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Books > Science & Mathematics > Mathematics > Geometry > General

Introduction to Topology and Geometry 2e (Hardcover, 2nd Edition): S. Stahl Introduction to Topology and Geometry 2e (Hardcover, 2nd Edition)
S. Stahl
R3,148 Discovery Miles 31 480 Ships in 12 - 17 working days

An easily accessible introduction to over three centuries of innovations in geometry

Praise for the First Edition

." . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." --CHOICE

This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics.

Illustrating modern mathematical topics, "Introduction to Topology and Geometry, Second Edition "discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the "Second Edition: "- Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being- Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods- Bridges seemingly disparate topics by creating thoughtful and logical connections- Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory"Introduction to Topology and Geometry, Second Edition "is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.

The Joy of Geometry (Paperback): Alfred S. Posamentier The Joy of Geometry (Paperback)
Alfred S. Posamentier
R490 R427 Discovery Miles 4 270 Save R63 (13%) Ships in 10 - 15 working days

A veteran math educator reveals the hidden fascinations of geometry and why this staple of math education is important. If you remember anything about high school geometry class, it's probably doing proofs. But geometry is more than axioms, postulates, theorems, and proofs. It's the science of beautiful and extraordinary geometric relationships--most of which is lost in high school classrooms where the focus is on the rigor of logically proving those relationships. This book will awaken readers to the appeal of geometry by placing the focus squarely on geometry's visually compelling features and intrinsic elegance. Who knew that straight lines, circles, and area could be so interesting? Not to mention optical illusions. So get out the rulers, compasses, or even a software program, and discover geometry for the first time.

Convex Surfaces (Paperback): Herbert Busemann Convex Surfaces (Paperback)
Herbert Busemann
R342 R285 Discovery Miles 2 850 Save R57 (17%) Ships in 10 - 15 working days

In this self-contained geometry text, the author describes the main results of convex surface theory, providing all definitions and precise theorems. The first half focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. The second part examines intrinsic geometry and the realization of intrinsic metrics.
Starting with a brief overview of notations and terminology, the text proceeds to convex curves, the theorems of Meusnier and Euler, extrinsic Gauss curvature, and the influence of the curvature on the local shape of a surface. A chapter on the Brunn-Minkowski theory and its applications is followed by examinations of intrinsic metrics, the metrics of convex hypersurfaces, geodesics, angles, triangulations, and the Gauss-Bonnet theorem. The final chapter explores the rigidity of convex polyhedra, the realization of polyhedral metrics, Weyl's problem, local realization of metrics with non-negative curvature, open and closed surfaces, and smoothness of realizations.

Projective Geometry (Paperback): T. Ewan Faulkner Projective Geometry (Paperback)
T. Ewan Faulkner
R262 R218 Discovery Miles 2 180 Save R44 (17%) Ships in 10 - 15 working days

Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. It derives the projective properties of the conic and discusses representation by the general equation of the 2nd degree, concluding with a study of the relationship between Euclidean and projective geometry. 1960 edition.

New Spaces in Mathematics and Physics 2 Volume Hardback Set - Formal and Conceptual Reflections (Hardcover): Mathieu Anel,... New Spaces in Mathematics and Physics 2 Volume Hardback Set - Formal and Conceptual Reflections (Hardcover)
Mathieu Anel, Gabriel Catren
R2,613 Discovery Miles 26 130 Ships in 12 - 17 working days

After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. These books explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincare in 2015. They are addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.

The Geometry of Universal Mind - Volume 2 (Paperback): Bob Mustin The Geometry of Universal Mind - Volume 2 (Paperback)
Bob Mustin
R487 R92 Discovery Miles 920 Save R395 (81%) Ships in 9 - 15 working days
Invariant Manifolds for Physical and Chemical Kinetics (Hardcover, 2005 ed.): Alexander N Gorban, Iliya V. Karlin Invariant Manifolds for Physical and Chemical Kinetics (Hardcover, 2005 ed.)
Alexander N Gorban, Iliya V. Karlin
R3,204 Discovery Miles 32 040 Ships in 10 - 15 working days

By bringing together various ideas and methods for extracting the slow manifolds, the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.

Revolutions of Geometry (Hardcover): M. O'Leary Revolutions of Geometry (Hardcover)
M. O'Leary
R3,682 Discovery Miles 36 820 Ships in 12 - 17 working days

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic

In an effort to fully appreciate the logic and structure of geometric proofs, "Revolutions of Geometry" places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems.

Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's "Elements." Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries.

The book promotes the belief that in order to learn how to write proofs, one needs to read finished proofs, studying both their logic and grammar. Each chapter features a concise introduction to the presented topic, and chapter sections conclude with exercises that are designed to reinforce the material and provide readers with ample practice in writing proofs. In addition, the overall presentation of topics in the book is in chronological order, helping readers appreciate the relevance of geometry within the historical development of mathematics.

Well organized and clearly written, "Revolutions of Geometry" is a valuable book for courses on modern geometry and the history of mathematics at the upper-undergraduate level. It is also a valuable reference for educators in the field of mathematics.

Arithmetic and Geometry - Ten Years in Alpbach (AMS-202) (Hardcover): Gisbert Wustholz, Clemens Fuchs Arithmetic and Geometry - Ten Years in Alpbach (AMS-202) (Hardcover)
Gisbert Wustholz, Clemens Fuchs
R3,327 Discovery Miles 33 270 Ships in 12 - 17 working days

Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures-which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria-provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces. The second course, taught by Umberto Zannier, addresses the famous Pell equation-not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course, taught by Shou-Wu Zhang, originates in the Chowla-Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross-Zagier formula on Shimura curves and verify the Colmez conjecture on average.

Index Theory for Symplectic Paths with Applications (Hardcover, 2002 ed.): Yiming Long Index Theory for Symplectic Paths with Applications (Hardcover, 2002 ed.)
Yiming Long
R3,631 Discovery Miles 36 310 Ships in 10 - 15 working days

This book is based upon my monograph Index Theory for Hamiltonian Systems with Applications published in 1993 in Chinese, and my notes for lectures and courses given at Nankai University, Brigham Young University, ICTP-Trieste, and the Institute of Mathematics of Academia Sinica during the last ten years. The aim of this book is twofold: (1) to give an introduction to the index theory for symplectic matrix paths and its iteration theory, which form a basis for the Morse theoretical study on Hamilto nian systems, and to give applications of this theory to periodic boundary value problems of nonlinear Hamiltonian systems. Here the iteration theory means the index theory of iterations of periodic solutions and symplectic matrix paths. (2) to serve as a reference book on these topics. There are many different ways to introduce the index theory for symplectic paths in order to establish Morse type index theory of Hamiltonian systems. In this book, I have chosen a relatively elementary way, i.e., the homotopy classification method of symplectic matrix paths. It depends only on linear algebra, point set topology, and certain basic parts of linear functional analysis. I have tried to make this part of the book self-contained and at the same time include all of the major results on these topics so that researchers and students interested in them can read it without substantial difficulties, and can learn the main results in this area for their possible applications."

Asymptotic Theory of Finite Dimensional Normed Spaces - Isoperimetric Inequalities in Riemannian Manifolds (Paperback, 1st ed.... Asymptotic Theory of Finite Dimensional Normed Spaces - Isoperimetric Inequalities in Riemannian Manifolds (Paperback, 1st ed. 1986. Corr. 2nd printing 2001)
Vitali D Milman, Gideon Schechtman
R1,292 Discovery Miles 12 920 Ships in 10 - 15 working days

Vol. 1200 of the LNM series deals with the geometrical structure of finite dimensional normed spaces. One of the main topics is the estimation of the dimensions of euclidean and l^n p spaces which nicely embed into diverse finite-dimensional normed spaces. An essential method here is the concentration of measure phenomenon which is closely related to large deviation inequalities in Probability on the one hand, and to isoperimetric inequalities in Geometry on the other. The book contains also an appendix, written by M. Gromov, which is an introduction to isoperimetric inequalities on riemannian manifolds. Only basic knowledge of Functional Analysis and Probability is expected of the reader. The book can be used (and was used by the authors) as a text for a first or second graduate course. The methods used here have been useful also in areas other than Functional Analysis (notably, Combinatorics).

Computational Topology for Data Analysis (Hardcover): Tamal Krishna Dey, Yusu Wang Computational Topology for Data Analysis (Hardcover)
Tamal Krishna Dey, Yusu Wang
R1,558 Discovery Miles 15 580 Ships in 9 - 15 working days

Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions - like zigzag persistence and multiparameter persistence - and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.

Geometry - A High School Course (Hardcover, 2nd ed. 1988. Corr. 6th printing 2000): Serge Lang, Gene Murrow Geometry - A High School Course (Hardcover, 2nd ed. 1988. Corr. 6th printing 2000)
Serge Lang, Gene Murrow
R1,894 Discovery Miles 18 940 Ships in 10 - 15 working days

This text presents geometry in an exemplary, accessible and attractive form. The book emphasizes both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications. The book also teaches the student fundamental concepts and the difference between important reults and minor technical routines. Altogether, the text presents a coherent high school curriculum for the geometry course. There are many examples and exercises.

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 .. (Paperback)
Euclid; Oliver. Byrne
R678 Discovery Miles 6 780 Ships in 10 - 15 working days
Mathematical Window Patterns - The Art of Creating Translucent Designs Using Geometric Principles (Paperback): William Gibbs Mathematical Window Patterns - The Art of Creating Translucent Designs Using Geometric Principles (Paperback)
William Gibbs
R269 R218 Discovery Miles 2 180 Save R51 (19%) Ships in 9 - 15 working days

This book is a splendid collection of beautiful patterns which can be created by arranging regular shapes, usually rectangles so that they overlap in a symmetrical way. When the finished design is placed on a window, the light shines through one, two, three or more layers and the underlying structure is revealed. These patterns are specially attractive if made from tinted paper. Full descriptions and plans are included. A perfect activity when you wish to dress your classroom - e.g. pre-Christmas - mathematics and art in action!

Geometry Revisited (Paperback): H.S.M. Coxeter, S. L. Greitzer Geometry Revisited (Paperback)
H.S.M. Coxeter, S. L. Greitzer
R2,053 R1,635 Discovery Miles 16 350 Save R418 (20%) Ships in 12 - 17 working days

Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.

Fundamental Concepts of Geometry (Paperback, New edition): Bruce E. Meserve Fundamental Concepts of Geometry (Paperback, New edition)
Bruce E. Meserve
R388 R318 Discovery Miles 3 180 Save R70 (18%) Ships in 9 - 15 working days

Demonstrates in a clear and lucid manner the relationships between several types of geometry. This highly regarded work is a superior teaching text, especially valuable in teacher preparation, as well as providing an excellent overview of the foundations and historical evolution of geometrical concepts. Preface. Index. Bibliography. Exercises (no solutions). 98 illustrations.

Advanced Polyhedra 3 - The Compound of Five Cubes (Paperback): Gerald Jenkins, Magdalen Bear Advanced Polyhedra 3 - The Compound of Five Cubes (Paperback)
Gerald Jenkins, Magdalen Bear
R152 R123 Discovery Miles 1 230 Save R29 (19%) Ships in 9 - 15 working days

This beautiful model to cut out and glue together is the result of arranging five interpenetrating cubes in a highly symmetrical way Each cube is printed in its own colour and so it is easy to see that exactly two cubes meet at every vertex and that there are twelve surfaces defining each face of each cube. There is a strong internal frame and multiple divisions in the golden ratio to discover. Simple and logical instructions followed carefully yield extraordinary results.

Topics in Topology (Paperback, 1997 ed.): Stevo Todorcevic Topics in Topology (Paperback, 1997 ed.)
Stevo Todorcevic
R1,414 Discovery Miles 14 140 Ships in 10 - 15 working days

The book describes some interactions of topology with other areas of mathematics and it requires only basic background. The first chapter deals with the topology of pointwise convergence and proves results of Bourgain, Fremlin, Talagrand and Rosenthal on compact sets of Baire class-1 functions. In the second chapter some topological dynamics of beta-N and its applications to combinatorial number theory are presented. The third chapter gives a proof of the Ivanovskii-Kuzminov-Vilenkin theorem that compact groups are dyadic. The last chapter presents Marjanovic's classification of hyperspaces of compact metric zerodimensional spaces.

Felix Hausdorff - Gesammelte Werke Band VI - Geometrie, Raum und Zeit (Hardcover, 1. Aufl. 2021): Moritz Epple Felix Hausdorff - Gesammelte Werke Band VI - Geometrie, Raum und Zeit (Hardcover, 1. Aufl. 2021)
Moritz Epple
R2,583 Discovery Miles 25 830 Ships in 12 - 17 working days

Band VI der Hausdorff Edition enthält veröffentlichte Aufsätze sowie bislang unveröffentlichte Schriften und Notizen von Felix Hausdorff zur Erkenntniskritik von Zeit und Raum sowie zur nichteuklidischen Geometrie. Er dokumentiert Hausdorffs lebenslanges Interesse an diesen Themen und erlaubt einen neuen Einblick in die Herausbildung einer modernen Epistemologie der Mathematik und der Naturwissenschaften. Er zeigt auch, wie Hausdorffs mathematische, philosophische und literarische Tätigkeiten in seiner intellektuellen Laufbahn interagierten. Die historische Einführung des Herausgebers bietet umfassende Informationen über Hausdorffs philosophischen Horizont. Alle Leserinnen und Leser, die an der Entstehung der modernen Mathematik und ihrer philosophischen Reflexion interessiert sind, werden diesen Band der Gesammelten Werke Hausdorffs mit Gewinn lesen. Volume VI of the Hausdorff Edition contains published articles and previously unpublished material by Felix Hausdorff relating to the epistemology of time and space, as well as on noneuclidean geometry. It documents Hausdorff’s lifelong interest in these issues and provides new insight into the formation of a modern epistemology of mathematics and of science. The volume also documents how Hausdorff’s mathematical, philosophical and literary work interacted throughout his career. The editor’s historical introduction provides a wealth of information about Hausdorff’s philosophical background. Everyone interested in the emergence of modern mathematics and its philosophical contexts will profit from reading this volume of Hausdorff’s Collected Works.

Flatland - An Edition with Notes and Commentary (Paperback): Edwin A. Abbott, William F. Lindgren, Thomas F. Banchoff Flatland - An Edition with Notes and Commentary (Paperback)
Edwin A. Abbott, William F. Lindgren, Thomas F. Banchoff
R569 R477 Discovery Miles 4 770 Save R92 (16%) Ships in 10 - 15 working days

Flatland, Edwin Abbott Abbott s story of a two-dimensional universe, as told by one of its inhabitants who is introduced to the mysteries of three-dimensional space, has enjoyed an enduring popularity from the time of its publication in 1884. This fully annotated edition enables the modern-day reader to understand and appreciate the many dimensions of this classic satire. Mathematical notes and illustrations enhance the usefulness of Flatland as an elementary introduction to higher-dimensional geometry. Historical notes show connections to late-Victorian England and to classical Greece. Citations from Abbott s other writings as well as the works of Plato and Aristotle serve to interpret the text. Commentary on language and literary style includes numerous definitions of obscure words. An appendix gives a comprehensive account of the life and work of Flatland s remarkable author."

Geometry of the Unit Sphere in Polynomial Spaces (Paperback, 1st ed. 2023): Jesus Ferrer, Domingo Garcia, Manuel Maestre,... Geometry of the Unit Sphere in Polynomial Spaces (Paperback, 1st ed. 2023)
Jesus Ferrer, Domingo Garcia, Manuel Maestre, Gustavo A. Mun oz, Daniel L. Rodriguez, …
R1,355 Discovery Miles 13 550 Ships in 10 - 15 working days

This brief presents a global perspective on the geometry of spaces of polynomials. Its particular focus is on polynomial spaces of dimension 3, providing, in that case, a graphical representation of the unit ball. Also, the extreme points in the unit ball of several polynomial spaces are characterized. Finally, a number of applications to obtain sharp classical polynomial inequalities are presented. The study performed is the first ever complete account on the geometry of the unit ball of polynomial spaces. Nowadays there are hundreds of research papers on this topic and our work gathers the state of the art of the main and/or relevant results up to now. This book is intended for a broad audience, including undergraduate and graduate students, junior and senior researchers and it also serves as a source book for consultation. In addition to that, we made this work visually attractive by including in it over 50 original figures in order to help in the understanding of all the results and techniques included in the book.

Perlen der Mathematik - 20 geometrische Figuren als Ausgangspunkte fur mathematische Erkundungsreisen (German, Paperback, 2015... Perlen der Mathematik - 20 geometrische Figuren als Ausgangspunkte fur mathematische Erkundungsreisen (German, Paperback, 2015 ed.)
Claudi Alsina, Roger B. Nelsen; Translated by Thomas Filk
R869 Discovery Miles 8 690 Ships in 12 - 17 working days

Dieses Buch handelt von 20 geometrischen Figuren (Icons), die eine wichtige Rolle bei der Veranschaulichung mathematischer Beweise spielen. Alsina und Nelsen untersuchen die Mathematik, die hinter diesen Figuren steckt und die sich aus ihnen ableiten lasst. Jedem in diesem Buch behandelten Icons ist ein eigenes Kapitel gewidmet, in dem sein Alltagsbezug, seine wesentlichen mathematischen Eigenschaften sowie seine Bedeutung fur visuelle Beweise vieler mathematischer Satze betont werden. Diese Satze umfassen unter anderem auch klassische Ergebnisse aus der ebenen Geometrie, Eigenschaften der naturlichen Zahlen, Mittelwerte und Ungleichungen, Beziehungen zwischen Winkelfunktionen, Satze aus der Differenzial- und Integralrechnung sowie Ratsel aus dem Bereich der Unterhaltungsmathematik. Daruber hinaus enthalt jedes Kapitel eine Auswahl an Aufgaben, anhand derer die Leser weitere Eigenschaften und Anwendungen der Diagramme erkunden koennen. Das Buch ist fur alle geschrieben, die Freude an der Mathematik haben; Lehrkrafte und Dozenten der Mathematik werden in diesem Buch sehr nutzliche Beispiele fur Problemloesungen sowie umfangreiches Unterrichts- und Seminarmaterial zu Beweisen und mathematischer Argumentation finden.

Common Core Math Grade 7 Study Guide Workbook and Practice Test Questions with Detailed Answer Explanations [7th Edition]... Common Core Math Grade 7 Study Guide Workbook and Practice Test Questions with Detailed Answer Explanations [7th Edition] (Paperback)
Joshua Rueda
R647 Discovery Miles 6 470 Ships in 10 - 15 working days
The Plaid Model - (AMS-198) (Paperback): Richard Evan Schwartz The Plaid Model - (AMS-198) (Paperback)
Richard Evan Schwartz
R2,051 R1,230 Discovery Miles 12 300 Save R821 (40%) Ships in 9 - 15 working days

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz's Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites. Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called "the plaid model," has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics. The book includes an extensive computer program that allows readers to explore the materials interactively and each theorem is accompanied by a computer demonstration.

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