The Realm of Sedenions
The Realm of Sedenions

Author: David R Ely

Publisher: David R Ely

Published: 2024-05-22

Total Pages: 88

ISBN-13:

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"The Realm of Sedenions: A Look Into Higher-Complex Numbers" dives into the fascinating world of sedenions, a 16-dimensional number system with unique properties. The book explores the motivation behind studying sedenions, their formal definition with addition and non-commutative, non-associative multiplication, and how they differ from familiar number systems like real and complex numbers. While sedenions lack widespread practical applications yet, the book delves into potential areas of exploration in physics and computer science. It also highlights the challenges mathematicians face due to the complex multiplication rules and the lack of a straightforward geometric interpretation for these high-dimensional numbers. The book provides historical context by mentioning James Joseph Sylvester, who introduced sedenions. While directly visualizing 16 dimensions is difficult, the book discusses potential approaches like subspace projections and geometric analogies to gain a better understanding. Exercises tailored to the audience's level and a resource section for further exploration round out the book, making it a valuable resource for anyone curious about venturing beyond the realm of familiar numbers.

Before the Beginning
Before the Beginning

Author: Martin J. Rees

Publisher:

Published: 2002

Total Pages: 288

ISBN-13: 9780743230995

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The experimental and theoretical successes of cosmology in recent years offer the most dramatic enlargement of our concept of the universe since astronomers first realised the Sun's true place among the stars. In this groundbreaking, thought-provoking and accessible book Professor Sir Martin Rees argues that our universe is just one element in an infinite ensemble, a cosmic archipelago where impassable barriers prohibit communication between the islands. Our 'home universe' is an exceptional member of this ensemble, however, not least because it contains creatures able to observe it and contemplate its nature, past and future. One of these is Rees himself: one of the most creative and original of contemporary scientists, and a wonderful guide to the mysteries of the cosmos.

Big Data Analytics for Internet of Things
Big Data Analytics for Internet of Things

Author: Tausifa Jan Saleem

Publisher: John Wiley & Sons

Published: 2021-04-20

Total Pages: 402

ISBN-13: 1119740754

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BIG DATA ANALYTICS FOR INTERNET OF THINGS Discover the latest developments in IoT Big Data with a new resource from established and emerging leaders in the field Big Data Analytics for Internet of Things delivers a comprehensive overview of all aspects of big data analytics in Internet of Things (IoT) systems. The book includes discussions of the enabling technologies of IoT data analytics, types of IoT data analytics, challenges in IoT data analytics, demand for IoT data analytics, computing platforms, analytical tools, privacy, and security. The distinguished editors have included resources that address key techniques in the analysis of IoT data. The book demonstrates how to select the appropriate techniques to unearth valuable insights from IoT data and offers novel designs for IoT systems. With an abiding focus on practical strategies with concrete applications for data analysts and IoT professionals, Big Data Analytics for Internet of Things also offers readers: A thorough introduction to the Internet of Things, including IoT architectures, enabling technologies, and applications An exploration of the intersection between the Internet of Things and Big Data, including IoT as a source of Big Data, the unique characteristics of IoT data, etc. A discussion of the IoT data analytics, including the data analytical requirements of IoT data and the types of IoT analytics, including predictive, descriptive, and prescriptive analytics A treatment of machine learning techniques for IoT data analytics Perfect for professionals, industry practitioners, and researchers engaged in big data analytics related to IoT systems, Big Data Analytics for Internet of Things will also earn a place in the libraries of IoT designers and manufacturers interested in facilitating the efficient implementation of data analytics strategies.

Visualizing Quaternions
Visualizing Quaternions

Author: Andrew J. Hanson

Publisher: Elsevier

Published: 2006-02-06

Total Pages: 530

ISBN-13: 0080474772

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Introduced 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.

Wandering Towards a Goal
Wandering Towards a Goal

Author: Anthony Aguirre

Publisher: Springer

Published: 2018-05-30

Total Pages: 251

ISBN-13: 3319757261

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This collection of prize-winning essays addresses the controversial question of how meaning and goals can emerge in a physical world governed by mathematical laws. What are the prerequisites for a system to have goals? What makes a physical process into a signal? Does eliminating the homunculus solve the problem? The three first-prize winners, Larissa Albantakis, Carlo Rovelli and Jochen Szangolies tackle exactly these challenges, while many other aspects (agency, the role of the observer, causality versus teleology, ghosts in the machine etc.) feature in the other award winning contributions. All contributions are accessible to non-specialists. These seventeen stimulating and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition in 2017.The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.

Origins of Osiris and his cult
Origins of Osiris and his cult

Author: John Gwyn Griffiths

Publisher: BRILL

Published: 2018-08-14

Total Pages: 301

ISBN-13: 9004378588

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Preliminary Material /J. Gwyn Griffiths -- The Original Myth /J. Gwyn Griffiths -- The Original Cult /J. Gwyn Griffiths -- An Upper Egyptian God of The Royal Dead /J. Gwyn Griffiths -- The Association with Water and Vegetation /J. Gwyn Griffiths -- The Ruler and Judge of the Dead /J. Gwyn Griffiths -- The Cult and the Society /J. Gwyn Griffiths -- An Embryonic System of Salvation /J. Gwyn Griffiths -- Addenda /J. Gwyn Griffiths -- Bibliography /J. Gwyn Griffiths -- Index of Texts Cited /J. Gwyn Griffiths -- General Index /J. Gwyn Griffiths -- Linguistic Indices /J. Gwyn Griffiths.

Complex Numbers in n Dimensions
Complex Numbers in n Dimensions

Author: S. Olariu

Publisher: Elsevier

Published: 2002-06-20

Total Pages: 286

ISBN-13: 0080529585

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Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers.The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functionsof the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions.In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible.The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.

Leonardo Pisano (Fibonacci)
Leonardo Pisano (Fibonacci)

Author: L. E. Sigler

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 147

ISBN-13: 0080886507

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The Book of Squares by Fibonacci is a gem in the mathematical literature and one of the most important mathematical treatises written in the Middle Ages. It is a collection of theorems on indeterminate analysis and equations of second degree which yield, among other results, a solution to a problem proposed by Master John of Palermo to Leonardo at the Court of Frederick II. The book was dedicated and presented to the Emperor at Pisa in 1225. Dating back to the 13th century the book exhibits the early and continued fascination of men with our number system and the relationship among numbers with special properties such as prime numbers, squares, and odd numbers. The faithful translation into modern English and the commentary by the translator make this book accessible to professional mathematicians and amateurs who have always been intrigued by the lure of our number system.