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Abstract Regular Polytopes

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Author : Peter McMullen
Category : Mathematics
Publisher : Cambridge University Press
Published : 2002-12-12
Type : PDF & EPUB
Page : 580
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Description: Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. They are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties; in many ways more fascinating than traditional regular polytopes and tessellations. The rapid development of the subject in the past 20 years has resulted in a rich new theory, featuring an attractive interplay of mathematical areas, including geometry, combinatorics, group theory and topology. Abstract regular polytopes and their groups provide an appealing new approach to understanding geometric and combinatorial symmetry. This is the first comprehensive up-to-date account of the subject and its ramifications, and meets a critical need for such a text, because no book has been published in this area of classical and modern discrete geometry since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974). The book should be of interest to researchers and graduate students in discrete geometry, combinatorics and group theory.

Polytopes

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Author : Tibor Bisztriczky
Category : Mathematics
Publisher : Springer Science & Business Media
Published : 2012-12-06
Type : PDF & EPUB
Page : 507
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Description: The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject. The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex. With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes. For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.

Regular Complex Polytopes

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Author : Coxeter
Category : Mathematics
Publisher : Cambridge University Press
Published : 1975-03-06
Type : PDF & EPUB
Page : 210
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Description: The properties of regular solids exercise a fascination which often appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book Professor Coxeter explores these properties in easy stages, introducing the reader to complex polyhedra (a beautiful generalization of regular solids derived from complex numbers) and unexpected relationships with concepts from various branches of mathematics: magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, crystallographic and non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. In the latter half of the book, these preliminary ideas are put together to describe a natural generalization of the Five Platonic Solids. This updated second edition contains a new chapter on Almost Regular Polytopes, with beautiful 'abstract art' drawings. New exercises and discussions have been added throughout the book, including an introduction to Hopf fibration and real representations for two complex polyhedra.

Geometric Regular Polytopes

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Author : Peter McMullen
Category : Mathematics
Publisher : Cambridge University Press
Published : 2020-02-20
Type : PDF & EPUB
Page :
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Description: Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.

Proceedings Of International Conference On Recent Trends In Computing

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Author : Rajendra Prasad Mahapatra
Category : Technology & Engineering
Publisher : Springer Nature
Published : 2022-01-15
Type : PDF & EPUB
Page : 837
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Description: This book is a collection of high-quality peer-reviewed research papers presented at International Conference on Recent Trends in Computing (ICRTC 2021) held at SRM Institute of Science and Technology, Ghaziabad, Delhi, India, during 4 – 5 June 2021. The book discusses a wide variety of industrial, engineering and scientific applications of the emerging techniques. The book presents original works from researchers from academic and industry in the field of networking, security, big data and the Internet of things.

The Words Of Mathematics An Etymological Dictionary Of Mathematical Terms In English

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Author : Steven Schwartzman
Category : Mathematics
Publisher : American Mathematical Soc.
Published : 1994-12-31
Type : PDF & EPUB
Page : 261
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Description: Explains the orgins of over 1500 mathematical terms used in English. This book concentrates on where those terms come from and what their literal meanings are.

Fishing The Sloe Black River

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Author : Colum McCann
Category : Fiction
Publisher : Bloomsbury Publishing
Published : 2021-01-07
Type : PDF & EPUB
Page : 192
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Description: An ageing nun is tracked to ground by her sister; a garrulous beautician must lay out the corpse of a loved one. These are eloquent tales of exile and displacement, of characters always in search of a way back home or of a way to leave it. Mischievous, assured and versatile, Colum McCann's collection of short stories marks him out as one of our best contemporary writers.

The Geometric Vein

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Author : C. Davis
Category : Mathematics
Publisher : Springer Science & Business Media
Published : 2012-12-06
Type : PDF & EPUB
Page : 598
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Description: 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.

Rigidity And Symmetry

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Author : Robert Connelly
Category : Mathematics
Publisher : Springer
Published : 2014-06-11
Type : PDF & EPUB
Page : 374
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Description: This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.

Educator Bandwidth

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Author : Jane A. G. Kise
Category : Education
Publisher : ASCD
Published : 2022-07-15
Type : PDF & EPUB
Page : 175
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Description: It's time to make your mental bandwidth work for you. Being an educator is more stressful than ever, and teachers and administrators must constantly shift gears to stay on top of the newest initiatives and students' ever-changing needs. Educator Bandwidth: How to Reclaim Your Energy, Passion, and Time provides the tools and strategies to reduce stress, avoid burnout, and regain the time that gets lost to interruptions, temptations, competing demands, and task-switching. The first step is to understand how much stress is weighing on your own mental bandwidth. Professional development experts Jane A. G. Kise and Ann Holm have developed the Brain Energy and Bandwidth Survey to help you self-assess the six key factors that contribute to bandwidth: * Balance between priorities * Filtering through possibilities * Mental habits that improve focus * Physical habits that fuel the brain * Connection with others * Workload and time management Kise and Holm combine the latest neuroscience research with their own extensive experience working with educators to bring the most effective strategies and habits that help you manage your mental bandwidth and prioritize drains on mental energy. When you can establish good habits, focus on what’s possible within your locus of control, and balance priorities, you can improve your educator bandwidth and feel more engaged, centered, and effective in your work.