A Visual Introduction To The Fourth Dimension Rectangular 4d Geometry

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A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry)

Chris McMullen,Chris McMullen Ph D
A Visual Introduction to the Fourth Dimension Rectangular 4D Geometry Book PDF

Author : Chris McMullen,Chris McMullen Ph D
Publisher : Unknown
Page : 92 pages
File Size : 41,6 Mb
Release : 2013-01-19
Category : Electronic
ISBN : 0615750044

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A Visual Introduction to the Fourth Dimension (Rectangular 4D Geometry) by Chris McMullen,Chris McMullen Ph D Pdf

This colorful, visual introduction to the fourth dimension provides a clear explanation of the concepts and numerous illustrations. It is written with a touch of personality that makes this an engaging read instead of a dry math text. The content is very accessible, yet at the same time detailed enough to satisfy the interests of advanced readers. This book is devoted to geometry; there are no spiritual or religious components to this book. May you enjoy your journey into the fascinating world of the fourth dimension! Contents: Introduction Chapter 0: What Is a Dimension? Chapter 1: Dimensions Zero and One Chapter 2: The Second Dimension Chapter 3: Three-Dimensional Space Chapter 4: A Fourth Dimension of Space Chapter 5: Tesseracts and Hypercubes Chapter 6: Hypercube Patterns Chapter 7: Planes and Hyperplanes Chapter 8: Tesseracts in Perspective Chapter 9: Rotations in 4D Space Chapter 10: Unfolding a Tesseract Chapter 11: Cross Sections of a Tesseract Chapter 12: Living in a 4D House Further Reading Glossary About the Author Put on your spacesuit, strap on your safety harness, swallow your anti-nausea medicine, and enjoy this journey into a fourth dimension of space! 10D, 9D, 8D, 7D, 6D, 5D, 4D, 3D, 2D, 1D, 0D. Blast off!

Projective Geometry

T. Ewan Faulkner
Projective Geometry Book PDF

Author : T. Ewan Faulkner
Publisher : Courier Corporation
Page : 148 pages
File Size : 41,5 Mb
Release : 2013-02-20
Category : Mathematics
ISBN : 9780486154893

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Projective Geometry by T. Ewan Faulkner Pdf

Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960 edition.

Full Color Illustrations of the Fourth Dimension

Chris McMullen Ph. D.,Chris McMullen
Full Color Illustrations of the Fourth Dimension Book PDF

Author : Chris McMullen Ph. D.,Chris McMullen
Publisher : CreateSpace
Page : 42 pages
File Size : 51,7 Mb
Release : 2009-10
Category : Mathematics
ISBN : 1449529348

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Full Color Illustrations of the Fourth Dimension by Chris McMullen Ph. D.,Chris McMullen Pdf

Visualize hypercheckers and hyperchess in the 4th dimension, rotate a Rubik's hypercube, stack tesseracts together to build a hyperpyramid or a hypercross, view a hypertable with hyperchairs, climb hyperstairs, open the hyperdoor to a hyperhouse, watch hypertelevision, read a hyperbook, arrange glomes in a 4D lattice structure to create hypercrystals, stack hyperfruits at a hypersupermarket, record the position of a hyperstar with hypercelestial coordinates, make a hypermap using hypercompass directions, watch a spinning hyperplanet with tilt revolve around a hypersun, see a sample alphanumeric system for writing and arithmetic in 4D space, line up a shot on a hyperbilliards table, enjoy hyperbowling or hypertennis, and contemplate an object's reflection from a hyperplanar or hyperspherical mirror - all on this colorful journey through the fourth dimension. Each page consists of colorful images of four-dimensional objects with a paragraph caption describing the figures at the bottom.

The Visual Guide to Extra Dimensions

Chris McMullen
The Visual Guide to Extra Dimensions Book PDF

Author : Chris McMullen
Publisher : CreateSpace
Page : 166 pages
File Size : 49,5 Mb
Release : 2008-08-17
Category : Mathematics
ISBN : 1438298927

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The Visual Guide to Extra Dimensions by Chris McMullen Pdf

Watch a tesseract unfold. See how the 3D cross section of a hypercube changes as the hypercube rotates. View 4D wheels with axles with a spherinder or cubinder structure. Imagine climbing a 4D staircase. Find 10 out of 120 dodecahedra of a hecatonicosachoron highlighted... all on this visual tour of the fourth dimension.The book is much more visual and conceptual than algebraic, yet it is detailed and technical, with the intention of satisfying the needs of mathematically-minded readers familiar with the fundamentals of algebra, geometry, and graphing.

The Fourth Dimension: Toward a Geometry of Higher Reality

Rudy Rucker
The Fourth Dimension Toward a Geometry of Higher Reality Book PDF

Author : Rudy Rucker
Publisher : Courier Corporation
Page : 240 pages
File Size : 54,9 Mb
Release : 2014-08-18
Category : Science
ISBN : 9780486798196

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The Fourth Dimension: Toward a Geometry of Higher Reality by Rudy Rucker Pdf

One of the most talented contemporary authors of cutting-edge math and science books conducts a fascinating tour of a higher reality, the fourth dimension. Includes problems, puzzles, and 200 drawings. "Informative and mind-dazzling." — Martin Gardner.

The Visual Guide to Extra Dimensions

Chris McMullen
The Visual Guide to Extra Dimensions Book PDF

Author : Chris McMullen
Publisher : CreateSpace
Page : 218 pages
File Size : 47,6 Mb
Release : 2009-03-05
Category : Science
ISBN : 1441497536

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The Visual Guide to Extra Dimensions by Chris McMullen Pdf

AUTHOR: Chris McMullen earned his Ph.D. in particle physics from Oklahoma State University. Dr. McMullen currently teaches physics at Northwestern State University of Louisiana. His background on the geometry and physics of a possible fourth dimension of space includes a half-dozen research papers on the prospects of discovering large extra dimensions at the Large Hadron Collider. DESCRIPTION: While Volume 1 covered the geometry of extra dimensions in detail, Volume 2 focuses on the physics of extra string-inspired dimensions. Consider the problem and solution of expressing the cross product in higher dimensions. See the effect that the extra flux of field lines has on Gauss's law in higher dimensions. Explore how extra dimensions may be hidden via compactification. Discover the recent motivation for the case of extra dimensions that are much larger than originally predicted by string theory. Read about current and upcoming experiments with the potential to detect the presence of large extra dimensions in our universe. Learn the fundamentals of special and general relativity, quantum mechanics, and string theory, and how these relate to extra dimensions... All on this visual introduction to the fourth and higher dimensions. This guide is conceptually and visually detailed, intended for mathematically-minded readers who may have not yet been exposed to calculus. PUZZLES: Several puzzles are included to challenge the reader to contemplate the fourth dimension. Answers are included at the back of the book.

The Fourth Dimension Simply Explained

Henry Parker Manning,Thomas F. Banchoff
The Fourth Dimension Simply Explained Book PDF

Author : Henry Parker Manning,Thomas F. Banchoff
Publisher : Courier Corporation
Page : 274 pages
File Size : 40,9 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 9780486438894

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The Fourth Dimension Simply Explained by Henry Parker Manning,Thomas F. Banchoff Pdf

Readable and informative, this collection of 22 essays employs a minimum of mathematics to explain how the fourth dimension may be studied, the relationship of non-Euclidean geometry to the fourth dimension, analogues to three-dimensional space, four-dimensional absurdities and curiosities, and the simpler properties of four-dimensional space. 1910 edition. 82 figures.

Multiple View Geometry in Computer Vision

Richard Hartley,Andrew Zisserman
Multiple View Geometry in Computer Vision Book PDF

Author : Richard Hartley,Andrew Zisserman
Publisher : Cambridge University Press
Page : 676 pages
File Size : 42,5 Mb
Release : 2004-03-25
Category : Computers
ISBN : 9781139449144

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Multiple View Geometry in Computer Vision by Richard Hartley,Andrew Zisserman Pdf

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Full Color Illustrations of the Fourth Dimension, Volume 1

Ph. D. Chris McMullen
Full Color Illustrations of the Fourth Dimension Volume 1 Book PDF

Author : Ph. D. Chris McMullen
Publisher : CreateSpace
Page : 42 pages
File Size : 52,7 Mb
Release : 2009-06
Category : Mathematics
ISBN : 1442141638

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Full Color Illustrations of the Fourth Dimension, Volume 1 by Ph. D. Chris McMullen Pdf

These full-color illustrations on 8"x10" pages are at once aesthetically captivating and instructive. Each page consists of colorful images of tesseracts (4D hypercubes) or glomes (4D hyperspheres) with a paragraph caption describing the figures at the bottom. Color is used effectively to show how to visualize the features of tesseracts and glomes, how to draw tesseracts in perspective, how a tesseract unfolds, how the features of tesseracts and glomes change as they rotate, how to find the intersection of a tesseract or glome with a hyperplane, how hyperspherical coordinates are defined, how to understand hypercompass directions, and how to draw longitudes, hyperlatitudes, and latitudes. Rectangular hyperboxes and a hyperellipsoid are also shown. Subsequent volumes of this series will build upon these fundamental 4D objects to help you imagine features of a 4D world such as a hyperchair, a hypercross, a hyperpyramid, a hyperhouse, crystal structures, and simple hypermachines.

The Planiverse

A.K. Dewdney
The Planiverse Book PDF

Author : A.K. Dewdney
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461301998

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The Planiverse by A.K. Dewdney Pdf

A classic book about life in a two-dimensional universe, written by a well-known author. Now brought back into print in this revised and updated edition, the book is written within the great tradition of Abbott's Flatland, and Hinton's famous Sphereland. Accessible, imaginative, and clever, it will appeal to a wide array of readers, from serious mathematicians and computer scientists, to science fiction fans.

Visualizing Quaternions

Andrew J. Hanson
Visualizing Quaternions Book PDF

Author : Andrew J. Hanson
Publisher : Elsevier
Page : 530 pages
File Size : 43,7 Mb
Release : 2006-02-06
Category : Mathematics
ISBN : 9780080474779

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Visualizing Quaternions by Andrew J. Hanson Pdf

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.

The Fourth Dimension

E. H. Neville
The Fourth Dimension Book PDF

Author : E. H. Neville
Publisher : Cambridge University Press
Page : 67 pages
File Size : 50,5 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9781316633328

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The Fourth Dimension by E. H. Neville Pdf

Originally published in 1921, this book by renowned British mathematician E. H. Neville attempts to develop geometrical methods in four-dimensional space.

R for Data Science

Hadley Wickham,Garrett Grolemund
R for Data Science Book PDF

Author : Hadley Wickham,Garrett Grolemund
Publisher : "O'Reilly Media, Inc."
Page : 521 pages
File Size : 55,6 Mb
Release : 2016-12-12
Category : Computers
ISBN : 9781491910368

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R for Data Science by Hadley Wickham,Garrett Grolemund Pdf

Learn how to use R to turn raw data into insight, knowledge, and understanding. This book introduces you to R, RStudio, and the tidyverse, a collection of R packages designed to work together to make data science fast, fluent, and fun. Suitable for readers with no previous programming experience, R for Data Science is designed to get you doing data science as quickly as possible. Authors Hadley Wickham and Garrett Grolemund guide you through the steps of importing, wrangling, exploring, and modeling your data and communicating the results. You'll get a complete, big-picture understanding of the data science cycle, along with basic tools you need to manage the details. Each section of the book is paired with exercises to help you practice what you've learned along the way. You'll learn how to: Wrangle—transform your datasets into a form convenient for analysis Program—learn powerful R tools for solving data problems with greater clarity and ease Explore—examine your data, generate hypotheses, and quickly test them Model—provide a low-dimensional summary that captures true "signals" in your dataset Communicate—learn R Markdown for integrating prose, code, and results

The Fourth Dimension

Rudy von Bitter Rucker,Rudy Rucker
The Fourth Dimension Book PDF

Author : Rudy von Bitter Rucker,Rudy Rucker
Publisher : Houghton Mifflin Harcourt
Page : 244 pages
File Size : 48,7 Mb
Release : 1985
Category : Philosophy
ISBN : 0395393884

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The Fourth Dimension by Rudy von Bitter Rucker,Rudy Rucker Pdf

A detailed description of what the fourth dimension would be like.

The Wild World of 4-Manifolds

Alexandru Scorpan
The Wild World of 4 Manifolds Book PDF

Author : Alexandru Scorpan
Publisher : American Mathematical Society
Page : 614 pages
File Size : 49,9 Mb
Release : 2022-01-26
Category : Mathematics
ISBN : 9781470468613

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The Wild World of 4-Manifolds by Alexandru Scorpan Pdf

What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. —MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. — Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold—the intersection form—and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.