The Visual Guide To Extra Dimensions: Visualizing The Fourth Dimension, Higher-Dimensional Polytopes, And Curved Hypersurfaces
by Chris McMullen
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Book Summary Information
Author: Chris McMullenEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 2008-08-17
ISBN: 1438298927
Number of pages: 166
Publisher: CreateSpace
Product features:
- ISBN13: 9781438298924
- Condition: New
- Notes: BRAND NEW FROM PUBLISHER! 100% Satisfaction Guarantee. Tracking provided on most orders. Buy with Confidence! Millions of books sold!
Book Reviews of The Visual Guide To Extra Dimensions: Visualizing The Fourth Dimension, Higher-Dimensional Polytopes, And Curved Hypersurfaces
Book Review: Packed with Illustrations
Summary: 5 Stars
* I was pleasantly surprised at the number and quality of diagrams included in this book on the fourth dimension. Many diagrams were instructive. They helped me visualize 4D objects, making the fourth dimension seem somewhat less abstract.
* This was the first time that I can recall seeing 4D graphs of hypersurfaces. This includes the cubinder, spherinder, hypercones, hyperparaboloids, hyperhyperboloids, and hypertori. The following chapter, A Hypothetical Hyperuniverse, describes possible 4D objects, machines, and beings in terms of such hypersurfaces. Put together, I can almost imagine a 4D world.
* There is also a very detailed chapter on objects with flat surfaces, called polytopes (such as the hypercube). The hypercube is analyzed extensively. The simplex and less common polytopes are also included. There are some neat features here, such as diagrams that break down the icositetrachoron.
* I've never found a book on the fourth dimension that suits me perfectly (I can always find something that I would like to change), but there was much that I enjoyed about this book. I highly recommend it to anyone who enjoys thinking about 4D objects.
* I also recommend Rudy Rucker's classic introduction, The 4th Dimension: Toward a Geometry of Higher Reality. Every fan of the fourth dimension should also read Edwin Abbott's Flatland a Romance of Many Dimensions - Edwin Abbott.
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Summary of The Visual Guide To Extra Dimensions: Visualizing The Fourth Dimension, Higher-Dimensional Polytopes, And Curved Hypersurfaces
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.Mathematics Books
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