Journey Into Geometries
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Journey Into Geometries
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Author : Marta Sved
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-31
Journey Into Geometries written by Marta Sved and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-31 with Mathematics categories.
Introduction To Projective Geometry
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Author : C. R. Wylie
language : en
Publisher: Courier Corporation
Release Date : 2008-12-09
Introduction To Projective Geometry written by C. R. Wylie and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-09 with Mathematics categories.
This lucid introductory text offers both analytic and axiomatic approaches to plane projective geometry. Strong reinforcement for its teachings include detailed examples and numerous theorems, proofs, and exercises, plus answers to all odd-numbered problems. In addition to its value to students, this volume provides an excellent reference for professionals. 1970 edition.
The Shape Of A Life
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Author : Shing-Tung Yau
language : en
Publisher: Yale University Press
Release Date : 2019-01-01
The Shape Of A Life written by Shing-Tung Yau and has been published by Yale University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-01 with Biography & Autobiography categories.
A Fields medalist recounts his lifelong transnational effort to uncover the geometric shape--the Calabi-Yau manifold--that may store the hidden dimensions of our universe. Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world's most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal-winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.
Thinking Geometrically
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Author : Thomas Q. Sibley
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-08-14
Thinking Geometrically written by Thomas Q. Sibley and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-14 with Mathematics categories.
Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. The text is self-contained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.
The Geometry Of Time
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Author : Dierck-Ekkehard Liebscher
language : de
Publisher: Wiley-VCH
Release Date : 2005-05-06
The Geometry Of Time written by Dierck-Ekkehard Liebscher and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-06 with Mathematics categories.
A description of the geometry of space-time with all the questions and issues explained without the need for formulas. As such, the author shows that this is indeed geometry, with actual constructions familiar from Euclidean geometry, and which allow exact demonstrations and proofs. The formal mathematics behind these constructions is provided in the appendices. The result is thus not a textbook introducing readers to the theory of special relativity so they may calculate formally, but rather aims to show the connection with synthetic geometry. It presents the relation to projective geometry and uses this to illustrate the starting points of general relativity. Written at an introductory level for undergraduates, this novel presentation will also benefit teaching staff.
The Changing Shape Of Geometry
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Author : Mathematical Association of America
language : en
Publisher: Cambridge University Press
Release Date : 2003-01-09
The Changing Shape Of Geometry written by Mathematical Association of America and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-09 with Mathematics categories.
Collection of popular articles on geometry from distinguished mathematicians and educationalists.
Untangling Geometries Unraveling The Labyrinth Of Space
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-05-20
Untangling Geometries Unraveling The Labyrinth Of Space written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-20 with Mathematics categories.
Embark on an intellectual odyssey through the fascinating world of non-Euclidean geometry, where the familiar rules of space and shape are challenged and new dimensions of mathematical exploration unfold. In this captivating journey, we delve into the minds of brilliant mathematicians like Janos Bolyai and Nikolai Lobachevsky, who dared to question the foundations of Euclidean geometry and opened up new vistas of mathematical understanding. Non-Euclidean geometry shatters the long-held belief that Euclid's postulates are the only possible framework for describing space. It reveals the existence of alternative geometries, where parallel lines diverge like the rays of the sun and triangles can have more or less than 180 degrees. These mind-bending concepts challenge our intuitions about space and lead to fascinating insights into the nature of reality and the structure of the universe. Discover the diverse applications of non-Euclidean geometry, which extend far beyond the realm of pure mathematics. In physics, it has been used to model the curvature of spacetime and explain the behavior of black holes. In cosmology, it has been used to explore the shape and evolution of the universe. In computer science, non-Euclidean geometry has been used to develop new algorithms and data structures, and in art, it has inspired breathtaking works that challenge our perception of reality. This book is an invitation to embark on a journey of intellectual exploration, where you will encounter concepts that push the boundaries of your imagination. It is a testament to the power of human curiosity and the relentless pursuit of understanding the universe we inhabit. Whether you are a mathematician, a physicist, an artist, or simply someone with an insatiable curiosity about the world around you, this book will captivate and inspire you. Delve into the pages of this book and unlock the secrets of non-Euclidean geometry, a realm where the familiar rules of space and shape dissolve into a mesmerizing tapestry of intellectual discovery. If you like this book, write a review on google books!
Geometry Of M Bius Transformations
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Author : Vladimir V. Kisil
language : en
Publisher: World Scientific
Release Date : 2012
Geometry Of M Bius Transformations written by Vladimir V. Kisil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action.The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered.
Exploring The Infinite Possibilities
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Author : Barrett Williams
language : en
Publisher: Barrett Williams
Release Date : 2024-10-24
Exploring The Infinite Possibilities written by Barrett Williams and has been published by Barrett Williams this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-24 with Mathematics categories.
**Exploring the Infinite Possibilities Unlock the Mysteries of Mathematics** Dive into a world where numbers weave patterns of breathtaking beauty and equations reveal the secrets of the universe. "Exploring the Infinite Possibilities" is a captivating journey through the landscape of mathematics, offering a fresh and insightful perspective on a subject often shrouded in mystery and complexity. Begin your exploration with the aesthetic allure of mathematics, where the harmony of numbers and the elegance of patterns and symmetry spark a sense of wonder. Venture into the rich history of mathematical thought, tracing its evolution from ancient civilizations, through the intellectual fervor of the Renaissance, to the innovations that define modern mathematics today. Discover the boundless nature of infinity, uncover the mysteries of fractals and chaos theory, and delve into the intriguing realm of transfinite numbers. Wander through the natural world, where the Fibonacci sequence and the Golden Ratio manifest in mesmerizing forms and patterns, and explore the symmetrical beauty inherent in biological structures. Unravel the intricacies of mathematical proofs, from historical breakthroughs to contemporary challenges that drive mathematical discovery. Appreciate mathematics as a universal language, bridging the gap between the abstract and the tangible, and see its unifying power in science. From the elegance of Euclidean geometry to the peculiarities of non-Euclidean spaces, geometric concepts open the door to endless possibilities. Explore the hidden symmetries in abstract algebra, the enigmatic nature of prime numbers, and the profound impacts of calculus—the mathematics of change. Venture into the realms of mathematical analysis, probability, and statistics, uncovering the profound insights these fields offer into our world. Engage with the foundations of mathematical logic and embark on a journey through the digital age, where algorithms and machine learning reshape our lives. "Exploring the Infinite Possibilities" is not just a book—it's an inspiring odyssey into a vibrant mathematical universe. Whether you're a curious enthusiast or a seasoned mathematician, this book invites you to continue the great journey of mathematical exploration, inspiring future generations and highlighting the global impact of mathematics.
Complex Numbers And Geometry
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Author : Liang-shin Hahn
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-26
Complex Numbers And Geometry written by Liang-shin Hahn and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-26 with Education categories.
The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained—no background in complex numbers is assumed—and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.