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Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.
Book Synopsis Regular Polytopes by : H. S. M. Coxeter
Download or read book Regular Polytopes written by H. S. M. Coxeter and published by Courier Corporation. This book was released on 2012-05-23 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.
Book Synopsis Abstract Regular Polytopes by : Peter McMullen
Download or read book Abstract Regular Polytopes written by Peter McMullen and published by Cambridge University Press. This book was released on 2002-12-12 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
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.
Book Synopsis Geometric Regular Polytopes by : Peter McMullen
Download or read book Geometric Regular Polytopes written by Peter McMullen and published by Cambridge University Press. This book was released on 2020-02-20 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analytical Treatment of the Polytopes Regularly Derived from the Regular Polytopes by : Pieter Hendrik Schoute
Download or read book Analytical Treatment of the Polytopes Regularly Derived from the Regular Polytopes written by Pieter Hendrik Schoute and published by . This book was released on 1913 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometrical Deduction of Semiregular from Regular Polytopes and Space Fillings by : Alicia Boole Stott
Download or read book Geometrical Deduction of Semiregular from Regular Polytopes and Space Fillings written by Alicia Boole Stott and published by . This book was released on 1913 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This work is set in the field of combinatorial topology, sometimes also referred to as discrete geometric topology, a field of research in the intersection of topology, geometry, polytope theory and combinatorics. The main objects of interest in the field are simplicial complexes that carry some additional structure, forming combinatorial triangulations of the underlying PL manifolds. In particular, polyhedral manifolds as subcomplexes of the boundary complex of a convex regular polytope are investigated. Such a subcomplex is called k-Hamiltonian if it contains the full k-skeleton of the polytope. The notion of tightness of a PL-embedding of a triangulated manifold is closely related to its property of being a Hamiltonian subcomplex of some convex polytope. Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplex-wise linear embedding of the triangulation into Euclidean space is ``as convex as possible''. It can thus be understood as a generalization of the concept of convexity. In even dimensions, there exist purely combinatorial conditions which imply the tightness of a triangulation. In this work, other sufficient and purely combinatorial conditions which can be applied to the odd-dimensional case as well are presented.
Book Synopsis Hamiltonian Submanifolds of Regular Polytopes by : Felix Effenberger
Download or read book Hamiltonian Submanifolds of Regular Polytopes written by Felix Effenberger and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is set in the field of combinatorial topology, sometimes also referred to as discrete geometric topology, a field of research in the intersection of topology, geometry, polytope theory and combinatorics. The main objects of interest in the field are simplicial complexes that carry some additional structure, forming combinatorial triangulations of the underlying PL manifolds. In particular, polyhedral manifolds as subcomplexes of the boundary complex of a convex regular polytope are investigated. Such a subcomplex is called k-Hamiltonian if it contains the full k-skeleton of the polytope. The notion of tightness of a PL-embedding of a triangulated manifold is closely related to its property of being a Hamiltonian subcomplex of some convex polytope. Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplex-wise linear embedding of the triangulation into Euclidean space is ``as convex as possible''. It can thus be understood as a generalization of the concept of convexity. In even dimensions, there exist purely combinatorial conditions which imply the tightness of a triangulation. In this work, other sufficient and purely combinatorial conditions which can be applied to the odd-dimensional case as well are presented.
The majority of the chemical elements form chemical compounds with molecules of higher dimension (i.e., substantially exceeding three). This fact is very important for the analysis of molecular interactions in various areas: nanomedicine, nanotoxicology, and quantum biology. The Geometry of Higher-Dimensional Polytopes contains innovative research on the methods and applications of the structures of binary compounds. It explores the study of geometry polytopes from a higher-dimensional perspective, taking into account the features of polytopes that are models of chemical compounds. While highlighting topics including chemical compounds, symmetry transformation, and DNA structures, this book is ideally designed for researchers, academicians, and students seeking current research on dimensions present in binary compounds.
Book Synopsis The Geometry of Higher-Dimensional Polytopes by : Zhizhin, Gennadiy Vladimirovich
Download or read book The Geometry of Higher-Dimensional Polytopes written by Zhizhin, Gennadiy Vladimirovich and published by IGI Global. This book was released on 2018-08-03 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The majority of the chemical elements form chemical compounds with molecules of higher dimension (i.e., substantially exceeding three). This fact is very important for the analysis of molecular interactions in various areas: nanomedicine, nanotoxicology, and quantum biology. The Geometry of Higher-Dimensional Polytopes contains innovative research on the methods and applications of the structures of binary compounds. It explores the study of geometry polytopes from a higher-dimensional perspective, taking into account the features of polytopes that are models of chemical compounds. While highlighting topics including chemical compounds, symmetry transformation, and DNA structures, this book is ideally designed for researchers, academicians, and students seeking current research on dimensions present in binary compounds.
An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.
Book Synopsis Math Without Numbers by : Milo Beckman
Download or read book Math Without Numbers written by Milo Beckman and published by Penguin. This book was released on 2022-01-11 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.
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.
Book Synopsis Regular Figures by : L. Fejes Tóth
Download or read book Regular Figures written by L. Fejes Tóth and published by Elsevier. This book was released on 2014-07-10 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Grobner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.
Book Synopsis Gröbner Bases and Convex Polytopes by : Bernd Sturmfels
Download or read book Gröbner Bases and Convex Polytopes written by Bernd Sturmfels and published by American Mathematical Soc.. This book was released on 1996 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Grobner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.