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Geometry In Action

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Geometry In Action

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Author : Clark Kimberling
language : en
Publisher: Springer Science & Business Media
Release Date : 2003

Geometry In Action written by Clark Kimberling 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 2003 with Mathematics categories.

Geometry in Action uses Sketchpad? to awaken student creativity through discovery-based learning. It supplements any college geometry course in which The Geometer's Sketchpad is used. All students must have access to The Geometer's Sketchpad.Each book is packaged with a CD-ROM for students that illustrates what is meant by geometry in action. Students explore 27 sketches prepared by the author to demonstrate Sketchpad's capabilities by dragging points to see shifts in graphs, by animating tesselations to create new patterns, and much, much more! Also included on this CD is the Poincare Disk, a Sketchpad file used to dig deeper into non-Euclidean geometry with The Geometer's Sketchpad.

Geometry Rigidity And Group Actions

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Author : Robert J Zimmer
language : en
Publisher: University of Chicago Press
Release Date : 2011-04-15

Geometry Rigidity And Group Actions written by Robert J Zimmer and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-15 with Mathematics categories.

The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.

The Principle Of Least Action In Geometry And Dynamics

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Author : Karl Friedrich Siburg
language : en
Publisher:
Release Date : 2014-01-15

The Principle Of Least Action In Geometry And Dynamics written by Karl Friedrich Siburg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Math In Action Pre Geometry

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Author : Teacher Created Resources
language : en
Publisher: Teacher Created Resources
Release Date : 2005-03

Math In Action Pre Geometry written by Teacher Created Resources and has been published by Teacher Created Resources this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03 with Education categories.

Special Metrics And Group Actions In Geometry

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Author : Simon G. Chiossi
language : en
Publisher: Springer
Release Date : 2017-11-27

Special Metrics And Group Actions In Geometry written by Simon G. Chiossi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-27 with Mathematics categories.

The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

Spectral Action In Noncommutative Geometry

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Author : Michał Eckstein
language : en
Publisher: Springer
Release Date : 2018-12-18

Spectral Action In Noncommutative Geometry written by Michał Eckstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-18 with Science categories.

What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations. The third chapter offers an in-depth view into the subtle links between the asymptotic expansions of traces of heat operators and meromorphic extensions of the associated spectral zeta functions. Chapter 4 studies the behaviour of the spectral action under fluctuations by gauge potentials. A subjective list of open problems in the field is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries. The book serves both as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts.

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.

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.

Geometry Mechanics And Control In Action For The Falling Cat

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Author : Toshihiro Iwai
language : en
Publisher: Springer Nature
Release Date : 2021-04-23

Geometry Mechanics And Control In Action For The Falling Cat written by Toshihiro Iwai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-23 with Mathematics categories.

The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together. As is well known, cats can almost always land on their feet when tossed into the air in an upside-down attitude. If cats are not given a non-vanishing angular momentum at an initial instant, they cannot rotate during their motion, and the motion they can make in the air is vibration only. However, cats accomplish a half turn without rotation when landing on their feet. In order to solve this apparent mystery, one needs to thoroughly understand rotations and vibrations. The connection theory in differential geometry can provide rigorous definitions of rotation and vibration for many-body systems. Deformable bodies of cats are not easy to treat mechanically. A feasible way to approach the question of the falling cat is to start with many-body systems and then proceed to rigid bodies and, further, to jointed rigid bodies, which can approximate the body of a cat. In this book, the connection theory is applied first to a many-body system to show that vibrational motions of the many-body system can result in rotations without performing rotational motions and then to the cat model consisting of jointed rigid bodies. On the basis of this geometric setting, mechanics of many-body systems and of jointed rigid bodies must be set up. In order to take into account the fact that cats can deform their bodies, three torque inputs which may give a twist to the cat model are applied as control inputs under the condition of the vanishing angular momentum. Then, a control is designed according to the port-controlled Hamiltonian method for the model cat to perform a half turn and to halt the motion upon landing. The book also gives a brief review of control systems through simple examples to explain the role of control inputs.

Lie Groups And Geometric Aspects Of Isometric Actions

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Author : Marcos M. Alexandrino
language : en
Publisher: Springer
Release Date : 2015-05-22

Lie Groups And Geometric Aspects Of Isometric Actions written by Marcos M. Alexandrino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-22 with Mathematics categories.

This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.

Geometry In Action

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