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Geometry, Solid  Géometrie dans l'espace  Euclid  Polyhedra  Early works to 1800  Polyhedral figures  Polyhedrons  Shapes  Early works to 1800  Géometrie dans l'espace  Polyhedral figures
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Polyhedra.  Polyhedra  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes  Géométrie  Polytopes  Geometry
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Lavishly illustrated and entertaining account of the surprising and useful results of the maths of folding and unfolding.
Polyhedra  Polyèdres  Models  Data processing  Modèles  Geometrical models  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes  Data processing.  Models.
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Polytopes  Combinatorial optimization  Polyhedra  #TELE:SISTA  Hyperspace  Topology  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes  Optimization, Combinatorial  Combinatorial analysis  Mathematical optimization  Geometry  Convex polytopes  Géométrie  Polytopes convexes
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Leonhard Euler's polyhedron formula describes the structure of many objectsfrom soccer balls and gemstones to Buckminster Fuller's buildings and giant allcarbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cuttingedge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its farreaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation VE+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenthcentury mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentiethcentury mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.
Polyhedra.  Topology  Analysis situs  Position analysis  Rubbersheet geometry  Geometry  Polyhedra  Set theory  Algebras, Linear  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes  History.
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How a simple equation reshaped mathematicsLeonhard Euler's polyhedron formula describes the structure of many objectsfrom soccer balls and gemstones to Buckminster Fuller's buildings and giant allcarbon molecules. Yet Euler's theorem is so simple it can be explained to a child. From ancient Greek geometry to today's cuttingedge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its farreaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
MATHEMATICS / History & Philosophy.  Topology.  Polyhedra.  Analysis situs  Position analysis  Rubbersheet geometry  Geometry  Polyhedra  Set theory  Algebras, Linear  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes
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This is the first book to present a complete characterization of SteinTomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all realanalytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to the given surface.Isroil Ikromov and Detlef Müller begin with Elias M. Stein's concept of Fourier restriction and some relations between the decay of the Fourier transform of the surface measure and SteinTomas type restriction estimates. Varchenko's ideas relating Fourier decay to associated Newton polyhedra are briefly explained, particularly the concept of adapted coordinates and the notion of height. It turns out that these classical tools essentially suffice already to treat the case where there exist linear adapted coordinates, and thus Ikromov and Müller concentrate on the remaining case. Here the notion of rheight is introduced, which proves to be the right new concept. They then describe decomposition techniques and related stopping time algorithms that allow to partition the given surface into various pieces, which can eventually be handled by means of oscillatory integral estimates. Different interpolation techniques are presented and used, from complex to more recent real methods by Bak and Seeger.Fourier restriction plays an important role in several fields, in particular in real and harmonic analysis, number theory, and PDEs. This book will interest graduate students and researchers working in such fields.
Hypersurfaces.  Polyhedra.  Surfaces, Algebraic.  Fourier analysis.  Analysis, Fourier  Mathematical analysis  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes  Algebraic surfaces  Geometry, Algebraic  Hyperspace  Surfaces
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Polyhedra  Polyèdres  Descartes, René,  51 <09>  MathematicsGeschiedenis van ...  Descartes, Rene  Polyhedra.  51 <09> MathematicsGeschiedenis van ...  Polyèdres  Descartes, René,  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes  MathematicsGeschiedenis van ..  MathematicsGeschiedenis van .
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Spaces of constant curvature  514.74  Algebraic and analytic methods in geometry  Polyhedra.  Spaces of constant curvature.  514.74 Algebraic and analytic methods in geometry  Polyhedra  Constant curvature, Spaces of  Curvature  Geometry, Differential  Polyhedral figures  Polyhedrons  Geometry, Solid  Shapes
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