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# Geometry

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**📒Geometry I ✍ Marcel Berger**

**✏Geometry I Book Summary :** Volume I of this 2-volume textbook provides a lively and readable presentation of large parts of classical geometry. For each topic the author presents an esthetically pleasing and easily stated theorem - although the proof may be difficult and concealed. The mathematical text is illustrated with figures, open problems and references to modern literature, providing a unified reference to geometry in the full breadth of its subfields and ramifications.

**📒Geometry Topology And Physics Second Edition ✍ Mikio Nakahara**

**✏Geometry Topology and Physics Second Edition Book Summary :** Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

**📒Euclidean Geometry In Mathematical Olympiads ✍ Evan Chen**

**✏Euclidean Geometry in Mathematical Olympiads Book Summary :** This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains as selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honor class.

**📒Axiomatic Geometry ✍ John M. Lee**

**✏Axiomatic Geometry Book Summary :** The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a mode of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom. -- P. [4] of cover.

**📒Differential Geometry ✍ J. J. Stoker**

**✏Differential Geometry Book Summary :** This classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations: vector algebra and calculus, tensor calculus, and the notation devised by Cartan, which employs invariant differential forms as elements in an algebra due to Grassman, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis.

**📒Projective And Euclidean Geometry ✍ William Thompson Fishback**

**✏Projective and Euclidean geometry Book Summary :**

**📒Applied Descriptive Geometry ✍ Kathryn Holliday-Darr**

**✏Applied Descriptive Geometry Book Summary :** Excellent for engineering and technology students, this text goes far beyond instruction in standard orthographic projection to clarify all the tools of descriptive geometry--and how they apply to individual fields. The text places special emphasis on applications in all the various engineering disciplines: mechanical, plastics, industrial, piping, aerospace, marine, civil, and structural. As a result, students quickly grasp the value of descriptive geometry as they apply the tools and techniques to practical problems. By organizing information around the field's central concept--line of sight--the presentation facilitates understanding in a way unmatched by any other text. The worktext format provides students with all the resources they need--text and workbook--under one cover.ALSO AVAILABLEINSTRUCTOR SUPPLEMENTS CALL CUSTOMER SUPPORT TO ORDER Instructor's Guide, ISBN: 0-7668-0118-7Keywords: Descriptive Geometry

**📒Geometry A Comprehensive Course ✍ Dan Pedoe**

**✏Geometry A Comprehensive Course Book Summary :** Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.