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Books > Science & Mathematics > Mathematics > Geometry

The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems (Hardcover): Gennadiy Vladimirovich... The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems (Hardcover)
Gennadiy Vladimirovich Zhizhin
R5,808 Discovery Miles 58 080 Ships in 12 - 17 working days

The study of the geometry of structures that arise in a variety of specific natural systems, such as chemical, physical, biological, and geological, revealed the existence of a wide range of types of polytopes of the highest dimension that were unknown in classical geometry. At the same time, new properties of polytopes were discovered as well as the geometric patterns to which they obey. There is a need to classify these types of polytopes of the highest dimension by listing their properties and formulating the laws to which they obey. The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems explains the meaning of higher dimensions and systematically generalizes the results of geometric research in various fields of knowledge. This book is useful both for the fundamental development of geometry and for the development of branches of science related to human activities. It builds upon previous books published by the author on this topic. Covering areas such as heredity, geometry, and dimensions, this reference work is ideal for researchers, scholars, academicians, practitioners, industry professionals, instructors, and students.

Geometric Sculptures - an Exploration of Building Blocks Construction Techniques. (Hardcover): Rocky Lau Geometric Sculptures - an Exploration of Building Blocks Construction Techniques. (Hardcover)
Rocky Lau
R1,776 Discovery Miles 17 760 Ships in 12 - 17 working days
Symmetry - A Journey into the Patterns of Nature (Paperback): Marcus du Sautoy Symmetry - A Journey into the Patterns of Nature (Paperback)
Marcus du Sautoy
R472 R442 Discovery Miles 4 420 Save R30 (6%) Ships in 10 - 15 working days

Symmetry is all around us. Of fundamental significance to the way we interpret the world, this unique, pervasive phenomenon indicates a dynamic relationship between objects. Combining a rich historical narrative with his own personal journey as a mathematician, Marcus du Sautoy takes a unique look into the mathematical mind as he explores deep conjectures about symmetry and brings us face-to-face with the oddball mathematicians, both past and present, who have battled to understand symmetry's elusive qualities.

Note-book on Plane Geometrical Drawing - With a Chapter on Scales, and an Introduction to Graphic Statics (Hardcover): Robert... Note-book on Plane Geometrical Drawing - With a Chapter on Scales, and an Introduction to Graphic Statics (Hardcover)
Robert Harris
R902 Discovery Miles 9 020 Ships in 12 - 17 working days
Associative Algebraic Geometry (Hardcover): Arvid Siqveland Associative Algebraic Geometry (Hardcover)
Arvid Siqveland
R3,822 Discovery Miles 38 220 Ships in 10 - 15 working days

Classical Deformation Theory is used for determining the completions of the local rings of an eventual moduli space. When a moduli variety exists, a main result in the book is that the local ring in a closed point can be explicitly computed as an algebraization of the pro-representing hull (therefore, called the local formal moduli) of the deformation functor for the corresponding closed point.The book gives explicit computational methods and includes the most necessary prerequisites. It focuses on the meaning and the place of deformation theory, resulting in a complete theory applicable to moduli theory. It answers the question 'why moduli theory' and it give examples in mathematical physics by looking at the universe as a moduli of molecules. Thereby giving a meaning to most noncommutative theories.The book contains the first explicit definition of a noncommutative scheme, covered by not necessarily commutative rings. This definition does not contradict any of the previous abstract definitions of noncommutative algebraic geometry, but rather gives interesting relations to other theories which is left for further investigation.

Plane and Solid Geometry Essentials (Hardcover): James Elander Plane and Solid Geometry Essentials (Hardcover)
James Elander
R949 Discovery Miles 9 490 Ships in 12 - 17 working days
An Elementary Treatise on Determinants - With Their Application to Simultaneous Linear Equations and Algebraical Geometry... An Elementary Treatise on Determinants - With Their Application to Simultaneous Linear Equations and Algebraical Geometry (Hardcover)
Lewis 1832-1898 Carroll
R830 Discovery Miles 8 300 Ships in 12 - 17 working days
Hardy Inequalities on Homogeneous Groups (Hardcover): Durvudkhan Suragan, Michael Ruzhansky Hardy Inequalities on Homogeneous Groups (Hardcover)
Durvudkhan Suragan, Michael Ruzhansky
R1,958 Discovery Miles 19 580 Ships in 12 - 17 working days
The Ontario High School Geometry [microform] - Theoretical (Hardcover): A H (Alexander Hiram) 1 McDougall The Ontario High School Geometry [microform] - Theoretical (Hardcover)
A H (Alexander Hiram) 1 McDougall
R905 Discovery Miles 9 050 Ships in 12 - 17 working days
Geometry In Our Three-dimensional World (Paperback): Alfred S. Posamentier, Guenter Maresch, Bernd Thaller, Christian... Geometry In Our Three-dimensional World (Paperback)
Alfred S. Posamentier, Guenter Maresch, Bernd Thaller, Christian Spreitzer, Robert Geretschlager, …
R1,389 Discovery Miles 13 890 Ships in 10 - 15 working days

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics - from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses - this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives.The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.

Closepacks & Quasi-closepacks - Being the Fifth Part of Several Comprising the Complete? Polyhedra (Paperback): Patrick John... Closepacks & Quasi-closepacks - Being the Fifth Part of Several Comprising the Complete? Polyhedra (Paperback)
Patrick John Taylor
R184 Discovery Miles 1 840 Ships in 12 - 17 working days
Four figure mathematical tables; comprising logarithmic and trigonometrical tables, and tables of squares, square roots, and... Four figure mathematical tables; comprising logarithmic and trigonometrical tables, and tables of squares, square roots, and reciprocals (Hardcover)
J. T. Bottomley
R689 R642 Discovery Miles 6 420 Save R47 (7%) Ships in 10 - 15 working days
Groups and Topological Dynamics (Paperback): Volodymyr Nekrashevych Groups and Topological Dynamics (Paperback)
Volodymyr Nekrashevych
R2,257 Discovery Miles 22 570 Ships in 12 - 17 working days

This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems. One of the main applications of this approach to group theory is the study of asymptotic properties of groups such as growth and amenability. The book presents recently developed techniques of studying groups of dynamical origin using the structure of their orbits and associated groupoids of germs, applications of the iterated monodromy groups to hyperbolic dynamical systems, topological full groups and their properties, amenable groups, groups of intermediate growth, and other topics. The book is suitable for graduate students and researchers interested in group theory, transformations defined by automata, topological and holomorphic dynamics, and theory of topological groupoids. Each chapter is supplemented by exercises of various levels of complexity.

The First Six Books of the Elements of Euclid, in Which Coloured Diagrams and Symbols Are Used Instead of Letters ..... The First Six Books of the Elements of Euclid, in Which Coloured Diagrams and Symbols Are Used Instead of Letters .. (Hardcover)
Euclid; Oliver. Byrne
R1,294 R902 Discovery Miles 9 020 Save R392 (30%) Ships in 12 - 17 working days
An Elementary Treatise on Conic Sections (Hardcover): Charles 1844-1916 Smith An Elementary Treatise on Conic Sections (Hardcover)
Charles 1844-1916 Smith
R938 Discovery Miles 9 380 Ships in 12 - 17 working days
Elements of geometry, plane and spherical trigonometry, and conic sections (Hardcover): H. N. Robinson Elements of geometry, plane and spherical trigonometry, and conic sections (Hardcover)
H. N. Robinson
R972 R884 Discovery Miles 8 840 Save R88 (9%) Ships in 10 - 15 working days
Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces (Hardcover): Gennadiy Vladimirovich Zhizhin Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces (Hardcover)
Gennadiy Vladimirovich Zhizhin
R5,812 Discovery Miles 58 120 Ships in 12 - 17 working days

In the study of the structure of substances in recent decades, phenomena in the higher dimension was discovered that was previously unknown. These include spontaneous zooming (scaling processes), discovery of crystals with the absence of translational symmetry in three-dimensional space, detection of the fractal nature of matter, hierarchical filling of space with polytopes of higher dimension, and the highest dimension of most molecules of chemical compounds. This forces research to expand the formulation of the question of constructing n-dimensional spaces, posed by David Hilbert in 1900, and to abandon the methods of considering the construction of spaces by geometric figures that do not take into account the accumulated discoveries in the physics of the structure of substances. There is a need for research that accounts for the new paradigm of the discrete world and provides a solution to Hilbert's 18th problem of constructing spaces of higher dimension using congruent figures. Normal Partitions and Hierarchical Fillings of N-Dimensional Spaces aims to consider the construction of spaces of various dimensions from two to any finite dimension n, taking into account the indicated conditions, including zooming in on shapes, properties of geometric figures of higher dimensions, which have no analogue in three-dimensional space. This book considers the conditions of existence of polytopes of higher dimension, clusters of chemical compounds as polytopes of the highest dimension, higher dimensions in the theory of heredity, the geometric structure of the product of polytopes, the products of polytopes on clusters and molecules, parallelohedron and stereohedron of Delaunay, parallelohedron of higher dimension and partition of n-dimensional spaces, hierarchical filling of n-dimensional spaces, joint normal partitions, and hierarchical fillings of n-dimensional spaces. In addition, it pays considerable attention to biological problems. This book is a valuable reference tool for practitioners, stakeholders, researchers, academicians, and students who are interested in learning more about the latest research on normal partitions and hierarchical fillings of n-dimensional spaces.

Algebras, Lattices, Varieties - Volume II (Paperback): Ralph S Freese, Ralph N. McKenzie, George F. McNulty, Walter F. Taylor Algebras, Lattices, Varieties - Volume II (Paperback)
Ralph S Freese, Ralph N. McKenzie, George F. McNulty, Walter F. Taylor
R3,224 Discovery Miles 32 240 Ships in 12 - 17 working days

This book is the second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.

Representation Theory and Geometry of the Flag Variety (Hardcover): William M. McGovern Representation Theory and Geometry of the Flag Variety (Hardcover)
William M. McGovern
R3,830 Discovery Miles 38 300 Ships in 12 - 17 working days

This comprehensive reference begins with a review of the basics followed by a presentation of flag varieties and finite- and infinite-dimensional representations in classical types and subvarieties of flag varieties and their singularities. Associated varieties and characteristic cycles are covered as well and Kazhdan-Lusztig polynomials are treated. The coverage concludes with a discussion of pattern avoidance and singularities and some recent results on Springer fibers.

Lectures on Poisson Geometry (Paperback): Marius Crainic, Rui Loja Fernandes, Ioan Marcut Lectures on Poisson Geometry (Paperback)
Marius Crainic, Rui Loja Fernandes, Ioan Marcut
R2,261 Discovery Miles 22 610 Ships in 12 - 17 working days
A System of Geometry and Trigonometry - With a Treatise on Surveying (Hardcover): Abel 1765-1825 Flint, George Gillet A System of Geometry and Trigonometry - With a Treatise on Surveying (Hardcover)
Abel 1765-1825 Flint, George Gillet; Created by Frederick A P (Frederick a Barnard
R902 Discovery Miles 9 020 Ships in 12 - 17 working days
Forbidden Configurations in Discrete Geometry (Hardcover): David Eppstein Forbidden Configurations in Discrete Geometry (Hardcover)
David Eppstein
R2,758 Discovery Miles 27 580 Ships in 12 - 17 working days

This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.

The Theory of Quantum Torus Knots - Its Foundation in Differential Geometry - Volume IV (Hardcover): Michael Ungs The Theory of Quantum Torus Knots - Its Foundation in Differential Geometry - Volume IV (Hardcover)
Michael Ungs; Contributions by Laura Paige Ungs, Agostinho Gize
R3,155 Discovery Miles 31 550 Ships in 12 - 17 working days
Incomplete Tilings - Being the Second Part of Several Comprising the Complete? Polyhedra (Paperback): Patrick John Taylor Incomplete Tilings - Being the Second Part of Several Comprising the Complete? Polyhedra (Paperback)
Patrick John Taylor
R186 Discovery Miles 1 860 Ships in 12 - 17 working days
The Theory of Quantum Torus Knots - Its Foundation in Differential Geometry - Volume II (Hardcover): Michael Ungs The Theory of Quantum Torus Knots - Its Foundation in Differential Geometry - Volume II (Hardcover)
Michael Ungs; Contributions by Laura Paige Ungs, Agostinho Gize
R3,153 Discovery Miles 31 530 Ships in 12 - 17 working days
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