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Books > Science & Mathematics > Mathematics > Geometry > General

Geometry of Surfaces - A Practical Guide for Mechanical Engineers (Hardcover): Stephen P. Radzevich Geometry of Surfaces - A Practical Guide for Mechanical Engineers (Hardcover)
Stephen P. Radzevich
R2,871 Discovery Miles 28 710 Ships in 12 - 17 working days

Presents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems

"Geometry of Surfaces: A Practical Guide for Mechanical Engineers" is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces.

"Geometry of Surfaces: A Practical Guide for Mechanical Engineers "combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering.Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineeringCombines differential geometry and gearing theoryHighlights new developments in the elementary theory of enveloping surfaces

Essential reading for researchers and practitioners in mechanical, automotive and aerospace engineering industries; CAD developers; and graduate students in Mechanical Engineering.

Lie Groups, Differential Equations, and Geometry - Advances and Surveys (Hardcover, 1st ed. 2017): Giovanni Falcone Lie Groups, Differential Equations, and Geometry - Advances and Surveys (Hardcover, 1st ed. 2017)
Giovanni Falcone
R2,805 R1,919 Discovery Miles 19 190 Save R886 (32%) Ships in 12 - 17 working days

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.

A Journey Through Discrete Mathematics - A Tribute to Jiri Matousek (Hardcover, 1st ed. 2017): Martin Loebl, Jaroslav Nesetril,... A Journey Through Discrete Mathematics - A Tribute to Jiri Matousek (Hardcover, 1st ed. 2017)
Martin Loebl, Jaroslav Nesetril, Robin Thomas
R3,839 R2,703 Discovery Miles 27 030 Save R1,136 (30%) Ships in 12 - 17 working days

This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiri Matousek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition - something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiri Matousek's numerous areas of mathematical interest.

Lectures on the Geometry of Poisson Manifolds (Hardcover, 1994 ed.): Izu Vaisman Lectures on the Geometry of Poisson Manifolds (Hardcover, 1994 ed.)
Izu Vaisman
R2,818 R1,985 Discovery Miles 19 850 Save R833 (30%) Ships in 12 - 17 working days

This book is addressed to graduate students and researchers in the fields of mathematics and physics who are interested in mathematical and theoretical physics, differential geometry, mechanics, quantization theories and quantum physics, quantum groups etc., and who are familiar with differentiable and symplectic manifolds. The aim of the book is to provide the reader with a monograph that enables him to study systematically basic and advanced material on the recently developed theory of Poisson manifolds, and that also offers ready access to bibliographical references for the continuation of his study. Until now, most of this material was dispersed in research papers published in many journals and languages. The main subjects treated are the Schouten-Nijenhuis bracket; the generalized Frobenius theorem; the basics of Poisson manifolds; Poisson calculus and cohomology; quantization; Poisson morphisms and reduction; realizations of Poisson manifolds by symplectic manifolds and by symplectic groupoids and Poisson-Lie groups. The book unifies terminology and notation. It also reports on some original developments stemming from the author's work, including new results on Poisson cohomology and geometric quantization, cofoliations and biinvariant Poisson structures on Lie groups.

Non-Euclidean Geometry and Curvature - Two-Dimensional Spaces, Volume 3 (Paperback): James W. Cannon Non-Euclidean Geometry and Curvature - Two-Dimensional Spaces, Volume 3 (Paperback)
James W. Cannon
R1,227 R1,024 Discovery Miles 10 240 Save R203 (17%) Ships in 12 - 17 working days

This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, which explains a more classical view of hyperbolic non-Euclidean geometry in all dimensions. Finally, the author explains a natural intrinsic obstruction to flattening a triangulated polyhedral surface into the plane without distorting the constituent triangles. That obstruction extends intrinsically to smooth surfaces by approximation and is called curvature. Gauss's original definition of curvature is extrinsic rather than intrinsic. The final two chapters show that the book's intrinsic definition is equivalent to Gauss's extrinsic definition (Gauss's "Theorema Egregium" ("Great Theorem")).

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) (Hardcover): Isroil A. Ikromov, Detlef... Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) (Hardcover)
Isroil A. Ikromov, Detlef Muller
R3,429 R2,535 Discovery Miles 25 350 Save R894 (26%) Ships in 12 - 17 working days

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to the given surface. Isroil Ikromov and Detlef Muller begin with Elias M. Stein's concept of Fourier restriction and some relations between the decay of the Fourier transform of the surface measure and Stein-Tomas type restriction estimates. Varchenko's ideas relating Fourier decay to associated Newton polyhedra are briefly explained, particularly the concept of adapted coordinates and the notion of height. It turns out that these classical tools essentially suffice already to treat the case where there exist linear adapted coordinates, and thus Ikromov and Muller concentrate on the remaining case. Here the notion of r-height is introduced, which proves to be the right new concept. They then describe decomposition techniques and related stopping time algorithms that allow to partition the given surface into various pieces, which can eventually be handled by means of oscillatory integral estimates. Different interpolation techniques are presented and used, from complex to more recent real methods by Bak and Seeger. Fourier restriction plays an important role in several fields, in particular in real and harmonic analysis, number theory, and PDEs. This book will interest graduate students and researchers working in such fields.

Continuous Semigroups of Holomorphic Self-maps of the Unit Disc (Hardcover, 1st ed. 2020): Filippo Bracci, Manuel D. Contreras,... Continuous Semigroups of Holomorphic Self-maps of the Unit Disc (Hardcover, 1st ed. 2020)
Filippo Bracci, Manuel D. Contreras, Santiago Diaz-Madrigal
R2,704 Discovery Miles 27 040 Ships in 12 - 17 working days

The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Caratheodory prime ends topology and Gromov hyperbolicity theory. This work is intended both as a reference source for researchers interested in the subject, and as an introductory book for beginners with a (undergraduate) background in real and complex analysis. For this purpose, the book is self-contained and all non-standard (and, mostly, all standard) results are proved in details.

The Golden Ratio - The Story of Phi The World's Most Astonishing Number (Paperback, 1st trade pbk. ed): Mario Livio The Golden Ratio - The Story of Phi The World's Most Astonishing Number (Paperback, 1st trade pbk. ed)
Mario Livio 1
R356 R302 Discovery Miles 3 020 Save R54 (15%) Ships in 7 - 11 working days

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!

The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.


From the Hardcover edition.

A History of Folding in Mathematics - Mathematizing the Margins (Hardcover, 1st ed. 2018): Michael Friedman A History of Folding in Mathematics - Mathematizing the Margins (Hardcover, 1st ed. 2018)
Michael Friedman
R4,054 R3,535 Discovery Miles 35 350 Save R519 (13%) Ships in 12 - 17 working days

While it is well known that the Delian problems are impossible to solve with a straightedge and compass - for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments - the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.

Mastering Essential Math Skills - GEOMETRY, 2nd Edition: GEOMETRY, 2nd Edition (Paperback): Richard Fisher Mastering Essential Math Skills - GEOMETRY, 2nd Edition: GEOMETRY, 2nd Edition (Paperback)
Richard Fisher
R711 Discovery Miles 7 110 Ships in 7 - 11 working days
Knots, Links, Spatial Graphs, and Algebraic Invariants (Paperback): Erica Flapan, Allison Henrich, Aaron Kaestner, Sam Nelson Knots, Links, Spatial Graphs, and Algebraic Invariants (Paperback)
Erica Flapan, Allison Henrich, Aaron Kaestner, Sam Nelson
R2,749 R2,237 Discovery Miles 22 370 Save R512 (19%) Ships in 12 - 17 working days

This volume contains the proceedings of the AMS Special Session on Algebraic and Combinatorial Structures in Knot Theory and the AMS Special Session on Spatial Graphs, both held from October 24-25, 2015, at California State University, Fullerton, CA. Included in this volume are articles that draw on techniques from geometry and algebra to address topological problems about knot theory and spatial graph theory, and their combinatorial generalizations to equivalence classes of diagrams that are preserved under a set of Reidemeister-type moves. The interconnections of these areas and their connections within the broader field of topology are illustrated by articles about knots and links in spatial graphs and symmetries of spatial graphs in $S^3$ and other 3-manifolds.

Geometry from Euclid to Knots (Paperback): Saul Stahl Geometry from Euclid to Knots (Paperback)
Saul Stahl
R527 R452 Discovery Miles 4 520 Save R75 (14%) Ships in 7 - 11 working days

Designed to inform readers about the formal development of Euclidean geometry and to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text closely follows Euclid's classic, "Elements. "The text augments Euclid's statements with appropriate historical commentary and many exercises -- more than 1,000 practice exercises provide readers with hands-on experience in solving geometrical problems.
In addition to providing a historical perspective on plane geometry, this text covers non-Euclidean geometries, allowing students to cultivate an appreciation of axiomatic systems. Additional topics include circles and regular polygons, projective geometry, symmetries, inversions, knots and links, graphs, surfaces, and informal topology. This republication of a popular text is substantially less expensive than prior editions and offers a new Preface by the author.

An Introduction to Incidence Geometry (Paperback, 1st ed. 2016): Bart de Bruyn An Introduction to Incidence Geometry (Paperback, 1st ed. 2016)
Bart de Bruyn
R3,177 R2,347 Discovery Miles 23 470 Save R830 (26%) Ships in 12 - 17 working days

This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.

Proofs from THE BOOK (Hardcover, 6th ed. 2018): Martin Aigner Proofs from THE BOOK (Hardcover, 6th ed. 2018)
Martin Aigner; Illustrated by Karl H. Hofmann; Gunter M. Ziegler
R1,433 R1,325 Discovery Miles 13 250 Save R108 (8%) Ships in 10 - 20 working days

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

The Impact of Scale on Children's Spatial Thought - A Quantitative Study for Two Settings in Geometry Education... The Impact of Scale on Children's Spatial Thought - A Quantitative Study for Two Settings in Geometry Education (Paperback, 1st ed. 2020)
Cathleen Heil
R2,013 Discovery Miles 20 130 Ships in 7 - 11 working days

In this book, Cathleen Heil addresses the question of how to conceptually understand children's spatial thought in the context of geometry education. She proposes that in order to help children develop their abilities to successfully grasp and manipulate the spatial relations they experience in their everyday lives, spatial thought should not only be addressed in written or tabletop settings at school. Instead, geometry education should also focus on settings involving real space, such as during reasoning with maps. In a first part of this book, she theoretically addresses the construct of spatial thought at different scales of space from a cognitive psychological point of view and shows that maps can be rich sources for spatial thinking. In a second part, she proposes how to measure children's spatial thought in a paper-and-pencil setting and map-based setting in real space. In a third, empirical part, she examines the relations between children's spatial thought in those two settings both at a manifest and latent level.

Geometric Methods in Physics - XXXIV Workshop, Bialowieza, Poland, June 28 - July 4, 2015 (Hardcover, 1st ed. 2016): Piotr... Geometric Methods in Physics - XXXIV Workshop, Bialowieza, Poland, June 28 - July 4, 2015 (Hardcover, 1st ed. 2016)
Piotr Kielanowski, S. Twareque Ali, Pierre Bieliavsky, Anatol Odzijewicz, Martin Schlichenmaier, …
R3,988 R2,488 Discovery Miles 24 880 Save R1,500 (38%) Ships in 12 - 17 working days

This book features a selection of articles based on the XXXIV Bialowieza Workshop on Geometric Methods in Physics, 2015. The articles presented are mathematically rigorous, include important physical implications and address the application of geometry in classical and quantum physics. Special attention deserves the session devoted to discussions of Gerard Emch's most important and lasting achievements in mathematical physics. The Bialowieza workshops are among the most important meetings in the field and gather participants from mathematics and physics alike. Despite their long tradition, the Workshops remain at the cutting edge of ongoing research. For the past several years, the Bialowieza Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented. The unique atmosphere of the Workshop and School is enhanced by the venue, framed by the natural beauty of the Bialowieza forest in eastern Poland.

Edmund Husserl's "Origin of Geometry" - An Introduction (Paperback, New ed): Jacques Derrida Edmund Husserl's "Origin of Geometry" - An Introduction (Paperback, New ed)
Jacques Derrida; Translated by John P. Leavey
R545 R471 Discovery Miles 4 710 Save R74 (14%) Ships in 12 - 17 working days

"Edmund Husserl's Origin of Geometry": An Introduction" (1962) is Jacques Derrida's earliest published work. In this commentary-interpretation of the famous appendix to Husserl's "The Crisis of European Sciences and Transcendental Phenomenology," Derrida relates writing to such key concepts as differing, consciousness, presence, and historicity. Starting from Husserl's method of historical investigation, Derrida gradually unravels a deconstructive critique of phenomenology itself, which forms the foundation for his later criticism of Western metaphysics as a metaphysics of presence. The complete text of Husserl's Origin of Geometry is included.

Planar Maps, Random Walks and Circle Packing - Ecole d'Ete de Probabilites de Saint-Flour XLVIII - 2018 (Paperback, 1st... Planar Maps, Random Walks and Circle Packing - Ecole d'Ete de Probabilites de Saint-Flour XLVIII - 2018 (Paperback, 1st ed. 2020)
Asaf Nachmias
R1,118 Discovery Miles 11 180 Ships in 12 - 17 working days

This open access book focuses on the interplay between random walks on planar maps and Koebe's circle packing theorem. Further topics covered include electric networks, the He-Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe's circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.

Lectures on K3 Surfaces (Hardcover): Daniel Huybrechts Lectures on K3 Surfaces (Hardcover)
Daniel Huybrechts
R1,496 Discovery Miles 14 960 Ships in 10 - 20 working days

K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi-Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin-Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

Unitals in Projective Planes (Hardcover, 2008 ed.): Susan Barwick, Gary Ebert Unitals in Projective Planes (Hardcover, 2008 ed.)
Susan Barwick, Gary Ebert
R2,261 Discovery Miles 22 610 Ships in 10 - 20 working days

This book is a monograph on unitals embedded in ?nite projective planes. Unitals are an interesting structure found in square order projective planes, and numerous research articles constructing and discussing these structures have appeared in print. More importantly, there still are many open pr- lems, and this remains a fruitful area for Ph.D. dissertations. Unitals play an important role in ?nite geometry as well as in related areas of mathematics. For example, unitals play a parallel role to Baer s- planes when considering extreme values for the size of a blocking set in a square order projective plane (see Section 2.3). Moreover, unitals meet the upper bound for the number of absolute points of any polarity in a square order projective plane (see Section 1.5). From an applications point of view, the linear codes arising from unitals have excellent technical properties (see 2 Section 6.4). The automorphism group of the classical unitalH =H(2, q ) is 2-transitive on the points ofH, and so unitals are of interest in group theory. In the ?eld of algebraic geometry over ?nite ?elds, H is a maximal curve that contains the largest number of F -rational points with respect to its genus, 2 q as established by the Hasse-Weil boun

Lemmas in Olympiad Geometry (Hardcover): Titu Andreescu, Sam Korsky, Cosmin Pohoata Lemmas in Olympiad Geometry (Hardcover)
Titu Andreescu, Sam Korsky, Cosmin Pohoata
R1,796 R1,657 Discovery Miles 16 570 Save R139 (8%) Ships in 12 - 17 working days

This book showcases the synthetic problem-solving methods which frequently appear in modern day Olympiad geometry, in the way we believe they should be taught to someone with little familiarity in the subject. In some sense, the text also represents an unofficial sequel to the recent problem collection published by XYZ Press, 110 Geometry Problems for the International Mathematical Olympiad, written by the first and third authors, but the two books can be studied completely independently of each other. The work is designed as a medley of the important Lemmas in classical geometry in a relatively linear fashion: gradually starting from Power of a Point and common results to more sophisticated topics, where knowing a lot of techniques can prove to be tremendously useful. We treat each chapter as a short story of its own and include numerous solved exercises with detailed explanations and related insights that will hopefully make your journey very enjoyable.

Discourse Perspective of Geometric Thoughts (Paperback, 1st ed. 2016): Sasha Wang Discourse Perspective of Geometric Thoughts (Paperback, 1st ed. 2016)
Sasha Wang
R1,848 R1,243 Discovery Miles 12 430 Save R605 (33%) Ships in 12 - 17 working days

Sasha Wang revisits the van Hiele model of geometric thinking with Sfard's discursive framework to investigate geometric thinking from a discourse perspective. The author focuses on describing and analyzing pre-service teachers' geometric discourse across different van Hiele levels. The explanatory power of Sfard's framework provides a rich description of how pre-service teachers think in the context of quadrilaterals. It also contributes to our understanding of human thinking that is illustrated through the analysis of geometric discourse accompanied by vignettes.

Analysis, Probability And Mathematical Physics On Fractals (Hardcover): Patricia Alonso Ruiz, Joe Po-chou Chen, Luke G Rogers Analysis, Probability And Mathematical Physics On Fractals (Hardcover)
Patricia Alonso Ruiz, Joe Po-chou Chen, Luke G Rogers; Edited by (editors-in-chief) Robert S. Strichartz; Edited by Alexander Teplyaev
R3,517 Discovery Miles 35 170 Ships in 12 - 17 working days

In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.

Geometry (Inside Mathematics) - Understanding Shapes and Sizes (Paperback): Mike Goldsmith Geometry (Inside Mathematics) - Understanding Shapes and Sizes (Paperback)
Mike Goldsmith
R368 R313 Discovery Miles 3 130 Save R55 (15%) Ships in 10 - 20 working days

Geometry does not have to be confusing! Inside Mathematics: Geometry helps make sense of all of those lines and angles by showing its fascinating origins and how that knowledge is applied in everyday life. Written to engage and enthuse young minds, this accessible overview introduces readers to the amazing people who figured out how shapes work and how they can be used to build spaces and study places we cannot go, like the beginning of the Universe. Filled with enlightening illustrations and images, Geometry is arranged chronologically, from Euclid's revolution to the Poincare conjecture, to clearly show how ideas in mathematics evolved from the Ancient Egyptians in 3000 BC to the present day. What began as scratched circles and squares in the dirt has evolved into a branch of mathematics used to create realistic landscapes in video games, build mile-high skyscrapers, and manufacture robots so tiny they can swim in your bloodstream.

Geometric Methods in Physics - XXXIII Workshop, Bialowieza, Poland, June 29 - July 5, 2014 (Hardcover, 1st ed. 2015): Piotr... Geometric Methods in Physics - XXXIII Workshop, Bialowieza, Poland, June 29 - July 5, 2014 (Hardcover, 1st ed. 2015)
Piotr Kielanowski, Pierre Bieliavsky, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov
R4,387 R1,944 Discovery Miles 19 440 Save R2,443 (56%) Ships in 12 - 17 working days

This book presents a selection of papers based on the XXXIII Bialowieza Workshop on Geometric Methods in Physics, 2014. The Bialowieza Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Bialowieza Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Bialowieza forest in eastern Poland.The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and mathematmtics.

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