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Sphere Packing, Lewis Carroll, and Reversi: Martin Gardner's New Mathematical Diversions (The New Martin Gardner Mathematical Library) [Hardcover]

Martin Gardner
5.0 out of 5 stars  See all reviews (4 customer reviews)

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Book Description

July 31, 2009 0521756073 978-0521756075 First Edition
Packing spheres, Reversi, braids, polyominoes, board games, and the puzzles of Lewis Carroll. These and other mathematical diversions return to readers with updates to all the chapters, including new game variations, proofs, and other developments and discoveries. Read about Knuth's Word Ladders program and the latest developments in the digits of pi. Once again these timeless puzzles will charm readers while demonstrating principles of logic, probability, geometry, and other fields of mathematics. It's the perfect stocking stuffer for the puzzle wizard on your list.

Editorial Reviews


"In this collection of 20 reprints of his "Mathematical Games" columns from 1959 and 1961 issues of Scientific American, Gardner shares his delight in recreational math. The renowned mathematics and science writer presents concepts exemplified by board games and puzzles by the author of Alice in Wonderland and others, with solutions, updated information, and references. Among Gardener's many books is The Annotated Alice. Published in association with the Mathematical Association of America."
Book News

"While Martin Gardner has always called himself "strictly a journalist," he should really be honored as one of this country's greatest cultural treasures."
The Washington Post For the full text visit:

Book Description

Martin Gardner returns to charm readers with the latest on packing spheres, Reversi, braids, polyominoes, board games, and the puzzles of Lewis Carroll. Read about Knuth's Word Ladders program, new ways of finding the digits of pi, and much much more.

Product Details

  • Series: The New Martin Gardner Mathematical Library (Book 3)
  • Hardcover: 298 pages
  • Publisher: Cambridge University Press; First Edition edition (July 31, 2009)
  • Language: English
  • ISBN-10: 0521756073
  • ISBN-13: 978-0521756075
  • Product Dimensions: 0.8 x 5.6 x 8.4 inches
  • Shipping Weight: 15.2 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #2,748,569 in Books (See Top 100 in Books)

More About the Author

For 25 of his 95 years, Martin Gardner wrote 'Mathematical Games and Recreations', a monthly column for Scientific American magazine. These columns have inspired hundreds of thousands of readers to delve more deeply into the large world of mathematics. He has also made significant contributions to magic, philosophy, debunking pseudoscience, and children's literature. He has produced more than 60 books, including many best sellers, most of which are still in print. His Annotated Alice has sold more than a million copies. He continues to write a regular column for the Skeptical Inquirer magazine.

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Most Helpful Customer Reviews
13 of 13 people found the following review helpful
5.0 out of 5 stars Amusements, Surprises, Mysteries, Challenges! July 24, 2009
Amusements, Surprises, Mysteries, Challenges!

Mathematics sometimes seems a matter of abstract symbols and calculations. Not in this book. Here it comes to life. Every chapter is filled with things to make or draw or think about. As you do these things, you learn what is going on and develop mathematics on your own.

Gardner leads off with the binary system and binary sorting, illustrated by use of a sorting deck similar to the commercial McBee Keysort system. Next, group theory is introduced via a game and illustrated by braiding leading to the "Dirac Belt Trick." This trick is the basis for a way to connect hoses and cords to rotating machinery and to avoid tangles. Dirac was interested in this trick because of its implications for the spins of electrons, a matter that is still a mystery to me, though I see how the trick works by trying it out as suggested.

Lewis Carroll's puzzles are here, with mazes and word ladders. Gardner shows how cutting and folding paper help you understand angle sums and dissections of figures. The references for the cutting and folding chapter include the recent work of Eric and Martin Demaine, Joseph O'Rourke, Greg N. Frederickson and others, useful if you want more technical details.

Senet opens the chapter on board games. This chapter winds up with a history of Reversi (and its kin Othello) which shows how tricky it can be to discover the origins of "new" games. A letter Peter Michaelsen sent Gardner in 1987 suggested Chinese origins for versions of this game, but those have yet to be traced and confirmed. Here is something to look into.

How can circles or spheres be packed most efficiently in a given area or volume? Sphere Packing is one of the greatest puzzles and most beautiful areas of geometry.
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1 of 1 people found the following review helpful
Format:Paperback|Verified Purchase
If you like Martin Gardner, then no more need be said.
If you do not know Charles Lutwidge Dodgson (a.k.a. Lewis Carroll) was a mathematician, logician and photographer you should read this book.

This is a book for people who enjoy math conundrums and physical puzzles in general. For example:
-Do you know how to pack a box efficiently with spheres?
-What is the best way to play Reversi?
-Have you ever read a Lewis Carroll puzzle?

Gardner is at his best entertaining us while showing us how to solve puzzles.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Some of the best writing on mathematics ever put on paper December 22, 2010
Even though I have read most of his writings more than once, Martin Gardner is one of the authors that will never take you down a path of satiation. There is no question that more people have been turned on to mathematics or had their mathematical motor revved by Martin Gardner's writings than by any other person in history. His signature writings were the "Mathematical Games and Recreations" column that appeared monthly for 25 years in "Scientific American." This book is a republication of 20 of his original columns, with subsequent addendum and postscript added.
The titles of the columns are:

*) The binary system
*) Group theory and braids
*) Eight problems
*) The games and puzzles of Lewis Carroll
*) Paper cutting
*) Board games
*) Packing spheres
*) The transcendental number đ
*) Victor Eigen: mathemagician
*) The four-color map theorem
*) Mr. Appollinax visits New York
*) Nine problems
*) Polyominoes and fault-free rectangles
*) Euler's spoilers: the discovery of an order-10 Greco-Latin square
*) The ellipse
*) The 24 color squares and the 30 color cubes
*) H. S. M. Coxeter
*) Bridg-it and other games
*) Nine more problems
*) The calculus of finite differences

"How Great Thou Art" is the title of a religious song, but it could also be the signature phrase used to describe Martin Gardner and the role he has had in the development of the modern mathematics community. That skill is demonstrated one more time in this book.
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3 of 4 people found the following review helpful
5.0 out of 5 stars A Martin Gardner Classic September 9, 2009
Format:Paperback|Verified Purchase
An excellent collection of Martin Gardner's columns from Scientific American. I have several of Gardner's books, and this particular series is the best production quality of the ones that I own.
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