proportioned they cannot fail to catch the eye, have no equivalent among the structures of today. From the time Shukhov built the first hyperbolic lattice tower at the end of the 19th century, he has been seen as the founder and developer of this then new form of construction. This structure, with a seemingly complex geometry definable with only a few basic parameters, has no predecessors in the history of construction. It excels through its high stability and economy of material but above all through the visual impact of its web–like arrangement of members. Setting Shukhov s work in the context of the history of construction shows that he and his new structural forms anticipated many of today′s engineering and lightweight structures. The principles of Shukhov s load–bearing systems are used in architecture today, for example in the structural engineering of high–rise buildings. Hyperbolic structures analyses the interactions of form with the structural behaviour of hyperbolic lattice towers, and the effects of the various influencing factors were determined with the help of parametric studies and load capacity analyses. This evaluation of Shukhov s historical calculations and the reconstruction of the design and development process of his water towers shows why the Russian engineer is considered not only a pathfinder for lightweight structures but also a pioneer of parametrised design processes.

Hyperboloid structures --- Structural frames --- Lattice theory --- Charpentes --- Théorie des treillis --- Design and construction --- Conception et construction --- Théorie des treillis --- Structural frames - Design and construction

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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.

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