Elliptic Tales
Author: Avner Ash
Publisher: Princeton University Press
Published: 2012
Total Pages: 277
ISBN-13: 0691151199
DOWNLOAD EBOOKDescribes the latest developments in number theory by looking at the Birch and Swinnerton-Dyer Conjecture.
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On Quaternions and Octonions
Author: John H. Conway
Publisher: CRC Press
Published: 2003-01-23
Total Pages: 172
ISBN-13: 1439864187
DOWNLOAD EBOOKThis book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less f
Elements of Quaternions
Author: Sir William Rowan Hamilton
Publisher: Arkose Press
Published: 2015-10-03
Total Pages: 846
ISBN-13: 9781343926431
DOWNLOAD EBOOKThis work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Four Pillars of Geometry
Author: John Stillwell
Publisher: Springer Science & Business Media
Published: 2005-08-09
Total Pages: 240
ISBN-13: 0387255303
DOWNLOAD EBOOKThis book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises
Visualizing Quaternions
Author: Andrew J. Hanson
Publisher: Elsevier
Published: 2006-02-06
Total Pages: 530
ISBN-13: 0080474772
DOWNLOAD EBOOKIntroduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. - Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. - Covers both non-mathematical and mathematical approaches to quaternions.
An Introduction to Projective Geometry
Author: Roy Martin Winger
Publisher:
Published: 1962
Total Pages: 488
ISBN-13:
DOWNLOAD EBOOKAffine and Projective Geometry
Author: M. K. Bennett
Publisher: John Wiley & Sons
Published: 2011-02-14
Total Pages: 251
ISBN-13: 1118030826
DOWNLOAD EBOOKAn important new perspective on AFFINE AND PROJECTIVEGEOMETRY This innovative book treats math majors and math education studentsto a fresh look at affine and projective geometry from algebraic,synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninetyillustrations, and numerous examples and exercises, coveringmaterial for two semesters of upper-level undergraduatemathematics. The first part of the book deals with the correlationbetween synthetic geometry and linear algebra. In the second part,geometry is used to introduce lattice theory, and the bookculminates with the fundamental theorem of projectivegeometry. While emphasizing affine geometry and its basis in Euclideanconcepts, the book: * Builds an appreciation of the geometric nature of linear algebra * Expands students' understanding of abstract algebra with itsnontraditional, geometry-driven approach * Demonstrates how one branch of mathematics can be used to provetheorems in another * Provides opportunities for further investigation of mathematicsby various means, including historical references at the ends ofchapters Throughout, the text explores geometry's correlation to algebra inways that are meant to foster inquiry and develop mathematicalinsights whether or not one has a background in algebra. Theinsight offered is particularly important for prospective secondaryteachers who must major in the subject they teach to fulfill thelicensing requirements of many states. Affine and ProjectiveGeometry's broad scope and its communicative tone make it an idealchoice for all students and professionals who would like to furthertheir understanding of things mathematical.
Proceedings of the Royal Society of London
Author: Royal Society (Great Britain)
Publisher:
Published: 1907
Total Pages: 1228
ISBN-13:
DOWNLOAD EBOOKThe Geometry Of The Octonions
Author: Tevian Dray
Publisher: World Scientific
Published: 2015-04-08
Total Pages: 229
ISBN-13: 9814401838
DOWNLOAD EBOOKThere are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generalization, the Lorentz group, as well as the eigenvalue problem for Hermitian matrices. In addition, more sophisticated applications include the exceptional Lie groups, octonionic projective spaces, and applications to particle physics including the remarkable fact that classical supersymmetry only exists in particular spacetime dimensions.
Visualizing More Quaternions
Author: Andrew J. Hanson
Publisher: Elsevier
Published: 2024-07-01
Total Pages: 602
ISBN-13: 0323993907
DOWNLOAD EBOOKVisualizing More Quaternions, Volume Two updates on proteomics-related material that will be useful for biochemists and biophysicists, including material related to electron microscopy (and specifically cryo-EVisualizing. Dr. Andrew J. Hanson's groundbreaking book updates and extends concepts that have evolved since the first book published in 2005, adding entirely new insights that Dr. Hanson's research has recently developed. This includes the applications of quaternion methods to proteomics and molecular crystallography problems, which are domains with significant current research and application activity.In addition to readers interested in quaternions for their own sake, scientists involved in computer graphics, animation, shape modeling, and scientific visualization, and readers from several other disciplines will benefit from this new volume. Foremost among these, and the target of the first several chapters, are scientists involved in molecular chemistry where techniques based on quaternion eigensystems have become a standard tool for evaluating the quality of shape matching. - Establishes basic principles for visual display of quaternions and their applications. - Explores quaternion based approaches to the matching of point cloud pairs, including approaches to data from orthographic and perspective projections. - Develops extensive applications of quaternion frames to protein orientation analysis. - Analyzes the application of quaternion methods to physics problems ranging from quantum computing to special relativity and gravitational instantons.
