Geometry Books

Book SynopsisLockhart’s Mathematician’s Lament outlined how we introduce math to students in the wrong way. Measurement explains how math should be done. With plain English and pictures, he makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living.Trade ReviewA love song and a philosophical manifesto about the pleasures and frustrations, but mainly the pleasures, of doing math.In place of the usual boxed and high-lighted formulas and tricks, Measurement offers questions to be pondered. Lockhart invites readers to trade tutorial fake problems about actual objects, which lead students to abhor school mathematics, for real problems about fantastical objects, which lead mathematicians to love math. * Science *A conversational book about mathematics as an art that invites the reader to join in the fun. Sounding every bit the teacher whose love for his subject is infectious, he guides us through exercises in geometry and calculus—giving information and hints along the way while always encouraging us to ask, and answer, ‘Why?’ Lockhart does not try to make math seem easy; instead he wants his readers to understand that the difficulty brings rewards. * Scientific American *This invitation to tackle mathematical questions is infused with the joys of the rarefied reality of maths. Paul Lockhart largely avoids complex formulae and the wilder shores of jargon, opting instead for simple geometric drawings, lucid instructions and honest warnings about the hurdles. Covering size, shape, space and time, Lockhart, a maths teacher, gets through scores of problems, from showing that a cone in a hemisphere occupies half the volume to determining the size of the largest circle that can sit at the bottom of a parabola. Elegant, amusing and challenging. * Nature *This book forced me to use mental muscles I haven’t exercised in a long time, but it felt fantastic! Paul Lockhart is a mathematics evangelist; his passion for his subject is evident on every page, in every line. Looking at the subject of Measurement, he takes the reader on a journey that covers geometry, algebra, trigonometry, and on through differential calculus. He has a conversational tone and self-deprecating humor that sets the reader at ease. He understands that many people have been turned off of mathematics. His attitude is playful and joyous… Math is usually taught in such a compartmentalized way that it loses any meaning or coherence, and certainly any sense of wonder or beauty, but Measurement restores the connection. Paul Lockhart feels that math is the most beautiful, abstract and pure art form, and that it is actually fun! By the end of the book, you come to agree with him. * Sacramento Book Review *There are many books available these days on what mathematicians do, and this is one of the best… Lockhart’s approach is fresh and effective. * Choice *Lockhart presents math as an art and argues that just as there is no systematic way to create beautiful and meaningful art, there is also no method for producing beautiful and meaningful mathematical arguments. Doing mathematics, according to Lockhart, is to make a discovery (by, say, physical objects like string or rubber bands) and then to explain it in the simplest and most elegant way possible. Using illustrations of various shapes and mathematical formulas, he leads readers through several problems step by step, encouraging them to collaborate with others in working through the problem. Measuring, for example, is relative because it involves comparing the object being measured to another object. Measurement is only one of the many rivers in the ‘vast, ever-expanding jungle’ of mathematics, which for Lockhart satisfies our need to find patterns as well as our curiosity… His playful and ingenious approach not only takes the fear out of math but also elegantly illustrates that universe and the joy he finds in it. * Publishers Weekly *No matter what mathematical education you had, or didn’t have, you will be delighted by this enticing book if you take up Paul Lockhart’s invitation to engage in the mathematical sensibility that radiates from its pages, and try your own hand—not only at answering, but even more fruitfully, at formulating questions as you explore the world of mathematics.

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Book SynopsisThe Golden Ratio examines the presence of this divine number in art and architecture throughout history, as well as its ubiquity among plants, animals, and even the cosmos. This gorgeous book—with layflat dimensions that closely approximate the golden ratio—features clear, enlightening, and entertaining commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. This book invites you to take a new look at this timeless topic, with a compilation of research and information worthy of a text book, accompanied by over 200 beautiful color illustrations that transform this into the ultimate coffee table book. Author Gary Meisner shares the results of his twenty-year investigation and collaboration with thousands of people across the globe in dozens of professions and walks of life. The evidence will close the gaps of understanding related to many claims of the golden ratio’s appearances and applications, and present new findings to take our knowledge further yet. Whoever you are, and whatever you may know about this topic, you’ll find something new, interesting, and informative in this book, and may find yourself challenged to see, apply, and share this unique number of mathematics and science in new ways.

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Book SynopsisA perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning aTrade Review"Every prospective teacher should read it. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.' "--E. T. Bell, Mathematical Monthly "[This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected."--Herman Weyl, Mathematical Review "I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it."--Scientific Monthly "Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art."--A. C. Schaeffer, American Journal of Psychology "Every mathematics student should experience and live this book"--Mathematics Magazine "In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let's hope this classic will remain a source of inspiration for several generations to come."--A. Bultheel, European Mathematical Society

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Book SynopsisHit the geometry wall? Get up and running with this no-nonsense guide! Does the thought of geometry make you jittery? You''re not alone. Fortunately, this down-to-earth guide helps you approach it from a new angle, making it easier than ever to conquer your fears and score your highest in geometry. From getting started with geometry basics to making friends with lines and angles, you''ll be proving triangles congruent, calculating circumference, using formulas, and serving up pi in no time. Geometry is a subject full of mathematical richness and beauty. But it''s a subject that bewilders many students because it''s so unlike the math they''ve done beforeit requires the use of deductive logic in formal proofs. If you''re having a hard time wrapping your mind around what that even means, you''ve come to the right place! Inside, you''ll find out how a proof''s chain of logic works and even discover some secrets for getting past rough spots along the way. You don''t have to beTable of ContentsIntroduction 1 Part 1: Getting Started with Geometry Basics 5 Chapter 1: Introducing Geometry 7 Chapter 2: Building Your Geometric Foundation 17 Chapter 3: Sizing Up Segments and Analyzing Angles 31 Part 2: Introducing Proofs 43 Chapter 4: Prelude to Proofs 45 Chapter 5: Your Starter Kit of Easy Theorems and Short Proofs 55 Chapter 6: The Ultimate Guide to Tackling a Longer Proof 75 Part 3: Triangles: Polygons of the Three-Sided Variety 87 Chapter 7: Grasping Triangle Fundamentals 89 Chapter 8: Regarding Right Triangles 107 Chapter 9: Completing Congruent Triangle Proofs 125 Part 4: Polygons of the Four-or-More-Sided Variety 153 Chapter 10: The Seven Wonders of the Quadrilateral World 155 Chapter 11: Proving That You Have a Particular Quadrilateral 177 Chapter 12: Polygon Formulas: Area, Angles, and Diagonals 193 Chapter 13: Similarity: Same Shape, Different Size 211 Part 5: Working with Not-So-Vicious Circles 235 Chapter 14: Coming Around to Circle Basics 237 Chapter 15: Circle Formulas and Theorems 255 Part 6: Going Deep with 3-D Geometry 277 Chapter 16: 3-D Space: Proofs in a Higher Plane of Existence 279 Chapter 17: Getting a Grip on Solid Geometry 287 Part 7: Placement, Points, and Pictures: Alternative Geometry Topics 303 Chapter 18: Coordinate Geometry 305 Chapter 19: Changing the Scene with Geometric Transformations 323 Chapter 20: Locating Loci and Constructing Constructions 343 Part 8: The Part of Tens 361 Chapter 21: Ten Things to Use as Reasons in Geometry Proofs 363 Chapter 22: Ten Cool Geometry Problems 369 Index 377

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Book SynopsisAcross the Islamic world, illuminating Korans from Morocco to Malaysia, and adorning mosques, mausoleums and palaces, are hidden some of the most exquisite geometrical devices ever conceived by man. In this excellent little book, geometer Daud Sutton unravels the mystery of Islamic patterns, explaining where they come from, how to draw them, and hinting at the Divine messages they encode. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

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Book SynopsisHow do you divide a line into three? Or five? Or seven? Is there a simple way to marry harmony and geometry? What is the secret diagram alluded to by writers of antiquity? In this groundbreaking book, philosopher Adam Tetlow reveals the long lost Helicon, the master diagram of the ancient arts and crafts.Watch in astonishment as this magical geometric figure produces simple fractions, musical harmonies, Pythagorean triangles, perspective and more. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

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Book SynopsisHow do you draw a heptagon? What about a heptakaidecagon? How do you fit circles perfectly into triangles? And around them? If the computer is down - could you do it with ruler and compass? In this unique little book, Andrew Sutton guides you through the once treasured principles of ruler and compass constructions, used for centuries by architects, carpenters, stonemasons and master craftsmen. Designed to last until the lights go out, this is a timeless book. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

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Book Synopsis'This book is a useful reference for faculty members involved in contest preparation or teaching Euclidean geometry at the college level.'MAA ReviewsThis new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems.This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry.Table of ContentsCongruent Triangles; Right-Angle Triangles; Quadrilaterals; Circumcenter; Angle Bisector; Incenter and Excenter; Similar Triangles; Area of Triangles; Intercept Theorem; Pythagoras' Theorem; Ceva's Theorem; Centroid and Orthocenter; Menelaus' Theorem; Circles and Angles; Simson's Line; Nine-point Circle; Intercept Chord Theorem; Tangent-Secant Theorem; Radical Axes; Commonly-Used Facts; Geometry Problems in Competitions (Searching for Clues and Insights; Developing Strategies).

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Book SynopsisA straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.

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Book SynopsisLucid, well-written introduction to elementary geometry usually included in undergraduate and first-year graduate courses in mathematics. Topics include vector algebra in the plane, circles and coaxial systems, mappings of the Euclidean plane, similitudes, isometries, mappings of the intensive plane, much more. Includes over 500 exercises.

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Book SynopsisCollection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and more. Arranged in order of difficulty. Detailed solutions.

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Book SynopsisIn the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature.It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Table of ContentsIntroduction ; 1. What is symmetry? ; 2. Origins of symmetry ; 3. Types of symmetry ; 4. Structure of groups ; 5. Groups and games ; 6. Nature's patterns ; 7. Nature's laws ; 8. Atoms of symmetry ; Further reading ; References

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Book SynopsisOlive Whicher's groundbreaking book presents an accessible - non-mathematician's - approach to projective geometry. Profusely illustrated, and written with fire and intuitive genius, this work will be of interest to anyone wishing to cultivate the power of inner visualization in a realm of structural beauty. Whicher explores the concepts of polarity and movement in modern projective geometry as a discipline of thought that transcends the limited and rigid space and forms of Euclid, and the corresponding material forces conceived in classical mechanics. Rudolf Steiner underlined the importance of projective geometry as, 'a method of training the imaginative faculties of thinking, so that they become an instrument of cognition no less conscious and exact than mathematical reasoning'. This seminal approach allows for precise scientific understanding of the concept of creative fields of formative (or etheric) forces at work in nature - in plants, animals and in the human being.

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Book SynopsisThis book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quadratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and graduate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.Table of ContentsPreface to the Second Edition.- Preface to the First Edition.- A Study Guide.- 1. Methods of Proof.- 2. Algebra.- 3. Real Analysis.- 4. Geometry and Trigonometry.- 5. Number Theory.- 6. Combinatorics and Probability.- Solutions.- Index of Notation.- Index.

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Book SynopsisAn essential introduction to discrete and computational geometryDiscrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only) Trade Review"Discrete and Computational Geometry meets an urgent need for an undergraduate text bridging the theoretical sides and the applied sides of the field. It is an excellent choice as a textbook for an undergraduate course in discrete and computational geometry! The presented material should be accessible for most mathematics or computer science majors in their second or third year in college. The book also is a valuable resource for graduate students and researchers."--Egon Schulte, Zentralblatt MATH "[W]e recommend this book for an undergraduate course on computational geometry. In fact, we hope to use this book ourselves when we teach such a class."--Brittany Terese Fasy and David L. Millman, SigAct News

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Book SynopsisDas Ziel des Buches ist eine umfassende Einführung sowohl in die geometrische wie die algebraische Topologie. Dabei werden lediglich gute Kenntnisse aus dem 1. Studienjahr in der Mathematik vorausgesetzt, die über die Analysis und lineare Algebra kaum hinausgehen; alle weiteren Hilfsmittel, wie die Grundbegriffe der mengentheoretischen Topologie, die Theorie der topologischen Gruppen und die algebraischen Grundlagen werden ebenfalls ausführlich dargestellt. Im Vordergrund stehen jedoch nicht die hieraus hervorgehenden technischen Apparate, sondern die geometrischen Fragestellungen, die erst den Anlass zu ihrer Entwicklung gaben.Table of ContentsEinführung - Allgemeine Topologie - Homotopie - Lie-Gruppen und homogene Räume - Homologie

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Book SynopsisWinner, Euler Book Prize, awarded by the Mathematical Association of America. With over 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion & quantum computing.Trade Review"This beautifully and profusely illustrated second edition of "Crocheting Adventures with Hyperbolic Planes" is a unique and extraordinary instructional manual and guide that is unreservedly recommended for personal, professional, community, and academic library"—James A. Cox, Editor-in-Chief, Midwest Book Review"This book shows just how fun deep mathematics can be and reveals the importance of thinking of mathematics with your hands, eyes and body — not just the brain. More importantly, it shows how good mathematics needs input from all sorts of people and cultures, in particular here the geometry essential to fibre arts."—Professor Edmund Harris, University of Arkansas, co-author of Patterns/Visions of the Universe with Alex Bellos"This is a lovely introduction to hyperbolic geometry and how to represent it in a tactile, playful way. The book takes you through a wonderful history of both the maths and the art, exploring how we have perceived the world around us over the centuries and how this applies today. You get to explore the concepts with your own hands and really see how it all works. As both a mathematician and a crocheter I’m itching to make my own hyperbolic planes and use them in all sorts of places!"—Samantha Durbin, The Royal Institution of Great BritainThis is the second edition of the book Crocheting Adventures with Hyperbolic Planes, which won the 2012 Euler Book Prize[. . . . ]This book presents an amazing hybrid approach to two seemingly different audiences: mathematicians and fiber artists.For the mathematician, the book presents a tactile approach to the very theoretical concepts in hyperbolic geometry, providing clear directions on how to construct objects in hyperbolic geometry. This book is a great introduction to hyperbolic geometry for anyone wanting to know about the subject and would be a great asset to any undergraduate math student studying non-Euclidean geometries.For the fiber artist interested in crochet, the book does a great job of explaining very advanced mathematics in an inviting and understanding way, encouraging artists to pursue more mathematics to incorporate into their creative works. It also provides insight into the creative process of developing mathematics, showing that mathematicians and artists both use very creative processes.This book is extremely well-written and organized. [. . . .] The book also weaves together the history and development of non-Euclidean geometries and their connections to many different areas such as art, biology and nature, physics, computer science, music, chemistry, and architecture. Each chapter has a clear purpose, and the imagery really complements the writing. At the end of the book, there is a section on how to make models. For the artist interested in crochet, the directions are a little bit more mathematical, but they are presented clearly. It will definitely be quite different than any pattern you have read before! For the mathematician who would like to have some tactile hyperbolic models, there are directions for making models out of paper as well. This book is more than just a great introduction to hyperbolic geometry, it is a great book to showcase the work of mathematicians and the process of discovering mathematics. As mathematicians, we often only present our finished and most-polished versions of our work, and we don’t let many people see the process by which this polished mathematics was developed.This book gives the reader insight into that process and illuminates the creativity involved in the development of mathematics.—Rachelle Bouchat, MAA Reviews October 2019Praise for previous edition"2012 Euler Book Prize Winner ...elegant, novel approach... that is perfectly capable of standing on its mathematical feet as a clear, rigorous, and beautifully illustrated introduction to hyperbolic geometry. It is truly a book where art, craft, science, and mathematics come together in perfect harmony."—MAA, December 2011"This book is richly illustrated with photographs and colored illustrations and it has been produced on high-quality paper. It would be a useful addition to the library of a school or university."—Gazette-Australia, May 2011"Daina's crochet models break through the austere, formal stereotype of mathematics and present a path to a whole-brain understanding of a beautiful cluster of simple and significant ideas. The book helps to change the way of thinking about mathematics - an art of human understanding!"—Corina Mohorianu, Zentralblatt MATH, September 2009"The models illustrated in this book are prime examples of art influencing mathematics. Daina provides the necessary instructions for even novices to crochet and create hyperbolic models of their own."—Swami Swaminathan, Canadian Mathematical Society Notes, October 2009"It lays out the fundamental knowledge for appreciation of tactile hyperbolic manifolds cautiously and accessibly. ... an enjoyable read for a general audience."—David Jacob Wildstrom, Mathematical Reviews, December 2009Table of ContentsForeword by William Thurston. Introduction. What Is the Hyperbolic Plane? Can We Crochet It?. What Can You Learn from Your Model?. Four Strands in the History of Geometry. Tidbits from the History of Crochet. What is Non-Euclidean Geometry?. Pseudosphere. Metamorphoses of the Hyperbolic Plane. Other Surfaces with Negative Curvature. Looking for Applications of Hyperbolic Geometry. Hyperbolic Crochet goes Viral. Appendix: How to Make Models.

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Book SynopsisTrade Review"There is something intoxicating about seeing one truth revealed in so many ways. It all makes for hours of glorious mathematical distraction."—Ben Longstaff, New Scientist"A popular account of important ideas and their development."—Peter M. Neumann, Times Higher Education Supplement"If one has never read a book by Eli Maor, this book is a great place to start."—J. Johnson, Choice"Maor expertly tells the story of how this simple theorem known to schoolchildren is part and parcel of much of mathematics itself."—Amy Shell-Gellasch, MAA Reviews"At last, a popular book that isn't afraid to print a mathematical formula in all its symbolic glory! Thanks to Eli Maor for proving—in his delightful, playful way—the eternal importance of a three-sided idea as old as humankind."—Dava Sobel, author of Longitude

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Book SynopsisEvery colorful page of Christopher Danielson’s children’s picture book, Which One Doesn’t Belong?, contains a thoughtfully designed set of four shapes. Each of the shapes can be a correct answer to the question “Which one doesn’t belong?” Because all their answers are right answers, students naturally shift their focus to justifications and arguments based on the shapes’ geometric properties. In the companion teacher’s guide, Danielson shows how to facilitate rich discussions and teach mathematical argumentation using Which One Doesn’t Belong? He models how to listen closely and respectfully to students’ ideas about shapes. Danielson synthesizes research about how children learn geometry, discusses the role of geometry in the mathematics curriculum, and gives plenty of practical advice about different ways to implement Which One Doesn’t Belong? in classrooms. He also discusses the mathematical ideas likely to emerge on each page and—drawing from his direct experience using Which One Doesn’t Belong? at several different grade levels—helps teachers anticipate and think about students’ likely answers. Most curricula treat geometry as little more than vocabulary lessons. Which One Doesn’t Belong? and its accompanying guide are powerful, flexible resources teachers can use to provoke lively discussions and deep learning about shapes with students of all ages.

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Book SynopsisAfter the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion 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 Poincaré in 2015. The chapters in this volume cover a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. It is addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.Trade Review'The essays are self-contained, providing motivation to read selectively. Examples in each chapter illustrate the usefulness of these new notions of space … Recommended.' M. Clay, Choice MagazineTable of ContentsIntroduction Mathieu Anel and Gabriel Catren; Part I. Differential geometry: 1. An Introduction to diffeology Patrick Iglesias-Zemmour; 2. New methods for old spaces: synthetic differential geometry Anders Kock; 3. Microlocal analysis and beyond Pierre Schapira; Part II. Topology and algebraic topology: 4. Topo-logie Mathieu Anel and André Joyal; 5. Spaces as infinity-groupoids Timothy Porter; 6. Homotopy type theory: the logic of space Michael Shulman; Part III. Algebraic geometry: 7. Sheaves and functors of points Michel Vaquié; 8. Stacks Nicole Mestrano and Carlos Simpson; 9. The geometry of ambiguity: an introduction to the ideas of derived geometry Mathieu Anel; 10. Geometry in dg categories Maxim Kontsevich.

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Book SynopsisWhat sort of things happen when space crystallises? Why were primordial sages fascinated with five simple forms? Does the three-dimensional jigsaw fit simply together? If so how? Find out about one of the languages spoken throughout the universe! An understanding of the Platonic Solids, and their close cousins, the Archimedean Solids has long been required of students seeking entry into ancient wizdom schools. This book, illustrated by the author, is a beautiful introduction to three-dimensional mathemagical space. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

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Book SynopsisThe original edition of The Geometry of Musical Rhythm was the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explained how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly disparate fields. The book also introduced the distance approach to phylogenetic analysis and illustrated its application to the study of musical rhythm. The new edition retains all of this, while also adding 100 pages, 93 figures, 225 new references, and six new chapters covering topics such as meter and metric complexity, rhythmic grouping, expressive timbre and timing in rhythmic performance, and evolution phylogenetic analysis of ancient Greek paeonic rhythms. In addition, further context is provided to give the reader a fuller and richer insight into the historical connections between music and mathematics.Trade Review"The late Godfried Toussaint studied the rhythms of the world like a gold panner, collecting with meticulousness and passion all the motifs that different cultures have given birth to. Thanks to his skill as a mathematician, he extracted fascinating properties from them. There is no doubt that this unique book will survive for a very long time."—Marc Chemillier, Directeur d'études, École des Hautes Études en Sciences Sociales"Through the original use of distance geometry for analyzing musical rhythm and the visualization of rhythms as cyclic polygons, Gottfried Tousssaint’s fascinating book will be extremely valuable to any researcher involved in in the field of rhythm."—Simha Arom, Ethnomusicologist "The new edition of The Geometry of Musical Rhythm takes us further along Godfried Toussaint’s journey through the world’s rhythms. There are new discussions of metric complexity, rhythm visualization, rhythmic performance, and the evolution of rhythmic patterns. Almost every chapter has been expanded and informed by the latest scholarship in music theory, music psychology, ethnomusicology, and music informatics. Specialists and lay readers alike will find this edition even more engaging and valuable than the first, giving us even more reasons to delight in what makes a "good" rhythm good."— Professor Justin London, Carleton College "A unique and seminal work of original and meticulously detailed scholarship, this newly published second edition of "The Geometry of Musical Rhythm : What Makes a "Good" Rhythm Good?" is unreservedly recommended as a core addition to both college and university library collections."—Midwest Book ReviewPraise for the previous edition"Toussaint’s Geometry presents a whirlwind tour of the world’s rhythms … For a reader interested in musical rhythm, Geometry is a great introduction to the computer science and mathematics of rhythm. For a reader interested in algorithms and mathematical reasoning, the musical focus provides compelling examples lying at the intersection of the arts and the sciences."—William A. Sethares, Journal of Mathematics and the Arts, 2014"… a delightful, informative, and innovative study in the geometric interpretation of rhythm. … It is a pleasure to find an author who has such good command of mathematics and music and who can explain their interconnections with such literary skill. I recommend this book wholeheartedly to every serious student of geometry and music."—Ilhan M. Izmirli, Mathematical Reviews, March 2014"This dynamic fluid presentation of mathematics is exactly what our undergraduate and graduate students need. … I would highly recommend this book for everyone."—Russell Jay Hendel, MAA Reviews, May 2013"The author of this book, the Canadian professor of computer science Godfried Toussaint, who died in 2019, describes music as one of his passions. This is apparent throughout this work, which draws on his wide knowledge of different musical styles from all cultures.The book is very informative about a wide range of styles of music and musical instruments and their history. If you have an interest in music and in a range of areas of mathematics, you are likely to find plenty of topics of interest."—Mathematical Gazette"The late Godfried Toussaint studied the rhythms of the world like a gold panner, collecting with meticulousness and passion all the motifs that different cultures have given birth to. Thanks to his skill as a mathematician, he extracted fascinating properties from them. There is no doubt that this unique book will survive for a very long time."—Marc Chemillier, Directeur d'études, École des Hautes Études en Sciences Sociales"Through the original use of distance geometry for analyzing musical rhythm and the visualization of rhythms as cyclic polygons, Gottfried Tousssaint’s fascinating book will be extremely valuable to any researcher involved in in the field of rhythm."—Simha Arom, Ethnomusicologist "The new edition of The Geometry of Musical Rhythm takes us further along Godfried Toussaint’s journey through the world’s rhythms. There are new discussions of metric complexity, rhythm visualization, rhythmic performance, and the evolution of rhythmic patterns. Almost every chapter has been expanded and informed by the latest scholarship in music theory, music psychology, ethnomusicology, and music informatics. Specialists and lay readers alike will find this edition even more engaging and valuable than the first, giving us even more reasons to delight in what makes a "good" rhythm good."— Professor Justin London, Carleton College "A unique and seminal work of original and meticulously detailed scholarship, this newly published second edition of "The Geometry of Musical Rhythm : What Makes a "Good" Rhythm Good?" is unreservedly recommended as a core addition to both college and university library collections."—Midwest Book ReviewPraise for the previous edition"Toussaint’s Geometry presents a whirlwind tour of the world’s rhythms … For a reader interested in musical rhythm, Geometry is a great introduction to the computer science and mathematics of rhythm. For a reader interested in algorithms and mathematical reasoning, the musical focus provides compelling examples lying at the intersection of the arts and the sciences."—William A. Sethares, Journal of Mathematics and the Arts, 2014"… a delightful, informative, and innovative study in the geometric interpretation of rhythm. … It is a pleasure to find an author who has such good command of mathematics and music and who can explain their interconnections with such literary skill. I recommend this book wholeheartedly to every serious student of geometry and music."—Ilhan M. Izmirli, Mathematical Reviews, March 2014"This dynamic fluid presentation of mathematics is exactly what our undergraduate and graduate students need. … I would highly recommend this book for everyone."—Russell Jay Hendel, MAA Reviews, May 2013Table of ContentsWhat Is Rhythm?. A Steady Beat. Timelines, Ostinatos, and Meter. The Wooden Claves. The Iron Bells. The Clave Son. Six Distinguished Rhythm Timelines. The Distance Geometry of Rhythm. Classification of Rhythms. Binary and Ternary Rhythms. The Isomorphism of Rhythm and Scale. Binarization, Ternarization, and Quantization of Rhythms. Syncopated Rhythms. Necklaces and Bracelets. Rhythmic Oddity. Off-Beat Rhythms. Rhythm Complexity. Dispersion Problems and Maximally Even Rhythms. Euclidean Rhythms. Leap Years: The Rhythm of the Stars. Approximately Even Rhythms. Rhythms and Crystallography. Complementary Rhythms. Radio Astronomy and Flat Rhythms. Deep Rhythms. Shelling Rhythms. Phantom Rhythms. Reflection Rhythms and Rhythmic Canons. Toggle Rhythms. Symmetric Rhythms. Odd Rhythms. Other Representations of Rhythm. Rhythmic Similarity and Dissimilarity. Regular and Irregular Rhythms. Evolution and Phylogenesis of Musical Rhythm. Rhythmic Combinatorics. What Makes the Clave Son Such a Good Rhythm?. The Origin, Evolution, and Migration of the Clave Son. Epilogue. References. Index.

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Book SynopsisHow the Greek temples and Greek statues were entirely based upon principles of sacred geometry.

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Book Synopsis- The only program that supports the Common Core State Standards throughout four-years of high school mathematics with an unmatched depth of resources and adaptive technology that helps you differentiate instruction for every student. * Connects students to math content with print, digital and interactive resources. * Prepares students to meet the rigorous Common Core Standards with aligned content and focus on Standards of Mathematical Practice. * Meets the needs of every student with resources that enable you to tailor your instruction at the classroom and individual level. * Assesses student mastery and achievement with dynamic, digital assessment and reporting. Includes Print Student EditionTable of ContentsChapter 0 Preparing for Geometry0-1Changing Units of Measure Within Systems 0-2Changing Units of Measure Between Systems0-3Simple Probability 0-4Algebraic Expressions0-5Linear Equations 0-6Linear Inequalities 0-7Ordered Pairs 0-8Systems of Linear Equations 0-9Square Roots and Simplifying Radicals Unit 1 Geometric StructureChapter 1 Tool of Geometry1-1Points, Lines, and Planes Extend 1-1 Geometry Lab: Describing What You See1-2Linear MeasureExtend 1-2 Extension Lesson: Precision and Accuracy 1-3Distance and Midpoints 1-4Angle Measure 1-5Angle Relationships Extend 1-5 Geometry Lab: Constructing Perpendiculars1-6Two-Dimensional Figures Extend 1-6 Geometry Software Lab: Two-Dimensional Figures 1-7Three-Dimensional FiguresExtend 1-7 Geometry Lab: Two-Dimensional Representations of Three-Dimensional Objects Chapter 2 Reasoning and Proof2-1Inductive Reasoning and Conjecture2-2Logic 2-3Conditional StatementsExtend 2-3 Geometry Lab: Biconditional Statements2-4Deductive Reasoning Explore 2-5 Geometry Lab: Necessary and Sufficient Conditions 2-5Postulates and Paragraph Proofs2-6Algebraic Proof2-7Proving Segment Relationships2-8Proving Angle RelationshipsChapter 3 Parallel and Perpendicular Lines3-1Parallel Lines and TransversalsExplore 3-2 Geometry Software Lab: Angles and Parallel Lines3-2Angles and Parallel LinesExplore 3-3 Graphing Technology Lab: Investigating Slope3-3Slopes of Lines3-4Equations of LinesExtend 3-4 Geometry Lab: Equations of Perpendicular Bisectors3-5Proving Lines Parallel 3-6Perpendiculars and DistanceUnit 2 CongruenceChapter 4 Congruent Triangles4-1Classifying Triangles Explore 4-2 Geometry Lab: Angles of Triangles4-2Angles of Triangles4-3Congruent Triangles 4-4Proving Triangles Congruent: SSS, SAS Extend 4-4 Geometry Lab: Proving Constructions4-5Proving Triangles Congruent: ASA, AAS Extend 4-5 Geometry Lab: Congruence in Right Triangles 4-6Isosceles and Equilateral TrianglesExplore 4-7 Graphing Technology Lab: Congruence Transformations4-7Congruence Transformations 4-8Triangles and Coordinate Proof Chapter 5 Relationships in TrianglesExplore 5-1 Geometry Lab: Constructing Bisectors5-1Bisectors of TrianglesExplore 5-2 Geometry Lab: Constructing Medians and Altitudes5-2Medians and Altitudes of Triangles 5-3Inequalities in One Triangle Explore 5-4 Geometry Lab: Matrix Logic5-4Indirect Proof Explore 5-5 Graphing Technology Lab: The Triangle Inequality5-5The Triangle Inequality5-6Inequalities in Two TrianglesChapter 6 Quadrilaterals6-1Angles of PolygonsExtend 6-1 Spreadsheet Lab: Angles of Polygons6-2ParallelogramsExplore 6-3 Graphing Technology Lab: Parallelograms6-3Tests for Parallelograms 6-4Rectangles6-5Rhombi and Squares6-6Trapezoids and KitesUnit 3 SimilarityChapter 7 Proportions and Similarity7-1Ratios and ProportionsExtend 7-1 Graphing Technology Lab: Fibonacci Sequence and Ratios7-2Similar Polygons7-3Similar TrianglesExtend 7-3 Geometry Lab: Proofs of Parallel and Perpendicular Lines7-4Parallel Lines and Proportional Parts7-5Parts of Similar TrianglesExtend 7-5 Geometry Lab: Fractals7-6Similarity Transformations7-7Scale Drawings and ModelsChapter 8 Right Triangles and Trigonometry8-1Geometric MeanExplore 8-2 Geometry Lab: Proofs Without Words8-2The Pythagorean Theorem and Its ConverseExtend 8-2 Geometry Lab: Coordinates in Space8-3Special Right TrianglesExplore 8-4 Graphing Technology Lab: Trigonometry8-4TrigonometryExtend 8-4 Graphing Technology Lab: Secant, Cosecant, and Cotangent8-5Angles of Elevation and Depression8-6The Law of Sines and Law of CosinesExtend 8-6 Geometry Lab: The Ambiguous Case8-7VectorsExtend 8-7 Geometry Lab: Adding VectorsChapter 9 Transformations and Symmetry9-1Reflections9-2TranslationsExplore 9-3 Geometry Lab: Rotations9-3RotationsExtend 9-3 Geometry Lab: Solids of Revolution Explore 9-4 Geometry Software Lab: Compositions of Transformations9-4Compositions of TransformationsExtend 9-4 Geometry Lab: Tessellations9-5SymmetryExtend 9-5 Geometry Lab: Exploring Constructions with a Reflective DeviceExplore 9-6 Geometry Software Lab: Dilations9-6DilationsExtend 9-6 Geometry Lab: Establishing Triangle Congruence and SimilarityUnit 4 MeasurementChapter 10 Circles10-1Circles and Circumference10-2Measuring Angles and Arcs10-3Arcs and Chords10-4Inscribed Angles10-5TangentsExtend 10-5 Geometry Lab: Inscribed and Circumscribed Circles10-6Secants, Tangents, and Angle Measures10-7Special Segments in a Circle10-8Equations of CirclesExtend 10-8 Geometry Lab: ParabolasChapter 11 Areas of Polygons and Circles11-1Areas of Parallelograms and TrianglesExplore 11-2 Graphing Technology Lab: Areas of Trapezoids, Rhombi, and Kites11-2Areas of Trapezoids, Rhombi, and KitesExtend 11-2 Geometry Lab: Population Density11-3Areas of Circles and SectorsExplore 11-4 Geometry Lab: Investigating Areas of Regular Polygons11-4Areas of Regular Polygons and Composite FiguresExtend 11-4 Geometry Lab: Regular Polygons on the Coordinate Plane11-5Areas of Similar FiguresChapter 12 Extending Surface Area and VolumeExplore 12-1 Geometry Lab: Solids Formed by Translations12-1Representations of Three-Dimensional FiguresExtend 12-1 Geometry Lab: Topographic Maps12-2Surface Areas of Prisms and Cylinders12-3Surface Areas of Pyramids and Cones12-4Volumes of Prisms and CylindersExtend 12-4 Graphing Technology Lab: Changing Dimensions12-5Volumes of Pyramids and Cones12-6Surface Areas and Volumes of SpheresExtend 12-6 Geometry Lab: Locus and Spheres12-7Spherical GeometryExtend 12-7 Geometry Lab: Navigational Coordinates12-8Congruent and Similar SolidsChapter 13 Probability and Measurement13-1Representing Sample Spaces13-2Probability with Permutations and Combinations13-3Geometric Probability13-4Simulations13-5Probabilities of Independent and Dependent EventsExtend 13-5 Geometry Lab: Two-Way Frequency Tables13-6Probabilities of Mutually Exclusive EventsExtend 13-6 Geometry Lab: Graph Theory

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Book Synopsis

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Book Synopsis

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Book Synopsis

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Book Synopsis

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Trade Review"Morgan’s book offers the best access I know into this difficult subject. It won’t make the reader an expert, but it does open the door to more detailed treatments. An excellent bibliography is provided." --MAA ReviewsTable of Contents1. Geometric Measure Theory2. Measures3. Lipschitz Functions and Rectifiable Sets4. Normal and Rectifiable Currents5. The Compactness Theorem and the Existence of Area-Minimizing Surfaces6. Examples of Area-Minimizing Surfaces7. The Approximation Theorem8. Survey of Regularity Results9. Monotonicity and Oriented Tangent Cones10. The Regularity of Area-Minimizing Hypersurfaces11. Flat Chains Modulo v, Varifolds, and (M,E,)-Minimal Sets12. Miscellaneous Useful Results13. Soap Bubble Clusters14. Proof of Double Bubble Conjecture15. The Hexagonal Honeycomb and Kelvin Conjectures16. Immiscible Fluids and Crystals17. Isoperimetric Theorems in General Codimension18. Manifolds with Density and Perelman's Proof of the Poincaré Conjecture19. Double Bubbles in Spheres, Gauss Space, and Tori20. The Log-Convex Density Conjecture21. Solutions to Exercises

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Book SynopsisThis manual contains a wealth of hands-on activities correlated with chapters in the text. These activities promote learning of concepts and provide valuable hands-on geometry experience.Table of ContentsChapter 1 Activity 1.1: “Division” Problems in Geometry Activity 1.2: The Soma Cube Problem Activity 1.3: Looking for Patterns Activity 1.4: The Painted Cube Problem Chapter 2 Activity 2.1: Quadrilaterals Activity 2.2: The Tangram Puzzle Activity 2.3: Symmetry Activity 2.4: Tessellations Activity 2.5: Angle Measures in Polygons Activity 2.6: Polyhedra Models Activity 2.7: Dimensional Analysis Chapter 3 Activity 3.1: Perimeter and Area Activity 3.2: Developing Area Formulas Activity 3.3: Developing Circle Formulas Activity 3.4: The Pythagorean Theorem Activity 3.5: The Tangram Puzzle Revisited Activity 3.6: Surface Area Activity 3.7: Volume Activity 3.8: Surface Area and Volume of Cylinders Activity 3.9: The Soup Can Problem Chapter 4 Activity 4.1: The Triangle Inequality and Revisiting the Pythagorean Theorem Activity 4.2: Paper Folding “Constructions” Activity 4.3: SAS Versus SSA Activity 4.4: Exploring More Triangles Chapter 5 Activity 5.1: Properties of Quadrilaterals Activity 5.2: Subdividing Line Segments Activity 5.3: Exploring Area and Constructions of Kites Chapter 6 Activity 6.1: Introduction to Similar Triangles Activity 6.2: Approximating Heights and Distances Chapter 7 Activity 7.1: Circle Description Activity 7.2: More Paper Folding “Constructions” Activity 7.3: Reconstructing a Circle Chapter 8 Activity 8.1: Slopes of Lines Activity 8.2: Midsegments and the Midquad Chapter 9 Activity 9.1: Tracing Paper Isometries Activity 9.2: Size Transformations ANSWERS TO ACTIVITIES MATERIALS PAGES

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Book SynopsisIn Euclid''s Window, Leonard Mlondinow takes us on a brilliantly entertaining journey through 3,000 years of genius and geometry, introducing the people who revolutionized the way we see the world around us. Ever since Pythagoras hatched a ''little scheme'' to invent a set of rules describing the entire universe, scientists and mathematicians have tried to seek order in the cosmos: Euclid, who in 300BC defined the nature of space; Descartes, a fourteenth-century gambler and idler who invented the graph; Gauss, the fifteen-year-old genius who discovered that space is curved; Einstein, who added time to the equation; and Witten, who ushered in today''s weird new world of extra, twisted dimensions. They all show how geometry is the key to understanding the universe. Once you have viewed life through Euclid''s Window, it will never be the same again... ''Elegant, attractive and concise ... also very readable. Buy it''  Ian Table of ContentsPart 1 The story of Euclid: the first revolution; the geometry of taxation; among the seven sages; the secret society; Euclid's manifesto; a beautiful woman, a library, and the end of civilization. Part 2 The story of Descartes: the revolution in place; the origin of latitude and longitude; the legacy of the rotten Romans; the discreet charm of the graph; a soldier's story; iced by the snow queen. Part 3 The story of Gauss: the curved space revolution; the trouble with Ptolemy; a Napoleonic hero; the fall of the fifth postulate; lost in hyperbolic space; some insects called the human race; a tale of two aliens; after 2000 years, a face-lift. Part 4 The story of Einstein: revolution at the speed of light; relativity's other Albert; the stuff of space; probationary technical expert, third class; a relatively Euclidean approach; Einstein's apple; from inspiration to perspiration; blue hair triumphs. Part 5 The story of Witten: the weird revolution; ten things I hate about your theory; the necessary uncertainty of being; clash of the Titans; a message in a Kaluza-Klein bottle; the birth of strings; particles, schmarticles!; the trouble with strings; the theory formerly known as strings.

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Book SynopsisThe international bestseller - a whip-smart, entertaining exploration of the geometry that underlies our world, from the author of How Not to Be WrongHow should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play chess? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? The answers to all these questions can be found in geometry.If you''re like most people, geometry is a dimly-remembered exercise, handed down from the ancients, that you gladly left behind in school. It seemed to be a tortuous way of proving some fact about triangles that was obvious to you in the first place. That''s not geometry. OK, it is geometry, but only a tiny part, that has as much to do with the modern, fast-moving discipline as conjugating a verb has to do with a great novel.In Shape, SundTrade ReviewThis mind-bending book will change how you see the world (Five stars) -- Simon Ings * Telegraph *Shape is a triumph of mathematical exposition, exposing profound truths - from the nature of distance to the predictability of randomness - as well as profound mistakes - from historical misattributions to Supreme Court justice hardheadedness - with eloquence and hilarious wit. Ellenberg's evident affection for both his subject and his reader makes us feel like the lucky ones who get to hear him hold forth in an intimate setting about his favorite subject, mathematics -- Cathy O'NeilEllenberg's skill as a storyteller, combined with a natural ability to spot otherwise obscure connections, enables him to capitalize on geometry as math's gateway drug... A deeply enjoyable and insightful book -- Matt Parker * New York Times *Ellenberg, in both his arguments and his enthusiasm, is persuasive -- Michael Prodger * New Statesman *Serious mathematics at its intriguing, transporting best . . . [A] humorous, anecdotally rich dive into numerous mathematical theories * Kirkus *Unreasonably entertaining... reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning -- Parul Sehgal * New York Times *Droopy cheese and the curve of the Earth, the everyday and the cosmic, are beautifully interwoven in the mathematician Jordan Ellenberg's new book Shape -- Derek Thompson * Atlantic *Almost anyone is likely to enjoy Ellenberg's prose, and mind * Harvard Magazine *

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Book SynopsisThis book provides the first lucid and accessible account to the modern study of the geometry of four-manifolds. It has become required reading for postgraduates and research workers whose research touches on this topic. Pre-requisites are a firm grounding in differential topology, and geometry as may be gained from the first year of a graduate course. The subject matter of this book is the most significant breakthrough in mathematics of the last fifty years, and Professor Donaldson won a Fields medal for his work in the area. The authors start from the standpoint that the fundamental group and intersection form of a four-manifold provides information about its homology and characteristic classes, but little of its differential topology. It turns out that the classification up to diffeomorphism of four-manifolds is very different from the classification of unimodular forms and that the study of this question leads naturally to the new Donaldson invariants of four-manifolds. A central tTrade Review... authoritative and comprehensive... it must be regarded as compulsory reading for any young researcher approaching this difficult but fascinating area. * Bulletin of the London Mathematical Society *Table of Contents1. Four-manifolds ; 2. Connections ; 3. The Fourier transform and ADHM construction ; 4. Yang-Mills moduli spaces ; 5. Topology and connections ; 6. Stable holomorphic bundles over Kahler surfaces ; 7. Excision and glueing ; 8. Non-existence results ; 9. Invariants of smooth four-manifolds ; 10. The differential topology of algebraic surfaces ; Appendix ; References ; Index

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