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Geometry Snacks is a mathematical puzzle book filled with geometrical figures and questions designed to challenge, confuse and ultimately enlighten enthusiasts of all ages. Each puzzle is carefully designed to draw out interesting phenomena and relationships between the areas and dimensions of various shapes. Furthermore, unlike most puzzle books, the authors offer multiple approaches to solutions so that once a puzzle is solved, there are further surprises, insights and challenges to be had. As a teaching tool, Geometry Snacks enables teachers to promote deep thinking and debate over how to solve geometry puzzles. Each figure is simple, but often deceptively tricky to solve - allowing for great classroom discussions about ways in which to approach them. By offering numerous solution approaches, the book also acts as a tool to help encourage creativity and develop a variety of strategies to chip away at problems that often seem to have no obvious way in. Contents: 1. What fraction is shaded? 2. Find the missing angle 3. What is the area? 4. Prove it 5. Sangaku Ed Southall is a teacher trainer at Huddersfield University in the UK, and the author of "Yes But Why? Teaching for Understanding in Mathematics". Ed has taught mathematics for 14 years in secondary schools both in the UK and the Middle East. He has developed a large following online as @solvemymaths on twitter where he regularly posts mathematical puzzles. Vincent Pantaloni is a French mathematics high school teacher since 2000. He teaches in Orleans in French but also in English to the European and International Sections. With these students he has developed a teaching based on cooperative problem solving. He believes that searching and sharing strategies for complex problems in teamwork helps students in building a stronger mathematical knowledge. He is also a teacher trainer specialised in the use of new technologies and flipped classroom and a member of different research groups. He posts about mathematics on twitter @panlepan and in French on his website Mathzani.
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
Excellent text approaches characters via rings (or algebras). In addition to techniques for applying characters to "pure" group theory, much of the book focuses on properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. Problems follow each chapter. Prerequisite a first-year graduate algebra course. "A pleasure to read."-American Mathematical Society. 1976 edition.
Roman geometric patterns radiate symmetry and order. Drawing the patterns is not just a question of mechanically copying the work of someone else square by square, but of understanding the underlying structure. The patterns are built up from simple elements which seem to 'grow' and develop in an almost organic or living way. This book is arranged as a series of drawing exercises. There is no better way of appreciating the skill and imagination of those artists than by drawing their designs yourself. To 'feel' how a cross 'grows' into a swastika pattern which then 'grows' into a complex interlocking design is something which can only be experienced at first hand. This second edition incorporates the same "drawing led" approach to learning about the subject and as such is invaluable in using the designs for contemporary mosaic, or pattern, design. New photographs and updated text strengthen this approach further. Ideal for schools, shops in or near Roman remains, and historical and art/design sections of shops.
More Geometry Snacks is a mathematical puzzle book filled with geometrical figures and questions designed to challenge, confuse and ultimately enlighten enthusiasts of all ages. It is the companion volume to the highly successful Geometry Snacks. Each puzzle is carefully designed to draw out interesting phenomena and relationships between the areas and dimensions of various shapes. Furthermore, unlike most puzzle books, the authors offer multiple approaches to solutions so that once a puzzle is solved, there are further surprises, insights and challenges to be had. As a teaching tool, More Geometry Snacks enables teachers to promote deep thinking and debate over how to solve geometry puzzles. Each figure is simple, but often deceptively tricky to solve - allowing for great classroom discussions about ways in which to approach them. By offering numerous solution approaches, the book also acts as a tool to help encourage creativity and develop a variety of strategies to chip away at problems that often seem to have no obvious way in. More Geometry Snacks offers another batch of puzzles.
Ten amazing curves personally selected by one of today's bestselling math writers Curves for the Mathematically Curious is an enticing collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and because many are downright beautiful. Each chapter of this anthology gives an account of the history and definition of each curve, providing a glimpse into the elegant and often surprising mathematics involved in their creation and evolution. In telling the ten stories, Havil visits many mathematicians and other innovators, some whose fame has withstood the passing of years, others who have blended into comparative obscurity. As well as the numerous mathematicians, you will meet in particular Pierre B (c)zier, whose name is perpetuated though his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the Normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers contributed to the challenges, incongruities, and insights to be found in this study of these remarkable curves "and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that the reader who chooses can follow the details with pencil and paper. Every curve has a story worthy of telling. This compendium tells the stories of ten remarkable curves personally selected by one of today (TM)s best-loved writers of popular mathematics.
Barron's E-Z Geometry contains everything students need to succeed in geometry. This edition covers the "how" and "why" of geometry, with examples, exercises, and solutions throughout, plus hundreds of drawings, graphs, and tables. The E-Z Series presents new, updated, and improved versions of Barron's longtime popular Easy Way books. Updated cover designs, interior layouts, and more graphic material than ever make these books ideal as self-teaching manuals. Teachers have discovered that E-Z titles also make excellent supplements to classroom textbooks. Skill levels range between senior high school and college-101 standards. All titles in the series present detailed reviews of the target subject plus short quizzes and longer tests to help students assess their learning progress.
Hit 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 before it 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 be a math genius to grasp geometry, and this book helps you get un-stumped in a hurry! * Find out how to decode complex geometry proofs * Learn to reason deductively and inductively * Make sense of angles, arcs, area, and more * Improve your chances of scoring higher in your geometry class There's no reason to let your nerves get jangled over geometry your understanding will take new shape with the help of Geometry For Dummies.
This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition" "... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty." From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Gunter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdoes. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011
A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia This volume celebrates Kanti V. Mardia's long and influential career in statistics. A common theme unifying much of Mardia s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high-profile researchers in the field. Geometry Driven Statistics covers a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations. Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia.
Building on the success of its first five editions, the Sixth Edition of the market-leading text explores the important principles and real-world applications of plane, coordinate, and solid geometry. Strongly influenced by both NCTM and AMATYC standards, the text includes intuitive, inductive, and deductive experiences in its explorations. Goals of the authors for the students include a comprehensive development of the vocabulary of geometry, an intuitive and inductive approach to development of principles, and the strengthening of deductive skills that leads to both verification of geometric theories and the solution of geometry-based real world applications. Updates in this edition include the addition of 150 new problems, new applications, new Discover! activities and examples and additional material on select topics such as parabolas and a Three-Dimensional Coordinate System.
How 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.
Euclid’s Window 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 Pythagorus 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.
Presenting theory while using "Mathematica" in a complementary way, Modern Differential Geometry of Curves and Surfaces with Mathematica, the third edition of Alfred Gray's famous textbook, covers how to define and compute standard geometric functions using "Mathematica" for constructing new curves and surfaces from existing ones. Since Gray's death, authors Abbena and Salamon have stepped in to bring the book up to date. While maintaining Gray's intuitive approach, they reorganized the material to provide a clearer division between the text and the "Mathematica" code and added a "Mathematica" notebook as an appendix to each chapter. They also address important new topics, such as quaternions.
The approach of this book is at times more computational than is usual for a book on the subject. For example, Brioshi's formula for the Gaussian curvature in terms of the first fundamental form can be too complicated for use in hand calculations, but"Mathematica "handles it easily, either through computations or through graphing curvature. Another part of "Mathematica" that can be used effectively in differential geometry is its special function library, where nonstandard spaces of constant curvature can be defined in terms of elliptic functions and then plotted.
Using the techniques described in this book, readers will understand concepts geometrically, plotting curves and surfaces on a monitor and then printing them. Containing more than 300 illustrations, the book demonstrates how to use "Mathematica" to plot many interesting curves and surfaces. Including as many topics of the classical differential geometry and surfaces as possible, it highlights important theorems with many examples.It includes 300 miniprograms for computing and plotting various geometric objects, alleviating the drudgery of computing things such as the curvature and torsion of a curve in space.
This textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for all even-numbered problems will be made available to instructors.
The art of origami, or paper folding, is carried out using a square piece of paper to obtain attractive figures of animals, flowers or other familiar figures. It is easy to see that origami has links with geometry. Creases and edges represent lines, intersecting creases and edges make angles, while the intersections themselves represent points. Because of its manipulative and experiential nature, origami could become an effective context for the learning and teaching of geometry. In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result. Rather, they lead the reader to study the effects of the folding and seek patterns. The experimental approach that characterizes much of science activity can be recognized throughout the book, as the manipulative nature of origami allows much experimenting, comparing, visualizing, discovering and conjecturing. The reader is encouraged to fill in all the proofs, for his/her own satisfaction and for the sake of mathematical completeness. Thus, this book provides a useful, alternative approach for reinforcing and applying the theorems of high school mathematics.
Reconciliation of Geometry and Perception in Radiation Physics approaches the topic of projective geometry as it applies to radiation physics and attempts to negate its negative reputation. With an original outlook and transversal approach, the book emphasizes common geometric properties and their potential transposition between domains. After defining both radiation and geometric properties, authors Benoit and Pierre Beckers explain the necessity of reconciling geometry and perception in fields like architectural and urban physics, which are notable for the regularity of their forms and the complexity of their interactions.
The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev-Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, the text covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi-Brauer varieties, and techniques in Milnor K-theory and K-cohomology, leading to a full proof of the Merkurjev-Suslin theorem and its application to the characterization of reduced norms. The final chapter rounds off the theory by presenting the results in positive characteristic, including the theorems of Bloch-Gabber-Kato and Izhboldin. This second edition has been carefully revised and updated, and contains important additional topics.
This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Moebius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.
Important developments in the progress of the theory of rock mechanics during recent years are based on fractals and damage mechanics. The concept of fractals has proved to be a useful way of describing the statistics of naturally occurring geometrics. Natural objects, from mountains and coastlines to clouds and forests, are found to have boundaries best described as fractals. Fluid flow through jointed rock masses and clusterings of earthquakes are found to follow fractal patterns in time and space. Fracturing in rocks at all scales, from the microscale (microcracks) to the continental scale (megafaults), can lead to fractal structures. The process of diagenesis and pore geometry of sedimentary rock can be quantitatively described by fractals, etc. The book is mainly concerned with these developments, as related to fractal descriptions of fragmentations, damage and fracture of rocks, rock burst, joint roughness, rock porosity and permeability, rock grain growth, rock and soil particles, shear slips, fluid flow through jointed rocks, faults, earthquake clustering, and so on. The prime concerns of the book are to give a simple account of the basic concepts, methods of fractal geometry, and their applications to rock mechanics, geology, and seismology, and also to discuss damage mechanics of rocks and its application to mining engineering. The book can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.
This brief undergraduate-level text by a prominent
Cambridge-educated mathematician explores the relationship between
algebra and geometry. An elementary course in plane geometry is the
sole requirement for Gilbert de B. Robinson's text, which is the
result of several years of teaching and learning the most effective
methods from discussions with students.
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