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Author : Viktor A. Zalgaller
Publisher : Springer
Page : 108 pages
File Size : 49,9 Mb
Release : 1969
Category : Juvenile Nonfiction
ISBN : UVA:X001456926
Author : Viktor A. Zalgaller
Publisher : Springer
Page : 0 pages
File Size : 47,5 Mb
Release : 2014-09-12
Category : Science
ISBN : 1489956697
Author : A. R. Rajwade
Publisher : Springer
Page : 203 pages
File Size : 41,8 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 9789386279064
Author : Peter R. Cromwell
Publisher : Cambridge University Press
Page : 498 pages
File Size : 43,9 Mb
Release : 1997
Category : Mathematics
ISBN : 0521664055
Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating.
Author : Anthony Pugh
Publisher : Univ of California Press
Page : 136 pages
File Size : 45,5 Mb
Release : 1976
Category : Mathematics
ISBN : 0520029267
Author : A.D. Alexandrov
Publisher : Springer Science & Business Media
Page : 545 pages
File Size : 48,7 Mb
Release : 2005-12-08
Category : Mathematics
ISBN : 9783540263401
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.
Author : Klaus Sattler
Publisher : CRC Press
Page : 318 pages
File Size : 43,5 Mb
Release : 1996
Category : Technology & Engineering
ISBN : 0878497471
It is now some 15 years since atomic clusters were first produced and investigated in laboratories. Since then, knowledge concerning clusters has enjoyed rapid and sustained growth, and cluster research has become a new branch of science.
Author : Anthony Pugh
Publisher : Univ of California Press
Page : 290 pages
File Size : 49,8 Mb
Release : 2023-11-10
Category : Electronic
ISBN : 9780520322042
Author : Sankt-Peterburgskoe matematicheskoe obshchestvo
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 48,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821848029
Contains articles on analysis, probability, partial differential operators, frames, and other areas of mathematics. This volume also contains a comprehensive article about the classification of pseudo-regular convex polyhedra. It is suitable for a broad group of graduate students and researchers interested in the topics presented here.
Author : L. Fejes Tóth
Publisher : Elsevier
Page : 360 pages
File Size : 52,6 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483151434
Regular Figures concerns the systematology and genetics of regular figures. The first part of the book deals with the classical theory of the regular figures. This topic includes description of plane ornaments, spherical arrangements, hyperbolic tessellations, polyhedral, and regular polytopes. The problem of geometry of the sphere and the two-dimensional hyperbolic space are considered. Classical theory is explained as describing all possible symmetrical groupings in different spaces of constant curvature. The second part deals with the genetics of the regular figures and the inequalities found in polygons; also presented as examples are the packing and covering problems of a given circle using the most or least number of discs. The problem of distributing n points on the sphere for these points to be placed as far as possible from each other is also discussed. The theories and problems discussed are then applied to pollen-grains, which are transported by animals or the wind. A closer look into the exterior composition of the grain shows many characteristics of uniform distribution of orifices, as well as irregular distribution. A formula that calculates such packing density is then explained. More advanced problems such as the genetics of the protean regular figures of higher spaces are also discussed. The book is ideal for physicists, mathematicians, architects, and students and professors in geometry.
Author : Aleksandr Danilovich Aleksandrov
Publisher : Unknown
Page : 539 pages
File Size : 45,5 Mb
Release : 2010
Category : Convex surfaces
ISBN : OCLC:988794706
Convex Polyhedra is one of the classics in geometry. There simply is no other book with so many of the aspects of the theory of 3-dimensional convex polyhedra in a comparable way, and in anywhere near its detail and completeness. It is the definitive source of the classical field of convex polyhedra and contains the available answers to the question of the data uniquely determining a convex polyhedron. This question concerns all data pertinent to the poly hedron, e.g. the lengths of edges, areas of faces, etc. This viatal and clearly written 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. It is a wonderful source of ideas for students. The English edition includes numerous comments as well as added material and a comprehensive bibliography by V.A. Zalgaller to bring the work up to date. Moreover, related papers by L.A. Shor and Yu. A. Volkov have been added as supplements to this book.
Author : Donald W. Grace,Stanford University. Computer Science Department
Publisher : Unknown
Page : 162 pages
File Size : 43,6 Mb
Release : 1965
Category : Image processing
ISBN : STANFORD:36105033224309
To classify the polyhedra, to survey the polyhedral shapes, and to exhaust their variety by orderly enumeration is a naturally attractive problem, noticed by Euler and Jakob Steiner, to which some mathematicians, especially Max Bruckner, devoted considerable work. With the latest high-speed digital computers decades of manual labor can be compressed into hours. This dissertation is concerned with the solution of the enumeration problem on a digital computer. A tri- linear polyhedron is one in which each vertex is incident with exactly three edges. Two polyhedra are isomorphic if a one-toone correspondence can be established between the vertices, edges, and faces of one with those of the other, so that the incidence relations between elements are preserved. Two polyhedra are called equi-surrounded if a one-to-one correspondence can be established between the faces of one and the faces of the other so that each pair of corresponding faces has equivalent surroundings -- i. e. the neighbors of the two faces in question, when taken in cyclic order clockwise, display the same pattern of edge-counts. Isomorphism implies equisurroundedness. A counter-example with 18 faces disproves the converse. However, for polyhedra with up to 17 faces we can apparently equate isomorphism with equisurroundedness.
Author : Magnus J. Wenninger
Publisher : Cambridge University Press
Page : 224 pages
File Size : 52,6 Mb
Release : 1971
Category : Mathematics
ISBN : 0521098599
he author describes simply and carefully how to make models of all the known uniform polyhedra and some of the stellated forms.
Author : David S. Richeson
Publisher : Princeton University Press
Page : 336 pages
File Size : 50,9 Mb
Release : 2019-07-23
Category : Mathematics
ISBN : 9780691191997
How a simple equation reshaped mathematics 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 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.
Author : Antoni P. Tomsia,Andreas M. Glaeser
Publisher : Springer Science & Business Media
Page : 841 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461553939
This volume, titled Proceedings of the International Materials Symposium on Ce ramic Microstructures: Control at the Atomic Level summarizes the progress that has been achieved during the past decade in understanding and controlling microstructures in ceram ics. A particular emphasis of the symposium, and therefore of this volume, is advances in the characterization, understanding, and control of micro structures at the atomic or near-atomic level. This symposium is the fourth in a series of meetings, held every ten years, devoted to ceramic microstructures. The inaugural meeting took place in 1966, and focussed on the analysis, significance, and production of microstructure; the symposium emphasized the need for, and importance of characterization in achieving a more complete understanding of the physical and chemical characteristics of ceramics. A consensus emerged at that meeting on the critical importance of characterization in achieving a more complete understanding of ceramic properties. That point of view became widely accepted in the ensuing decade. The second meeting took place in 1976 at a time of world-wide energy shortages and thus emphasized energy-related applications of ceramics, and more specifically, microstructure-property relationships of those materials. The third meeting, held in 1986, was devoted to the role that interfaces played both during processing, and in influencing the ultimate properties of single and polyphase ceramics, and ceramic-metal systems.
