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Geometry, Relativity and the Fourth Dimension (Dover Books on Mathematics) [Paperback]

Rudolf Rucker
5.0 out of 5 stars  See all reviews (1 customer review)
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Book Description

28 Mar 2003 Dover Books on Mathematics
Exposition of 4th dimension, concepts of relativity as Flatland characters continue adventures. Popular, easily followed yet accurate, profound. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Accessible to lay readers but also of interest to specialists. Includes 141 illustrations.

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Geometry, Relativity and the Fourth Dimension (Dover Books on Mathematics) + Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension
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Product details

  • Paperback: 133 pages
  • Publisher: Dover Publications Inc.; annotated edition edition (28 Mar 2003)
  • Language: English
  • ISBN-10: 0486234002
  • ISBN-13: 978-0486234007
  • Product Dimensions: 21.5 x 13.7 x 0.8 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 276,837 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Most Helpful Customer Reviews
2 of 2 people found the following review helpful
5.0 out of 5 stars An excellent buy for the layman. 29 Oct 2013
Format:Paperback
The mathematics assumes knowledge of infinitesimals and integration, but don't let that put you off. The real difficulty here is with conceptualisation. The author takes you into an Alice in Wonderland where concepts are genuinely mind bending. A fourth spatial dimension is presented by analogy with the life of A Square, 2-D citizen of Flatland, whose existence is, quite literally, turned around by his encounter with a 3-D sphere. Non-Euclidean geometry and curved space becomes easier to grasp with reference to Flatland and its dimensionally impoverished inhabitants, where even a straight line can be shown to bend in the direction of a higher dimension.

Mind-boggling perceptions of simultaneity, the constant speed of light irrespective of the velocity of its source, and changes in length and mass are discussed in the chapter on Special Relativity. Every event is shown via easy to understand Minowski diagrams as a world line framed in the common 4-D crystalline coordinates of spacetime - the shape of which receives its own chapter.

Every chapter ends with a series of thought-provoking questions and there is a detailed bibliography at the end of this fascinating (and often humorous) little book.
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Amazon.com: 4.3 out of 5 stars  30 reviews
46 of 46 people found the following review helpful
4.0 out of 5 stars Solid Intro to Special Relativity and Non-Euclidean Geometry 25 April 2001
By Fred - Published on Amazon.com
Format:Paperback|Verified Purchase
In his own introduction the author, Mr. R. Rucker, states, "My goal has been to present an intuitive picture of the curved space-time we call home. There are a number of excellent introductions to the separate topics treated here, but there has been no prior weaving of them into a sustained visual account. I looked for a book like this for many years- and finding none, I wrote it." His dedication has been rewarded, as the text is one of the finer introductory books on the curvature of space time and special relativity.
The 'book like this' as the author calls it, walks the reader through several visual explanations that allow a solid mathematical and graphical explanation of modern physics. This isn't always a simple explanation, but there is a certain reward to struggling with the concepts before understanding them. In particular, Chapter 4 on time as a higher dimension makes the entire book worth reading, with many fascinating examples and a host of thought-provoking examples, such as "Schrodinger's Cat."
This is a very interesting book which would be of use to anyone who wishes to push just a little bit further than the typical popular physics text. For those who wish to push even further to solidify their knowledge, there are even questions at the end of each chapter. I highly recommend this book.
38 of 39 people found the following review helpful
5.0 out of 5 stars Weird in all the right ways 13 Dec 2002
By John S. Ryan - Published on Amazon.com
Format:Paperback
I really enjoy Rudy Rucker's nonfiction, and some of his fiction too (_White Light_ is great). He's very good at presenting mind-blowingly cool ideas in accessible expository prose, and he knows _just_ when to throw in the bombs.
This particular book is published by Dover, and it's not one of their usual reprints; it was _originally_ published by Dover. (In 1977, but the geometry of spacetime hasn't changed much since then.) It's an exploration of just what the title says: the geometry of the four-dimensional spacetime that the theory of relativity says is Really Out There.
Well, this is a good book on the subject, but you can get others (although one of the best -- Cornelius Lanczos's delightful _Space Through the Ages_ -- has long been out of print). What's coolest about this one is that Rudy Rucker wrote it.
Which means you get those little bombs thrown in at all the right places. Of course Rucker gives you what any competent mathematician will give you -- a sound introductory presentation of the mathematics of 4D spacetime and relativity theory, which are weird enough if you haven't encountered them before (and maybe even if you have) -- but he doesn't stop there. You also get an argument that the apparent passage of time is an illusion, and a little speculation about how this might tie in with the Many-Worlds Interpretation of quantum mechanics. And even that isn't all: you get a suggestion that it's possible to _develop a spacetime consciousness_ via some sort of meditation techniques or mystical insight, together with an entry in the annotated bibliography referring you (cautiously) to Robert A. Monroe's _Journeys Out of the Body_, whose experiments Rucker himself has tried.
It's like Raymond Smullyan on acid, if you know what I mean. But honest, it really does make sense. And it really will knock your mind loose from your brain even without the use of chemical aids.
This is the sort of thing Rucker does best. He does it in _Infinity and the Mind_, too (with which this volume has a little bit of overlap, but you won't care). Check out that book as well, along with _White Light_. Mathematical hippie mysticism just doesn't get any better.
18 of 19 people found the following review helpful
5.0 out of 5 stars Intro to Non-Euclidean Geometry 8 Jun 2000
By "gsibbery" - Published on Amazon.com
Format:Paperback
This is the best introduction to non-Euclidean geometry and special relativity that I have ever encountered. The book is basic enough to be understandable (at least to a degree) by any intelligent (and determined) adolescent, but deep enough for the physics or math undergraduate and perhaps even graduate student to find continual interest in. Rucker has a way of introducing complex ideas in a rather simple fashion so trhat one doesn't often realise how deep the subject matter is at first. Unlike some of his other books, however, considerable math background is required and a substantial amount of effort and force of will on the part of the reader will be necessary. All the same, the book is an intensely interesting foray into the world of geometry and relativistic physics. His adaption af Abbott's "A.Square" character to ealborated his ideas are particularly amusing and helpful.
18 of 19 people found the following review helpful
5.0 out of 5 stars Now I get it!!! 21 Aug 2001
By Random Joys - Published on Amazon.com
Format:Paperback
Yes, finally, I get the hoopla with the fourth dimension. Rucker explains things with lots of classsical geometric illustrations. Not intending to scare you, I must warn you that he takes the reader all the way to a 5-dimensional world. Still, it is simple to explain, because he uses line-land (the 2-dimansional version of flatland) adds a dimension, then one more, and the result can be visualized in 3-D. I am just astounded that I could understand this without mind-crunching effort. It was not an easy read, but it was not very hard either. No derivatives, matrixes, integrals, or any of the other off-putting versions of mathematics. Just straight (actually fairly wrinkled) geometry.
14 of 16 people found the following review helpful
5.0 out of 5 stars Amazing concepts of space and time !!! 5 Mar 1999
By A Customer - Published on Amazon.com
Format:Paperback
An excellent introduction to concepts of space and time in modern physics, including non-Euclidean geometry - the geometry of the curved spaces. Minimal background in mathematics is requested and multiple diagrams help a better understanding of the most difficult passages. The book is so interesting that I finished it in 5 days !!!
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