Convex Polyhedra

Author: A.D. Alexandrov

Publisher: Springer Science & Business Media


Category: Mathematics

Page: 542

View: 935

This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.

The Geometric Vein

The Coxeter Festschrift

Author: C. Davis

Publisher: Springer Science & Business Media


Category: Mathematics

Page: 598

View: 255

Geometry has been defined as that part of mathematics which makes appeal to the sense of sight; but this definition is thrown in doubt by the existence of great geometers who were blind or nearly so, such as Leonhard Euler. Sometimes it seems that geometric methods in analysis, so-called, consist in having recourse to notions outside those apparently relevant, so that geometry must be the joining of unlike strands; but then what shall we say of the importance of axiomatic programmes in geometry, where reference to notions outside a restricted reper tory is banned? Whatever its definition, geometry clearly has been more than the sum of its results, more than the consequences of some few axiom sets. It has been a major current in mathematics, with a distinctive approach and a distinc ti v e spirit. A current, furthermore, which has not been constant. In the 1930s, after a period of pervasive prominence, it appeared to be in decline, even passe. These same years were those in which H. S. M. Coxeter was beginning his scientific work. Undeterred by the unfashionability of geometry, Coxeter pursued it with devotion and inspiration. By the 1950s he appeared to the broader mathematical world as a consummate practitioner of a peculiar, out-of-the-way art. Today there is no longer anything that out-of-the-way about it. Coxeter has contributed to, exemplified, we could almost say presided over an unanticipated and dra matic revival of geometry.

Handbook of Convex Geometry

Author: Gerard Meurant

Publisher: Elsevier


Category: Mathematics

Page: 801

View: 868

Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.

New Trends in Intuitive Geometry

Author: Gergely Ambrus

Publisher: Springer


Category: Mathematics

Page: 458

View: 573

This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.

Convex Bodies

The Brunn-Minkowski Theory

Author: Rolf Schneider

Publisher: Cambridge University Press


Category: Mathematics

Page: 490

View: 266

A comprehensive introduction to convex bodies giving full proofs for some deeper theorems which have never previously been brought together.


revue internationale de h'istoire de sciences, de la médicine, de la pharmacie et de la technique




Category: Science


View: 648

Unobstructed Shortest Paths in Polyhedral Environments

Author: Varol Akman

Publisher: Springer Science & Business Media


Category: Computers

Page: 106

View: 454

The first examination of the cervical spine is always made using standard radiographs and, often enough, this suffices as a basis for diagnosis. Malformations, tumours, and more frequently traumas, rheumatism, and even ordinary neck pain require radiological examination of the spine. Interpretation, however, is difficult. Take a cervical vertebra in your hand and you will see that it is complex enough itself. In radiology the overlapping pieces of bone, summation phenomena and the diversity of viewing angles complicate interpretation of the images still further. The book by J.-F. Bonneville and F. Cattin suggests an original method of reading the radiographs, strict but very attractive, which considerably simplifies the interpretation of images of the cervical spine. This book shows that two- or threedimensional computed tomograms accompany standard radiographs as an excellent aid to comprehension. It is as though the reader had access to each part of the bony anatomy shown in the radiographs and from then on everything becomes easy, superimpositions disappear, traps become visible, anatomy triumphs, the image lives.