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The 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
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.
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
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.
166 pages, Paperback
First published March 5, 2009
53 people are currently reading
110 people want to read
About the author
Chris McMullen
181 books322 followersDr. Chris McMullen has over 20 years of experience teaching university physics in California, Oklahoma, Pennsylvania, and Louisiana. Dr. McMullen is also an author of math and science books. Whether in the classroom or as a writer, Dr. McMullen loves sharing knowledge and the art of motivating and engaging students.
Chris McMullen earned his Ph.D. in phenomenological high-energy physics (particle physics) from Oklahoma State University in 2002. Originally from California, Dr. McMullen earned his Master's degree from California State University, Northridge, where his thesis was in the field of electron spin resonance.
Dr. McMullen is well-known for:
• engaging students in challenging ideas through creativity
• breaking difficult problems down into manageable steps
• providing clear and convincing explanations to subtle issues
• his mastery of physics and strong background in mathematics
• helping students become more fluent in practical math skills
As a physics teacher, Dr. McMullen observed that many students lack fluency in fundamental math skills. In an effort to help students of all ages and levels master basic math skills, he published a series of math workbooks on arithmetic, fractions, algebra, geometry, trigonometry, and calculus called the Improve Your Math Fluency Series. Dr. McMullen has also published a variety of science books, including introductions to basic astronomy and chemistry concepts in addition to physics workbooks.
Dr. McMullen is very passionate about teaching. Many students and observers have been impressed with the transformation that occurs when he walks into the classroom, and the interactive engaged discussions that he leads during class time. Dr. McMullen is well-known for drawing monkeys and using them in his physics examples and problems, using his creativity to inspire students. A stressed-out student is likely to be told to throw some bananas at monkeys, smile, and think happy physics thoughts.
Dr. McMullen first published The Visual Guide to Extra Dimensions, Volumes 1 and 2, to share his passion for the geometry and physics of the fourth dimension. Dr. McMullen has coauthored a half-dozen articles on current and future collider searches for large extra dimensions.
In addition to writing and teaching, Dr. McMullen enjoys Scrabble, golf, and chess.
Chris McMullen earned his Ph.D. in phenomenological high-energy physics (particle physics) from Oklahoma State University in 2002. Originally from California, Dr. McMullen earned his Master's degree from California State University, Northridge, where his thesis was in the field of electron spin resonance.
Dr. McMullen is well-known for:
• engaging students in challenging ideas through creativity
• breaking difficult problems down into manageable steps
• providing clear and convincing explanations to subtle issues
• his mastery of physics and strong background in mathematics
• helping students become more fluent in practical math skills
As a physics teacher, Dr. McMullen observed that many students lack fluency in fundamental math skills. In an effort to help students of all ages and levels master basic math skills, he published a series of math workbooks on arithmetic, fractions, algebra, geometry, trigonometry, and calculus called the Improve Your Math Fluency Series. Dr. McMullen has also published a variety of science books, including introductions to basic astronomy and chemistry concepts in addition to physics workbooks.
Dr. McMullen is very passionate about teaching. Many students and observers have been impressed with the transformation that occurs when he walks into the classroom, and the interactive engaged discussions that he leads during class time. Dr. McMullen is well-known for drawing monkeys and using them in his physics examples and problems, using his creativity to inspire students. A stressed-out student is likely to be told to throw some bananas at monkeys, smile, and think happy physics thoughts.
Dr. McMullen first published The Visual Guide to Extra Dimensions, Volumes 1 and 2, to share his passion for the geometry and physics of the fourth dimension. Dr. McMullen has coauthored a half-dozen articles on current and future collider searches for large extra dimensions.
In addition to writing and teaching, Dr. McMullen enjoys Scrabble, golf, and chess.
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Displaying 1 - 4 of 4 reviews
November 24, 2017
I really like the topic and really appreciate the fact that the author is not afraid to tackle the difficulties that arise in representing 4D objects. However, I think some adjustments could make the figures a bit easier to grasp.
For example, something that would clear things up a bit is drawing the edges that a 4D being could see in solid lines (while I do realize those are a lot), instead of randomly assigning solid lines for the part of the figure which is in front of a plane and dashed lines for the part of it that is behind.
Maybe some of the figures with hyperspheres could be made a bit clearer too, but I understand glomes are especially tricky to draw.
By the way, in chapter 5.3, I think I found a mistake. When describing the kinds of 2D tetraminos, shouldn't there be another "zig-zag", the enantiomer of the one depicted? If I'm not mistaken, that zigzag is also quiral! (Just remember Tetris).
The book is, nonetheless, a really good introduction to representing 4D objects, and it has been really useful for me for trying to grasp 4D geometry.
For example, something that would clear things up a bit is drawing the edges that a 4D being could see in solid lines (while I do realize those are a lot), instead of randomly assigning solid lines for the part of the figure which is in front of a plane and dashed lines for the part of it that is behind.
Maybe some of the figures with hyperspheres could be made a bit clearer too, but I understand glomes are especially tricky to draw.
By the way, in chapter 5.3, I think I found a mistake. When describing the kinds of 2D tetraminos, shouldn't there be another "zig-zag", the enantiomer of the one depicted? If I'm not mistaken, that zigzag is also quiral! (Just remember Tetris).
The book is, nonetheless, a really good introduction to representing 4D objects, and it has been really useful for me for trying to grasp 4D geometry.
February 21, 2021
Now this is what I've been looking for! Quick, to the point, and pursuing the hypothetical such as what life would be like in 4D. Math is simple as far as math goes, and sorry, it's later in abundance as thats the only way to visualize it without a front row seat.
November 1, 2017
This book teaches the reader how to comprehend the 4th dimension with dimensions like 5 dimensions with mathematics, and visual representations.
January 28, 2024
Gets better every time I read it. Fantastic. Non-trivial. Well written.
Displaying 1 - 4 of 4 reviews