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The Art of the Infinite: The Pleasures of…
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The Art of the Infinite: The Pleasures of Mathematics (original 2003; edition 2003)

by Robert Kaplan (Author)

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383440,582 (3.57)3
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Title:The Art of the Infinite: The Pleasures of Mathematics
Authors:Robert Kaplan (Author)
Info:Oxford University Press (2003), Edition: 1st, 336 pages
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The Art of the Infinite: The Pleasures of Mathematics by Robert Kaplan (2003)

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Showing 4 of 4
An engaging mix of history, exposition, and explanation of a unique range of topics, including several which I've never seen explained elsewhere. Well-written and conversational without dumbing down the math at all. ( )
  byorgey | Nov 2, 2009 |
Yes, The Art of the Infinite has a lot of equations, schematics, graphs, and geometric projections (although the really intricate ones are kindly set aside in the Appendix). But don't let that scare you. Remember, we are relaxing into the idea of really understanding how cool upper-level mathematics is -- don't tense up at all those Greek symbols and acute angles, just let them wash over you and the Kaplan's will lead you through some pretty amazing mathematical concepts one step at a time. Along the way, you will get a taste of the major mathematical figures: from Pythagoras to Cantor -- all nicely illustrated by Ellen Kaplan, who also hand-draws all the mathematical figures in the book.

I wouldn't claim to have understood (or really thought out) every proof in this book, but I feel like I got enough of a taste to understand what was going on every step of the way and why it was interesting. I feel like I really understand the definitions and distinctions between Real, Natural, Rational and Imaginary numbers. I have a huge appreciation for the imagination and creativity of mathematicians who attack the mind-blowing complications of infinite numbers and come up with something that can be wrangled into an equation and applied to any number at all.

[full review here: http://spacebeer.blogspot.com/2008/06/art-of-infinite-pleasures-of.html ] ( )
1 vote kristykay22 | Jun 28, 2008 |
Subtitled, "The Pleasures of Mathematics" this book is a collection of interesting recreations and problems, in algebra, number theory, geometry and constructons, and infinite set theory. Some of the proofs are very hard, and there is no coherent theme to the book, but a loose organization of interesting points. The authors are entertaining, though, and I enjoyed reading this, and being a little stretched by the abstract conceptions. ( )
  neurodrew | Mar 24, 2007 |
Properties (especially infinitistic ones) of different kinds of numbers, including Cantor's transfinite ordinals and cardinals. Suffused with equations, diagrams, *and* lyrical prose. Not a terribly advanced book, but a delightful one.
  fpagan | Dec 16, 2006 |
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Robert Kaplanprimary authorall editionscalculated
Kaplan, EllenIllustratorsecondary authorall editionsconfirmed
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Amazon.com Product Description (ISBN 019514743X, Hardcover)

Robert Kaplan's The Nothing That Is: A Natural History of Zero was an international best-seller, translated into eight languages. The Times called it "elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf" and The Philadelphia Inquirer praised it as "absolutely scintillating."
In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics. Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the "Republic of Numbers," where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it.
"Less than All," wrote William Blake, "cannot satisfy Man." The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.

(retrieved from Amazon Thu, 12 Mar 2015 18:15:05 -0400)

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Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.

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