Why Beauty Is Truth: The History of Symmetry by Basic Books

	Title: Why Beauty Is Truth: The History of Symmetry Purchase Item Manufacturer: Basic Books List Price: $26.95 Our Price: $4.87
Customer Reviews:
Why Beauty Is Truth: The History of Symmetry by Basic Books You can't trisect an angle with a compass and straightedge
Why Beauty Is Truth: A History of Symmetry S. Marsh statement "you can trisect an angle" is not true in its historical context. Historical context: It is not possible to trisect all angles using only a compass and a straightedge (unmarked ruler). In his book, Stewart says that it is possible to compute values to great precision,(which includes using iteration) but not by compass and ruler. He does mention that it is possible to trisect some angles, specifically mentioning 180 which trisects to 60 which can be constructed by making a regular hexagon. But trisecting 60 degrees by compass and ruler to produce 20 degrees is impossible, Note that 20 is the exact value of a trisected 60 degree angle but you cannot construct that angle, with a straightedge and compass. As Stewart makes clear in this book, the important thing is not that you can't, but why you can't. And the why leads to group theory and other advances. I found this book to be extremely interesting. Group theory is new to me. I found this book is an introduction as to why it was important to Einstein and to modern physics. I recommend this book. I found the following on-line tutorial on Galois theory useful: http://nrich.maths.org/public/viewer.php?obj_id=1422
Why Beauty Is Truth: The History of Symmetry by Basic Books I liked it, but, you can trisect an angle
Not only can Achilles catch a tortise, he can also trisect an angle. It just takes infinite iterations. As iterations -> infinity, angle -> trisection I figured it out in eighth grade, and later was glad to see that the theory of limits wasn't something I'd made up. But for a book that is a combination of light history and fun explorations, it makes for a good holiday read. Other than repeating the old saw that you can't tri-sect an angle one too many times. You just have to be very patient. ;)
Why Beauty Is Truth: The History of Symmetry by Basic Books let's judge this book by its cover!
It would take most people just a few milliseconds to recognize that the butterfly on the book's cover is asymmetric. Indeed, the claim that nature is symmetric, made in this book (and so often elsewhere - e.g., by Weyl) is manifestly false. (BTW: check the dimensions of Leonardo's so-called Vitruvian Man to discover - perhaps - the real Da Vinci code!) The apotheosis of symmetry is to be found in the architecture of Albert Speer. The apotheosis of asymmetry is to be found in the architecture of the universe -- or,just as well, in any of those extraordinary formations photographed by the Hubble telescope.
Why Beauty Is Truth: The History of Symmetry by Basic Books "Beauty, Truth & Mathematics via Transformation"
"Why Beauty Is Truth: A History of Symmetry", by Ian Stewart, Basic Books, NY 2007. ISBN-13: 978-0-465-08236-0. HC 290/280 pgs., includes Preface, Further Readings, Index & a few cartoons. 9 1/2" x 6 1/2". Stewart, Mathematics Professor, Warwick, authored six prior books and here he provides an entertaining survey of the history of symmetry with especial reference to mathematical purity, elegance, simplicity and symmetry of divers sorts, group theory, imaginary numbers & much more. Tolerantly technical, and despite reader caution not need to complete calculations, those reader's lacking math background and basic comprehension of quantum and particle physics will be awash. The emboldened cover enveiglement, an Azure Lepidoptera, is enticing but not pertinent to book's contents. Written in engaging, but oft meandering prose attitude as met in Mario Livio's "The Golden Ratio", but more earthy than encountered in 'historicisms', tolerably askance or tangential, it is chock full of anecdotal informatories adding to it's intelligibility. String theory, supersymmetry and Feynam sketches are helpful as apt diagrams. The semi-chronological format delves into contributions made by the "usual suspects" of math and physics -- beginning in ancient Babylon (60 miles South of Baghdad), and onto Euclid, Einstein, Weber, Planck, Witten, etc. An excellent primer and a good read.
Why Beauty Is Truth: The History of Symmetry by Basic Books Spreads itself too thinly
This book covers an enormous range of topics beginning with Mesopotamia number systems and ending with string theory. It simultaneously describes mathematical theories, the history of how these ideas evolved over time, and details about the lives of the mathematicians. Several of the brief biographies are very well done; the treatments of Gauss, Omar Khayyám, and Galois are outstanding. Others are sketchy, hardly more than a list of parent's occupations, siblings, spouse, and children. As a result of the broad coverage, each mathematical concept gets very brief treatment. I often felt that I wasn't given enough information to understand a concept. Lie groups, in particular, turn out to be very important for contemporary physics but the description is so brief and jargon encrusted that the physical applications were unintelligible to me. The author is not certain about his intended audience. He apologizes to the reader for the complexity of the solution to the cubic equation, even though this is a straightforward extension of high school algebra. Yet later on he assumes that the reader will easily grasp that a Fano plane is a finite projective geometry. The book was simultaneously too nontechnical and too technical for me (a computer technologist and a former scientist). It is not clear what the purpose of the book is. Many of the topics covered have no obvious connection to symmetry except in the sense that everything is related to symmetry. The historical evolution of representations of numbers is interesting, for example, but doesn't help understanding the multidimensional algebras that somehow relate to symmetry.
Why Beauty Is Truth: The History of Symmetry by Basic Books Product Description
At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry. In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study. Stewart introduces us to such characters as the Renaissance Italian genius, rogue, scholar, and gambler Girolamo Cardano, who stole the modern method of solving cubic equations and published it in the first important book on algebra, and the young revolutionary Evariste Galois, who refashioned the whole of mathematics and founded the field of group theory only to die in a pointless duel over a woman before his work was published. Stewart also explores the strange numerology of real mathematics, in which particular numbers have unique and unpredictable properties related to symmetry. He shows how Wilhelm Killing discovered “Lie groups” with 14, 52, 78, 133, and 248 dimensions-groups whose very existence is a profound puzzle. Finally, Stewart describes the world beyond superstrings: the “octonionic” symmetries that may explain the very existence of the universe.