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

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

Author: Chris McMullen

Publisher:

Published: 2013-01-19

Total Pages: 92

ISBN-13: 9780615750040

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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!

Full Color Illustrations of the Fourth Dimension

Full Color Illustrations of the Fourth Dimension PDF

Author: Chris McMullen Ph. D.

Publisher: CreateSpace

Published: 2009-10

Total Pages: 42

ISBN-13: 9781449529345

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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

The Visual Guide to Extra Dimensions PDF

Author: Chris McMullen

Publisher: CreateSpace

Published: 2008-08-17

Total Pages: 166

ISBN-13: 9781438298924

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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 Visual Guide to Extra Dimensions

The Visual Guide to Extra Dimensions PDF

Author: Chris McMullen

Publisher: CreateSpace

Published: 2009-03-05

Total Pages: 218

ISBN-13: 9781441497536

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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: Toward a Geometry of Higher Reality

The Fourth Dimension: Toward a Geometry of Higher Reality PDF

Author: Rudy Rucker

Publisher: Courier Corporation

Published: 2014-08-18

Total Pages: 240

ISBN-13: 0486798194

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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.

Art Meets Mathematics in the Fourth Dimension

Art Meets Mathematics in the Fourth Dimension PDF

Author: Stephen Leon Lipscomb

Publisher: Springer

Published: 2014-10-13

Total Pages: 184

ISBN-13: 3319062549

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To see objects that live in the fourth dimension we humans would need to add a fourth dimension to our three-dimensional vision. An example of such an object that lives in the fourth dimension is a hyper-sphere or “3-sphere.” The quest to imagine the elusive 3-sphere has deep historical roots: medieval poet Dante Alighieri used a 3-sphere to convey his allegorical vision of the Christian afterlife in his Divine Comedy. In 1917, Albert Einstein visualized the universe as a 3-sphere, describing this imagery as “the place where the reader’s imagination boggles. Nobody can imagine this thing.” Over time, however, understanding of the concept of a dimension evolved. By 2003, a researcher had successfully rendered into human vision the structure of a 4-web (think of an ever increasingly-dense spider’s web). In this text, Stephen Lipscomb takes his innovative dimension theory research a step further, using the 4-web to reveal a new partial image of a 3-sphere. Illustrations support the reader’s understanding of the mathematics behind this process. Lipscomb describes a computer program that can produce partial images of a 3-sphere and suggests methods of discerning other fourth-dimensional objects that may serve as the basis for future artwork.

The Fourth Dimension Simply Explained (Illustrated Edition) (Dodo Press)

The Fourth Dimension Simply Explained (Illustrated Edition) (Dodo Press) PDF

Author: Henry P. Manning

Publisher:

Published: 2009-06

Total Pages: 210

ISBN-13: 9781409989240

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Henry Parker Manning (1859-1956) was an American professor of mathematics. In 1889, he entered Johns Hopkins University to study mathematics, astronomy and physics. When he received his Ph. D. degree in 1891, his first printed paper had already appeared in the American Journal of Mathematics. When he was nearly seventy, Manning learned early Egyptian hieroglypics, and collaborated with Arnold Buffum Chace in his publication of the Rhind Mathematical Papyrus. He retired in 1930 and spent several years as associate editor of the American Mathematical Monthly. Amongst his other works are Non-Euclidean Geometry (1901), Irrational Numbers and Their Representation by Sequences and Series (1906), The Fourth Dimension Simply Explained (1910) and Geometry of Four Dimensions (1914).

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