History: Fiction or Science? (Chronology, No. 1)

Book Description

Recorded history is a finely-woven magic fabric of intricate lies about events predating the sixteenth century. There is not a single piece of evidence that can be reliably and independently traced back earlier than the eleventh century. This book details events that are substantiated by hard facts and logic, and validated by new astronomical research and statistical analysis of ancient sources.

Customer Reviews:

Calculations are only as good as your numbers.......2007-08-03

Yes, we can all agree that mainstream history is nearly 100% BS due to politics, economics, ego, problems with dating techniques, and various conspiracies. Agreed. But, I've been researching the distinct possibility that human history (in terms of civilizations) are much more ancient than we've been told, so coming across this book was very interesting to me. I wondered how Fomenko could be wrong (if at all) because he is very persuasive in his presentations. Then it dawned on me. If at previous times in prehistory, due to the various catastrophies that are well documented (comets, asteroids, planetary disruptions, plasma discharge, pole reversals, etc) the Earth was in a different position in relation to the sun, different tilt on its axis, different orbit, different rotation (in terms of velocity and DIRECTION), and the continents were in different positions, then would this not cause the ancients to see the sky (constellations) differently? In other words, is Fomenko making erronious assumptions about the physics of the Earth in pre-history, which then corrupt his data with regards to dating the relevant astrology? The last event to seriously disrupt our planet occured roughly 3500 years ago, according to other good researchers, so is it possible Fomenko has been confused by this? The vastly different physics of our planet in the not so distant past may explain this confusion, which is not to say the "mainstream" version of history is correct; on the contrary. I am not an expert in these fields, but wanted to see if this idea could spark discussion.

Pants on fire?.......2007-07-19

Will people ever read before spamming? Yes, Jesuits could not rewrite world history alone, they had help. Anyway, Dr Prof Acad A.Fomenko does not point to jesuits as the driving force of world wide history manipulation in published volumes 1,2,3;, actually he barely mentions the poor devils. Check it with 'Search inside' feature, please. China is rarely mentioned either, in fact, Dr Fomenko is completely eurocentric. Right, his theory contradicts all mainstream schools of history, because in their actual state they are all built on blatantly erroneus chronology. You don't need a mysterious cabal (conspiracy) to falsify history, the falsification is its modus operandi. It is inherent to history(ians) to falsify (distort) events, as it is inherent to humans to boast as it is inherent to power (authority) to legimize itself by referrring to glorious past made to its own order. Dr Prof Fomenko and team have identified scores of instances of such manipulation in Russian, European, etc.. history, and delivered valid statistical proof thereof. His own 'reconstruction' is completely another story. Forget c14 as a valid method of dating. W.Libby has initially discovered a brilliant method of INDEPENDENT dating. Too bad, c14 method has become a joke after a forced marrige with dendrochronology with consensual chronological scale inbuilt. Radiocarbon method can't stand blind tests, but is so very productive as a rubberstamp.

Accepted History & Chronology Must Be Changed. .......2007-04-09

There is no doubt that history as most know it is a sham, & institution's version of History both University & Church is fradulent & inaccurate. Everything was established with an agenda, The real "Dark Ages" are now when we have access to incredible amounts of information past authorities & more important 'common folk' didn't have but our institutions & educators are slow to evolve because of what has ignorantly & arrogantly been taught for too long. This is on many subjects not just Chronology.

For anyone to question "Why would a Mathematician have anything credible to say of History?" The answer is from Dr. Fomenko's preface in the book: "It would be worthwhile to remind the reader that in the XVI-XVII century Chronology was considered to be a subdivision of Mathematics." These volumes could possibly be some of the most important works to date & should be read by everyone with an interest in History, especially professors & educators who have a duty to the public. I have read both books & must say that 'Chronology 1' has some very eye opening & revolutionary information. Even if these volumes are part true the implications are profound & opens the doors to further investigations & questions which must be done. I speak several different lanquages & must say the logic Dr. Fomenko uses with "inflection" of words & words being read from left to right in one region & right to left in another then written backwards, the removal of vowels & get down to basics of words, or different cities & locations having the same name etc. is correct. Vowel usage has always been optional & varied, actually complicating linquistics & study. The first thing one has to understand is that words never had a fixed spelling in history like we do now, the spelling of words was mutable & regional, as well as names & titles of people were vast, varied & changed, NOTHING WAS FIXED or understood linear. Matters of Life & Death as well as financial profiteering yesterday & today were & are made with ignorant, illogical & conspiratorial views of history & reality, it's time people get closer to the Truth & society collectively grow up.

Very Interesting.......2007-03-07

It is a good proposal and I believe it will mature into something even better in the future. I think it deserves to be read.

History as Science Fiction.......2007-01-10

Anatoly Fomenko has written a very intriguing book, full of pictures, charts, and computer 'proof' of his thesis: backwards of AD900 we don't really know what happened or when. Between AD900 and AD1600 there is more certainty, but there is still a lot of fuzzy ground, and things don't get reliable until we get past the 1600's where the printing press made it very difficult for the perpetrators of this timeline manipulation to change anything that had been committed to print. The Dark Ages did not happen. Books were burned for a reason. One organization has doubled the actual length of its existence by expanding the real chronology. Read why.

I had always wondered why Christ died about AD33 and yet men waited until the 11th century to form the Knights Templar, the Cathars, etc and go after the Holy Land by force. Why the 1000 year gap? Turns out there wasn't more than a 10-12 year gap and he proves it using astronomy. This also implies that the planet is not as old as we have been told, and current Christian and other creationist scientists are already championing that idea without being aware of Fomenko's book. The two groups, creationist scientists and the Russian mathematical analysts corroborate each other. Fascinating.

Of course, all this flies in the face of what we have been told traditionally is the 'proper' chronology of western civilization, and most readers will experience 'cognitive dissonance' in reading this book. It means that our history going backwards from AD1600 becomes progressively more incorrect and unreliable until it cannot be trusted at all... in the space of 700-800 years.

Naturally, the curious, open-minded reader will want to know WHO did this, WHY, and did any of the events we think of as really ancient ever happen?
Dr. Fomenko is a respected scientist/mathematician at Moscow State University who has already answered these questions to the satisfaction of his initially skeptical colleagues. Most of them are now believers, a few still refuse to believe (the usual diehards), and of course the western press has ignored Fomenko's work -- for obvious reasons when you read the book. The ones who perpetrated this chronology ruse have a lot to answer for. They are still with us. That's why this book is a well-kept secret.

I gave the book a 4-star rating because I was unable to check out some of his claims; those I checked were as he said. But if even 1/3 of his claims are true, this punches a big hole in what we think is our history, the meaning of western civilization, our educational process (for repeating the ruse as gospel), and the trustworthiness of the organization that perpetrated this ruse, well-intentioned or not.

This book relates to current research into a Young Earth paradigm, to John Keel's discoveries about our planet, and Fr Malachi Martin's insights (in his now out-of-print books). We are indeed sheep who are manipulated and kept ignorant -- for a reason. While knowing what these men have to say may be the "booby prize" (as in: 'what can you do with this knowledge?'), it will provide interesting reading. Didn't someone say: "...and the Truth will set you free."?? For you to judge if this book contains the truth.

Average customer rating:

Caution - There are Mistakes
Recommended for one chapter
Excellent if you need a refresher course in geometry
Review and practice
Good for drilling but not for teaching

Schaum's Outline of Geometry
Barnett Rich
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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ASIN: 0070527660

Book Description

Three million high school students and 172, 000 college students enroll in geometry classes every year. Schaum's Outline of Geometry, Third Edition, is fully updated to reflect the many changes in geometry curriculum, including new terminology and notation and a new chapter on how to use the graphing calculator.

Customer Reviews:

Caution - There are Mistakes.......2007-10-01

I bought this book to use with my daughter for added drill and review of Geometry and was shocked to find an inaccurate mathematical statement after the Commutative Law of Multiplication (3a X 5 = 5 X 2a = 10a) and three errors in the solutions provided to practice questions in the first eight pages. I haven't ventured further, but based on my experience thus far, I will need to review every example and problem for accuracy, something I hadn't planned to do and shouldn't need to do.

Recommended for one chapter.......2007-06-16

I encourage you to buy "Geometry Made Easy" over this one, but yet you need this book for the chapter on transformations because the former doesn't include it. The biggest reason for discouraging the use of "Schaum's Outline of Geometry" is that it's so unmotivated and clustered up with lots of details. If this book is going to come with a new edition, it needs to be spaced out with a lot of whitespace around the words. Give the details a breathing space. A good mathematics book is the one that motivates, not strangle the reader. Unfortunately, the details threw "Schaum's Outline of Geometry" into a quagmire.

Excellent if you need a refresher course in geometry.......2007-03-17

I found myself needing to review geometry for the SAT and needed a succinct, clear, and accurate guide. This outline has more than exceeded my expectations. By the time I worked through most of the problems in this book, my geometry skills had doubled and the SAT geometry was relatively easy.

I highly reccomend this book as either a refresher guide or as a textbook.

Review and practice.......2006-11-10

This is a great way to reivew principles and then use the problems for additional practice. Some problems are fully worked, others have only the answer listed. Great addition for someone who learns best by doing problems.

Good for drilling but not for teaching.......2006-11-05

We know from the book's success and from other reviewers that it is good for preparing students who need many easy exercises to drill for a rudimentary exam in geometry. I want to discuss it from the point of view of teaching a student who is interested or could become interested in learning geometry.

In a rigorous presentation of geometry one starts by treating "point", "straight line" (and "plane" in solid geometry) as undefined terms. One states their assumed properties as postulates. One defines all other objects in geometry in terms of these and one derives all other assertions about about geometric objects by logical reasoning alone; one may not use without proof even what is obvious from looking at a figure, e.g., that if two points A, B are inside a triangle then the entire line segment AB is inside.

The teaching of geometry in high school has long been intended as an example of rigorous reasoning but to fully adhere to the above standard would make a course too subtle, long and boring. The challenge for the writer of a school textbook or a curriculum is to present a reasonable amount of geometry, especially geometry needed in applications, and to loosen the standards of rigor by not dwelling much on rigorously proving what is obvious.

How does this book handle the problem? A thin veneer of rigor appears in some places, to be abandoned after a few paragraphs. On pp. 64-65 the book stresses that "point", "line" and "plane" are undefined terms. But it immediately goes on to tell us that if a line segment is divided into parts the length of a line segment is the sum of the lengths of its parts. So, "line" is an undefined term but the book feels free to talk about its segments and their lengths without further explanation.

On pp. 85-86 the book lists 10 postulates of algebra. They are all instances of the fact that in an algebraic expression we may replace any quantity by one that is equal to it. The distributive, associative and commutative laws are not among the postulates but of course the book does not hesitate to use those. After the 10 postulates of algebra come the geometry postulates 11-19. Postulate 14 says that one and only one circle can be drawn with a given point as center and a given radius. Since a circle has been defined on p. 67 as the set of all points at a given distance from the center, it should have been obvious to the authors that there is no need to state this as a postulate. Postulate 15 says that any geometric figure can be moved without changing its size or shape. Needless to say, nowhere was "moving" defined in terms of the undefined concepts point and line.

In sum, there are a few pages in the book where the student is told that geometry is built up by deductive reasoning but they seem to have been inserted as an afterthought and bear no relation to the bulk of the book. With the logic of the book muddled, how are students to know what they can use in a proof? Here "principle"-s come to the rescue. The book contains about 200 "principles". Examples: principle 6 on p. 146: The diagonals of a parallelogram bisect each other. Principle 4 on p. 153: the median of a trapezoid is parallel to its bases and its length is equal to one half the sum of its bases. A few pages later the student is asked to prove some trivialities and if he guesses that of the countless "principles" he has read, the ones he needs to use are among the ones immediately preceding the problem, he will be right.

How far does the book get into geometry? Let A,B,C,D be points on a circle and E be the intersection of AC and BD. Facts about the angles and lengths of this configuration are given much space and, together with Pythagoras' Theorem, represent the limits of the book's scope. As another reviewer noted already, the cover promises solid geometry but the book has none.

Redeeming features of the book are chapter 15, pp. 291-305, which gives the basic ruler and compass constructions and chapter 16, pp. 306-317, which lists and properly proves the theorems of substance in the book. The way I see it, these 27 pages contain the mathematics of the book; the rest is drill.

If your student has or could develop an interest in math, science or technology, the geometry book for him/her is Harold R. Jacobs: Geometry (W.H. Freeman). Math has been my preoccupaton for 60 years but it was still a revelation that geometry could be presented in such a stimulating and attractive manner. There is no straying from or diluting the subject as in other big colorful textbooks. The price is high but worth it. [...]

Schaum's Outline of Finite Element Analysis

Average customer rating:

Worthless - too bad no Zero Stars.
Study Aid
Good Elementary Book
Schaum's on FEA Needs to be Updated
Don't waste your money with other books

Schaum's Outline of Finite Element Analysis
George R. Buchanan
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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ASIN: 0070087148

Book Description

If you want top grades and thorough understanding of finite element analysis, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you accompanying related problems with fully worked solutions. You also get additional problems to solve on your own, working at your own speed. (Answers at the back show you how youÕre doing.) Famous for their clarity, wealth of illustrations and examplesÑand lack of dreary minutiaeÑSchaumÕs Outlines have sold more than 30 million copies worldwide. This guide will show you why!

Customer Reviews:

Worthless - too bad no Zero Stars........2007-06-15

Worthless. My class used Reddy's latest FEA book, and the teacher was pretty good with his supplemental notes - meaning they went well with Reddy's book. This book is outdated. I couldn't use to help with any of the hw problems. My advice is to "Search Inside", look at it with Google Books, or better yet find one at a bookstore somewhere and compare to your class text before buying. I've used a few Schaum's before and this is by far the worst (least helpful).

Study Aid.......2007-02-06

The whole Schuams series is an excellent way to refresh your various math skills, and is also a good introduction to any new concepts.

Good Elementary Book.......2006-03-21

It is a good primer book for the newby in Finite Element Analysis. It has good and clear simple examples

Schaum's on FEA Needs to be Updated.......2006-03-21

Schaum's Outline on Finite Element Analysis was a valuable and important source at the time it was first published in 1995. However, in the intervening 11 years, this field has advanced rapidly, and the material in Professor Buchanan's otherwise excellent outline is now seriously dated.

The outline is still useful for some purposes, but anyone who is looking for a brief introduction and overview of FEA as it is done today will be disappointed or even misled if they depend only on this outline.

On the other hand, the outline does provide a number of useful supplementary problems that may help students who are learning to employ modern FEA software and need to build their understanding of the fundamental ideas behind these methods.

Don't waste your money with other books.......2002-12-14

Don't waste your money buying those hardcover books on Finite Element Method. If you wanna learn this subject soon this is the right book. Beside it you should study the book "An Introduction to Finite Element Method" by J. N. Reddy.

Geometry, Relativity and the Fourth Dimension

Average customer rating:

With few exceptions, it is a readable, stepwise explanation of how the universe is structured
The best book ever in its field
explain dimensions very well
See what's outside the box
excellent book, fascinating author, start your exploration! :)

Geometry, Relativity and the Fourth Dimension
Rudolf Rucker
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486234002

Book Description

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.

Customer Reviews:

With few exceptions, it is a readable, stepwise explanation of how the universe is structured.......2007-06-29

To understand relativity, it is necessary to understand geometry, specifically how a straight line can be curved. For nearly everyone, any attempt to understand four-dimensional space begins with understanding how a three-dimensional creature would appear to a two-dimensional one. One of the earliest and still the greatest of all introductions to going up a dimension is "Flatland" by Edwin A. Abbott. Quite naturally and sensibly, Rucker starts with Abbott's rendition of the properties of Flatland.
Rucker then moves on to the idea of curved space, where the shortest distance between two points is a "straight line", which is curved by the properties of the space. The space that we occupy is curved by the presence of matter, as Einstein claimed in his relativity theories. Furthermore, movement causes shrinkage in the direction of the movement and the slowing of time, which causes time to become just another dimension of space. As counterintuitive as this may appear, Einstein's relativity theory has been verified over and over again to a large number of significant figures.
One of the best things about this book is that Rucker has included problems at the end of each chapter. These problems reinforce the concepts of the chapter; it is unfortunate that no solutions were included.
In this book, Rucker steps the reader through all of the background material necessary to understand relativity and four-dimensional space. With few exceptions, the accounts are understandable to anyone with an understanding of college algebra.

The best book ever in its field.......2007-04-19

This book has presented the most difficult topics of our world with the easiest words. After reading this book many of my questions that I had in my mind for a long time were answered. It's worth thousands more than its price.
Congratulation to Mr. Rudolf Rucker for his great book.

explain dimensions very well.......2007-03-31

it is published years before but it is almost new for today and it explain dimensions and shape of space well and clearly .thanx to amazon for sending me timely.

See what's outside the box.......2007-03-30

Over two millenia ago, Euclid wrote his masterpiece Elements and stated in his fifth postulate that only one perpendicular line could pass through any one point adjacent to another line.

One hundred fifty years ago, it was proven that yet another geometry could be described by asserting that more than one parallel line could pass through such a point.

Building on these ideas, Rucker briefly yet thoroughly surveys the relevant mathematics outside the box of Euclidian geometry.

It's a fascinating place too because it involves considerations of hyperspace, four dimensional travels and ultimately Einstein's theory of relativity.

Copiously filled with illustrations to help drive home his points, Rucker has produced a book that meaningful helps one visualize and better understand the fourth dimension.

This book is an excellent read along with Choas, Coincidences and All that Math Jazz, The Fourth Dimension Simply Explained, Einstein's own Relativity and Hyperspace by Michio Kaku which discusses all these ideas as well as contemporary string theory (which purports to pull it all together).

excellent book, fascinating author, start your exploration! :).......2005-12-31

Mr. Rucker is a 'genius educator' in my opinion :) he can open your mind and get you started - no matter what direction you wanna take! :) whether it be philosophy, math, physics, or even spirtual things - Mr. Rucker can get you going! to me, he is one of the great men of these modern times :) ah, i remember! pay particular attention to visualizing hyper-dimensional objects .. it can be done! good luck and may god bless all of you! :)

Average customer rating:

Very good
OK as a supliment
Great resource for college-level math students...
If you are a good researcher, this is a good resource!

Schaum's Outline of General Topology
Seymour Lipschutz
Manufacturer: McGraw-Hill
ProductGroup: Book
Binding: Paperback

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ASIN: 0070379882

Book Description

With more than 30 million copies sold, Schaum's are the most popular study guide on the planet. Mathematics students around the world turn to this clear and complete guide to general topology for its through introduction to the subject, including easy-to-follow explanations of topology of the line and plane and topological spaces. With 650 fully solved problems and hundreds more to solve on your own (with answers supplied), this guide can help you spend less time studying while you make better grades!

Customer Reviews:

Very good.......2006-06-30

The book is wonderful, recommends to all. Very good

Geraldo Tavares -Campinas/SP- Brasil.

OK as a supliment.......2006-01-27

If you're taking a basic topology class (or any other abstract math class), it is usefull to have other books to reference. This book was only OK as a supliment. I found that you had to be careful the definitions, as some topologists will axiomize ideas differently (I found this happened the most when dealing with seperation axioms). I found that there are a few dover books out there that are a little more readable (Gemignani's, Mendelson's and Willard's books all come to my mind). This book won't hurt, but there are other options within it's price range.

Great resource for college-level math students..........2005-01-08

I wish I had known about this summary when I was taking my Fundamental Concepts in Math course at the university. I would have done a lot better! I agree with the previous reviewer about adding REA's Problem Solver book for a complete set.

The topics covered include: (1) Sets and relations, (2) Functions, (3) Cardinality and Order, (4) Topology of the line and plane, (5) Topological Spaces, (6) Bases and Subbases [sic], (7) Continuity and topological equivalence, (7) Metric and normed spaces, (8)Countability, (10) Separation axioms, (11) Compactness, (12) Product spaces, (13) Connectedness, (14) Complete metric spaces, and (15) Function spaces. There is an appendix about Properties of real numbers.

This is a technical book and not for a casual reader. I believe this will be difficult for a teach-yourself-to-know reader, unless the reader has considerable math experience.

Another book that I found helpful in Fundamental Concepts (not simply Topology) was Courant et al., What is mathematics? 2nd ed.

My Fundamental Concepts professor taught the course with only lecture notes, and I was completely lost. Had I had this outline, I think I would have done better, because this Outline has a number of solved problems and exercises.

Good luck.

If you are a good researcher, this is a good resource!.......2002-07-23

If you are taking an introductory Topology course, I recommend using this book. It is a little old, and some of the problems are not solved, but it will offer you an advantage when using your class text. You should use Lipschutz's book together with REA's Topology Problem Solver to give you full study advantage when taking on this most difficult subject. With some moderate study, you should do better on your assignements!

General Relativity (Springer Undergraduate Mathematics Series)

Average customer rating:

General Relativity (Springer Undergraduate Mathematics Series)
N.M.J. Woodhouse
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Accessories:

ASIN: 1846284864

Book Description

Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the "local inertial coordinates" set up by an observer in free fall, in which special relativity is valid over short times and distances.

In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study.

While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicists who would like to see a more mathematical approach to the ideas.

Spinors and Space-Time (Cambridge Monographs on Mathematical Physics)

Average customer rating:

Complete introduction to spinors and space-time physics

Spinors and Space-Time (Cambridge Monographs on Mathematical Physics)
Roger Penrose , and Wolfgang Rindler
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521337070

Book Description

This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.

Customer Reviews:

Complete introduction to spinors and space-time physics.......2006-04-16

This book provides a very comprehensive account of two-spinor calculus, along with some of its applications to physics. This material is intrinsically interesting and has some applications to physics, in addition it also provides the background needed to study volume II. The second volume covers applications to physics in more detail and twistors too.

Spinors unquestionably play a central role in quantum mechanics. Some problems in general relativity are certainly more transparent when approached with spinors, as compared to the usual tensor analysis. This combined with the fact that one can roughly view a spinor as the square root of a null vector and considering things like Dirac's scissors suggest the possibility that spinors are more fundamental than tensors and may provide a deeper insight into the nature of space-time than tensors do. This is one of the main themes of the book, I personally find the arguments intriguing.

The first two chapters establish the geometry and algebra of spinors. The pace is reasonable and the approach is very geometrical. Then the correspondence between tensors and spinors is developed. First the authors show how to represent tensors as spinors and then they show how to represent spinors as tensors. As an application of this they show how a Lorentz transformation is represented by two spin transformations. This is followed by a chapter that takes many concepts from differential geometry and puts them in spinor form, including Einstein's equation.

The final chapter mostly considers fields formulated in terms of spinors. This includes the electromagnetic field, Yang-Mills fields (a nice introduction to fibre bundles is included) and general relativity.

On the whole I think this book provides an excellent development of two-spinor calculus, with a nice emphasis on the geometry of spinors. It takes some familiar fields, such as the electromagnetic field, and formulates them in terms of spinors. However, one thing I thought was missing was more extended discussions of the known situations in general relativity where spinor methods prove more useful than tensor methods, e.g. the classification of the Weyl tensor or Witten's proof of the positive energy theorem. More material like this is presented in volume II. This book also gives some general arguments that spinors may be more fundamental than tensors and hence provide more insight into the nature of space-time, in fact this is one of the central themes of the book. I find the arguments to be very plausible, but I think it's safe to say that even twenty years after the publication of the book that it has yet to be demonstrated.

Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions (Scientific American Library Series)

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Geometrical Illustrations of Fourth Dimension
Concise Well-Written And Beautifully Illustrated Work
The royal road to geometry!
What is a dimension?
A must reading for any geometry enthusiast!

Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions (Scientific American Library Series)

Manufacturer: Scientific American Library
ProductGroup: Book
Binding: Hardcover

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ASIN: 0716750252

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Geometrical Illustrations of Fourth Dimension.......2004-01-29

Living in a world of three dimensional space makes it hard for us to conceive fourth dimension and it gets even harder to visualize the fifth and higher dimension. Superstring theorists predict the existence of 10th and 26th dimensions in universe; hence it seems reasonable for many of us to understand how it would be like to be living in fourth dimension. Thomas Banchoff is one of the leaders in the study of higher dimension using computer graphics; he has illustrated fourth dimension using basic geometrical approach such as slicing the spatial dimension, observing the shadows of structures, comparing the folded and foldout versions of polytops and description of configuration of spaces. This book is useful for someone who appreciates geometry, but for a reader who likes to visualize the fourth dimension he/she may read Clifford Pickover's Surfing through Hyperspace, which does a better job in illustrating fourth dimension.

Concise Well-Written And Beautifully Illustrated Work.......2003-04-23

Mathematical ideas, when first learned, tend to undergo a curious inner transformation. At the outset, some tangible representation is necessary to effectively latch onto the concept. Thereafter, the symbolic elaboration using the language of mathematics is sufficient to encompass not only that particular figure, but limitless others like it as well. The underlying geometry is still there, but there are simply too many possibilities to illustrate in any amount of time.

The first step of illustrating must be manifest, using ink or chalk or sand or digital pixels. In this way, even the finest geometric illustrations can be considered extremely crude and innacurate in comparison to rigorous mathematical precision. Consider, however, how extraordinarily difficult it would be to grasp trigonometric functions, vector spaces, or even the basic Cartesian coordinate system, without first observing supporting representative illustrations. Even if later forgotten, those initial images are crucial for understanding.

This work provides a wide range of richly color-illustrated examples of the abstract geometric structures dealt with regularly in mathematics and the sciences. It is unique in its quality and affordability, and is supported with excellent prose, briefly describing the developmental history, and frequently how to reconstruct the figures from a sparse handful of assumptions. From an introductory description of dimension, this book then branches into numerous and diverse major topics: scaling, slices, regular polytopes, perspective, coordinate geometry, and non-euclidean geometry. While sparing in its level of mathematical description and precision, it never diverges into a fully artistic exposition on the subjects either. There is a careful balance, to guide the reader into better understanding the particular system under discussion.

Certainly reading this book is merely the first step of a far longer term process. Symbolic computing programs, such as Mathematica, Maple or MatLab, will assist in visualization, as well as in understanding the pragmatic relation between the graphical and set-theoretic descriptions of the figures. Other books will also assist in this. Many of Rucker's works provide further descriptions of certain topics, specifically Geometry Relativity & The Fourth Dimension is admirable in its brevity and profundity. Abbott's classic Flatland is the foundational book on non-technical description of dimensions. The venerable What Is Mathematics? by Courant and Robbins combines illustration and mathematics as well as any work written since. Design science touches on these topics frequently as well, Kappraff's Connections is an extraordinary example of this. Deeper mathematical topics include set theory, algebraic groups, vector analysis, and too many others to list.

However abstract the concepts diagrams and illustrations in this book may seem initially, most if not all have been utilized for practical application in recent times. You may very well be using devices on a daily basis, which have these concepts as a basis for their functionality. Keep this in mind while reveling in what the individual imagination can conjure.

The royal road to geometry!.......2001-02-26

This book is a jewel! It contains a wide collection of visual geometry. Professor Banchoff is able to link geometry to many aspects of life. It's a treasure trove for anybody teaching geometry at any level. It's a book that can be read at many levels. If you're willing to skip a bit here and there, you can get a very good general idea. But if you want to really understand all the details, it can make for hours of challenging reading. I'm still reading it! :-)

What is a dimension?.......2000-11-26

A comfortable introduction to modern geometry for the general reader, with emphasis on the concept of the dimension. This reference concludes with an introduction to non-euclidean geometry.

A must reading for any geometry enthusiast!.......1998-11-30

After reading this book, no doubt Thomas Banchoff is a deeply experienced geometry enthusiast.Unlike many schoolbooks, his book shows the main ideas underlying a multi-faceted geometry with minimal technical complication nonsense, using simple concepts and a bright argumentation, almost without losing insight! He never misses an opportunity to connect geometry to other sciences like algebra, relativity, optics, mechanics and to arts. It is not only the 'Everything you desired to know about the 4th dimensions' but also a bunch of 2D and 3D geometry 'master tricks' as well as a historical narration (including recent discoveries).

Examples: - how to find yourself the polytopes (4D 'polyhedra') with 3D representations - how to easily calculate vertex coordinates of the 5 polyhedra - how to draw a torus on a hypersphère! -.. and many others

Book Description

Naber provides an elementary introduction to the geometrical methods and notions used in special and general relativity. Particular emphasis is placed on the ideas concerned with the structure of space-time and that play a role in the Penrose-Hawking singularity theorems. The author's primary purpose is to give a rigorous proof of the simplest of these theorems, by the one that is representative of the whole. He provides exercises and examples at the end of each chapter. No previous exposure either to relativity theory of differential geometry is required of the reader, as necessary concepts are developed when needed, though some restrictions ae imposed on the types of space considered.

Customer Reviews:

A Stimulating and Interesting Book.......2000-11-01

This book is concerned primarily with a geometrical and in places, a topological approach to spacetime, leading to a full proof of one of Hawking's singularity theorems.The first part introduces the geometry of Minkowski Spacetime as.. 'a 4-dimensional ral vector space on which is defined a nondegenerate symmetric bilinear form of index one'.Some mathematical maturity is required to attempt this book on one's own.Chapter two develops relativistic mechanics in quite an abstract way (certainly for a first encounter) and chapter three develops spacetimes from the point of view of maps between manifolds.This chapter ends with a statement of one of Hawking's theorems. Chapter four sets out a full rigorous proof. There are no hints/partial solutions for the exercises although there are some 'examples'. The first three chapters were enjoyable and I managed to do quite a lot of the exercises and problems.As someone who works entirely independently at this kind of thing for 'fun',I found chapter four very hard going.Having no-one to ask when stuck made it a bit frustrating.The book was very stimulating though and encouraged me to research other sources for similar material to fill in gaps in my mathematical knowledge.

Pyramids of Light: Awakening to Multi-Dimensional Realities

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Pyramids of Light: Awakening to Multi-Dimensional Realities
Meg Blackburn Losey
Manufacturer: Spirit Light Resources
ProductGroup: Book
Binding: Paperback

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ASIN: 0975322303

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Is this reality an illusion? What is the connection between our consciousness and our body? Are we really part of everything? If so, what is our relationship to it all? Can we interrelate with beings in other dimensional realities? Can we travel in time to other places, experience events in history, or our future? Sure we can! How do we manifest what we want? Can we change our lives by creating a reality different from the one we know? How? How do miracles happen? Can we really produce them? How does our soul enter our body? When? What happens when we die and where do we really go, or is this life all there is? Recognize the simplicity of all creation as step by step; Dr. Blackburn Losey answers these questions and more by weaving a straightforward yet comprehensive account of the universal construct, its relationship with sacred geometry, the manifestation of matter, consciousness and the harmonic relationship of all things beyond quantum physics from the essence and fabric of creation to this here and now. Understand how to tap in to the Akashic records, the universal consciousness, to access any and all information you desire! Realize how you can experience unlimited realities through easy and fun exercises that assist you to leap from third dimensional reality to existing as multi-dimensional beings. Learn how to apply these techniques to create unlimited possibilities within your life and the lives of others! You are the creator that you seek!

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