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Exercices pour les éléments des solides : essai en complément d'Euclide
Authors: --- --- --- ---
ISBN: 213040099X Year: 1987 Publisher: Paris PUF

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Space structures : their harmony and counterpoint
Authors: ---
ISBN: 0201046512 0201046504 Year: 1977 Publisher: Reading (Mass.) Addison-Wesley

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Geometric folding algorithms : linkages, origami, polyhedra
Authors: ---
ISBN: 9780521857574 0521857570 9780511735172 9780521715225 9781461949183 1461949181 0511735170 9781107390430 1107390435 0521715229 9781107387515 1107387515 1139883283 1107384001 1107386209 1107398843 1107395232 Year: 2007 Publisher: Cambridge ; New York : Cambridge University Press,

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Lavishly illustrated and entertaining account of the surprising and useful results of the maths of folding and unfolding.


Book
Polytopes, graphs and optimisations
Authors: --- --- ---
ISBN: 052125597X Year: 1984 Publisher: Cambridge Cambridge University press


Book
Polyhedra primer
Authors: ---
ISBN: 0442264968 Year: 1978 Publisher: New York (N.Y.): Van Nostrand Reinhold


Book
Euler's Gem : The Polyhedron Formula and the Birth of Topology
Author:
ISBN: 1283129264 9786613129260 1400838568 Year: 2012 Publisher: Princeton, NJ : Princeton University Press,

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Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon 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 cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching 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 V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century 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 twentieth-century 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.


Book
Euler's Gem : The Polyhedron Formula and the Birth of Topology
Author:
ISBN: 0691191999 Year: 2019 Publisher: Princeton, NJ : Princeton University Press,

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How a simple equation reshaped mathematicsLeonhard Euler's polyhedron formula describes the structure of many objects-from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's theorem is so simple it can be explained to a child. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching 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.


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Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra
Authors: ---
ISBN: 1400881242 Year: 2016 Publisher: Princeton : Princeton University Press,

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This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic 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 Stein-Tomas 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 r-height 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.

Descartes on polyhedra : a study of the de solidorum elementis.
Author:
ISBN: 0387907602 1461257611 146125759X Year: 1982 Volume: 4 Publisher: New York Springer ill.


Book
Polyedergeometrie in n-dimensionalen Räumen konstanter Krümmung
Authors: ---
ISBN: 3764311606 Year: 1981 Volume: 70 Publisher: Basel Birkhäuser

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