Visual Guide to Extra Dimensions : Visualizing the Fourth Dimension, Higher-Dimensional Polytopes, and Curved Hypersurfaces

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: 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.

PUZZLES: Several puzzles are included to challenge the reader to contemplate the fourth dimension. Answers are included at the back of the book.

AUDIENCE: 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.

Chris McMullen is a physics instructor at Northwestern State University of Louisiana. He earned his Ph.D. in phenomenological high-energy physics (particle physics) from Oklahoma State University in 2002. Originally from California, he earned his Master's degree from California State University, Northridge, where his thesis was in the field of electron spin resonance. He has published several papers on the prospects for discovering large superstring-inspired extra dimensions at the Large Hadron Collider, which is his area of specialization. Dr. McMullen published The Visual Guide to Extra Dimensions, Volumes 1 and 2, to share his passion for the geometry and physics of the fourth dimension. He also wrote these books, Full-Color Illustrations of the Fourth Dimension, Volumes 1 and 2, to help illustrate the geometry of a fourth dimension of space. Dr. McMullen was fascinated with a fourth dimension of space when he first read Rudy Rucker's introduction to the subject during high school. He happened to be working on his Ph.D. in particle physics when Arkani-Hamed, Dimopoulos, and Dvali wrote a famous technical paper motivating large superstring-inspired extra dimensions, which transformed the subject of the fourth dimension from philosophy to a plausibly experimental science. Dr. McMullen has published these general-audience books on the fourth dimension to share his passion for the math and physics of extra dimensions. One of his favorite sayings is: May your contemplation of a fourth dimension of space enhance the dimensionality of your thoughts.