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Classical Geometries In Modern Contexts

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Classical Geometries In Modern Contexts

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Author : Walter Benz
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-15

Classical Geometries In Modern Contexts written by Walter Benz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-15 with Mathematics categories.

This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. Designed as a two term graduate course, the book helps students to understand great ideas of classical geometries in a modern and general context. A real benefit is the dimension-free approach to important geometrical theories. The only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry.

Classical Geometries In Modern Contexts

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Author : Walter Benz
language : en
Publisher: Springer Science & Business Media
Release Date : 2005

For new staffer Amanda Wells at one of the hot spots of conflict, what begins as an embarrassing false alarm ends in a dead-run adventure with rogue decisions made in exchange for a hostage... her boss!

Classical Geometries In Modern Contexts

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Author : Walter Benz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-13

The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Möbius and Lie as well as geometries where Lorentz transformations play the key role. Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. New to this third edition is a chapter dealing with a simple and great idea of Leibniz that allows us to characterize, for these same spaces X, hyperplanes of euclidean, hyperbolic geometry, or spherical geometry, the geometries of Lorentz-Minkowski and de Sitter, and this through finite or infinite dimensions greater than 1. Another new and fundamental result in this edition concerns the representation of hyperbolic motions, their form and their transformations. Further we show that the geometry (P,G) of segments based on X is isomorphic to the hyperbolic geometry over X. Here P collects all x in X of norm less than one, G is defined to be the group of bijections of P transforming segments of P onto segments. The only prerequisites for reading this book are basic linear algebra and basic 2- and 3-dimensional real geometry. This implies that mathematicians who have not so far been especially interested in geometry could study and understand some of the great ideas of classical geometries in modern and general contexts.

Classical Geometries In Modern Contexts

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Author :
language : en
Publisher:
Release Date : 2012

Classical Geometries In Modern Contexts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.

Points And Lines

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Author : Ernest E. Shult
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-13

Points And Lines written by Ernest E. Shult and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-13 with Mathematics categories.

The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to recognize the action of a Lie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such a course, or to elicit new research directions.

Handbook Of Research On Form And Morphogenesis In Modern Architectural Contexts

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Author : D'Uva, Domenico
language : en
Publisher: IGI Global
Release Date : 2018-02-23

Handbook Of Research On Form And Morphogenesis In Modern Architectural Contexts written by D'Uva, Domenico and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Art categories.

As architectural designs continue to push boundaries, there is more exploration into the bound shape of architecture within the limits of spaces made for human usability and interaction. The Handbook of Research on Form and Morphogenesis in Modern Architectural Contexts provides emerging research on the process of architectural form-finding as an effort to balance perceptive efficiency with functionality. While highlighting topics such as architectural geometry, reverse modeling, and digital fabrication, this book details the geometric process that forms the shape of a building. This publication is a vital resource for scholars, IT professionals, engineers, architects, and business managers seeking current research on the development and creation of architectural design.

Geometry From Isometries To Special Relativity

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Author : Nam-Hoon Lee
language : en
Publisher: Springer Nature
Release Date : 2020-04-28

Geometry From Isometries To Special Relativity written by Nam-Hoon Lee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-28 with Mathematics categories.

This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.

Geometry Of Mobius Transformations Elliptic Parabolic And Hyperbolic Actions Of Sl2 R With Dvd Rom

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Author : Vladimir V Kisil
language : en
Publisher: World Scientific
Release Date : 2012-06-19

Geometry Of Mobius Transformations Elliptic Parabolic And Hyperbolic Actions Of Sl2 R With Dvd Rom 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 2012-06-19 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./a

New Horizons For Observational Cosmology

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Author : A. Cooray
language : en
Publisher: IOS Press
Release Date : 2015-01-06

New Horizons For Observational Cosmology written by A. Cooray and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-06 with Science categories.

Our understanding of the universe has been revolutionized by observations of the cosmic microwave background, the large-scale structure of the universe, and distant supernovae. These studies have shown that we are living in a strange universe: 96% of the present day energy density of the universe is dominated by so-called dark matter and dark energy. But we still do not know what dark matter and dark energy actually are. This book presents lectures from the 186th Course in the Enrico Fermi International School of Physics entitled New Horizons for Observational Cosmology, held in Varenna, Italy, in July 2013. Topics covered at this school included: cosmic microwave background anisotropies; galaxy clustering; weak lensing; dark energy; dark matter; inflation; modified gravity; neutrino physics; reionization; galaxy formation; and first stars. The anticipated release of Planck data at the end of 2014 will provide a more complete view of temperature anisotropy of the cosmic microwave background, and the reporting of other important results is also expected soon. These new data will undoubtedly address fundamental questions about the universe. This book prepares the ground for future work which may answer some of these exciting questions.

A Course In Modern Geometries

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Author : Judith N. Cederberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

A Course In Modern Geometries written by Judith N. Cederberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 continues the synthetic approach as it introduces Euclid's geometry and ideas of non-Euclidean geometry. In Chapter 3, a new introduction to symmetry and hands-on explorations of isometries precedes the extensive analytic treatment of isometries, similarities and affinities. A new concluding section explores isometries of space. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3-4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. The new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Each chapter includes a list of suggested resources for applications or related topics in areas such as art and history. The second edition also includes pointers to the web location of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for "Cabri Geometry" and "Geometer's Sketchpad". Judith N. Cederberg is an associate professor of mathematics at St. Olaf College in Minnesota.

Classical Geometries In Modern Contexts

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