The Visual Guide to Extra Dimensions Volume 1, Chris McMullen
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About this book :-
The Visual Guide to Extra Dimensions Volume 1
This book takes you on a visual tour of a fourth dimension of space. It 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. Here is a sample of what you will find: A fascinating tour of the second and lower dimensions, which will help to understand the fourth dimension by analogy. A chapter dedicated toward imagining what it might be like to live in a hypothetical 4D hyperuniverse. This includes details like 4D wheels with axles, a 4D staircase, and a 4D room. Pictures of flat 4D objects called polytopes, like the tesseract, pentachoron, and icositetrachoron. A unique graph of a hecatonicosachoron has 12 of its 120 bounding dodecahedra highlighted to help visualize its complicated structure. In-depth discussion of the hypercube, including numerical patterns, rotations, cross sections, and perspective. Watch a tesseract unfold. Visual intersections of 15 pairs of perpendicular planes and 6 pairs of orthogonal hyperplanes in 4D space. Unique graphs of curved hypersurfaces in 4D space, like the glome, spherinder, cubinder, and hyperparaboloid.
Several puzzles are included to challenge the reader to contemplate the fourth dimension. Answers are included at the back of the book. This book is highly visual and very conceptual such that anyone with an appreciation for geometry may understand it, while at the same time including ample detail to also satisfy readers with a strong background in mathematics.
Book Detail :-
Title: The Visual Guide to Extra Dimensions Volume 1
Author(s): Chris McMullen
Publisher: CreateSpace Independent Publishing Platform
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About Author :-
The author Curtis Tracy McMullen is an American mathematician who is the Professor of Mathematics at
Harvard University . He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüller theory. McMullen graduated as valedictorian in 1980 from Williams College and obtained his Ph.D. in 1985 from Harvard University, supervised by Dennis Sullivan. He held post-doctoral positions at the
Massachusetts Institute of Technology , the Mathematical Sciences Research Institute, and the Institute for Advanced Study, after which he was on the faculty at
Princeton University (1987–1990) and the
University of California, Berkeley (1990–1997), before joining Harvard in 1997.
The author, Dr. Chris McMullen, has over 20 years of experience teaching university physics in California, Oklahoma, Pennsylvania, and Louisiana (and has also taught physics to gifted high school students). Dr. McMullen currently teaches physics at Northwestern State University of Louisiana. He has also published a half-dozen papers on the collider phenomenology of superstring-inspired large extra dimensions. Chris McMullen earned his Ph.D. in particle physics from Oklahoma State University (and his M.S. in physics from California State University, Northridge).
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Book Contents :-
The Visual Guide to Extra Dimensions Volume 1
cover the following topics.
1. Common Objections
1.0 Is Time the Fourth Dimension?
1.1 Where Are the Extra Dimensions?
1.2 Why Study Extra Dimensions?
1.3 How Can Extra Dimensions Be Detected?
2. Visualizing the Fourth Dimension
2.0 The Fourth Dimension
2.1 Projective Geometry
2.2 Drawing the Fourth Dimension
2.3 Constructing the Fourth Dimension
2.4 Higher-Dimensional Perspective
2.5 Lower-Dimensional Analogies
2.6 Snapshots of the Fourth Dimension
3. Higher-Dimensional Polytopes
3.0 Polygons, Polyhedra, and Polychora
3.1 Anatomy of a Tesseract
3.2 Hypercube Patterns
3.3 Anatomy of a Pentachoron
3.4 Simplex Patterns
3.5 Other Polytopes
4. Curved Hypersurfaces
4.3 Anatomy of a Glome
4.5 Quadric Hypersurfaces
5. A Hypothetical Hyperuniverse
5.0 Hyperuniverse NCF4D-U
5.1 The Physics of NCF4D-U
5.2 Humanoids in the Fourth Dimension
5.3 Higher-Dimensional Chirality
5.4 Construction in the Fourth Dimension
5.5 Life in NCF4D-U
Volume 2 Contents
References and Further Reading
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