A Garden of Mathematical Delights

Martin Gardner's Mathematical Games columns collected in book form

2 min read
A Garden of Mathematical Delights

Sphere Packing, Lewis Carroll, and Reversi

By Martin Gardner;
Cambridge University Press, 2009; 296 pp.;
US $14.99, ISBN 978-0-521-74701-1 (paperback);
$50.00, ISBN 978-0-521-75607-5 (hardback)

"If Martin Gardner wrote a cookbook," my editor said, "we'd review it." Sphere Packing, Lewis Carroll, and Reversi isn't a cookbook, but it does include recipes for a couple of tricks with crackers.

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From WinZips to Cat GIFs, Jacob Ziv’s Algorithms Have Powered Decades of Compression

The lossless-compression pioneer received the 2021 IEEE Medal of Honor

11 min read
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Photo of Jacob Ziv
Photo: Rami Shlush
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Lossless data compression seems a bit like a magic trick. Its cousin, lossy compression, is easier to comprehend. Lossy algorithms are used to get music into the popular MP3 format and turn a digital image into a standard JPEG file. They do this by selectively removing bits, taking what scientists know about the way we see and hear to determine which bits we'd least miss. But no one can make the case that the resulting file is a perfect replica of the original.

Not so with lossless data compression. Bits do disappear, making the data file dramatically smaller and thus easier to store and transmit. The important difference is that the bits reappear on command. It's as if the bits are rabbits in a magician's act, disappearing and then reappearing from inside a hat at the wave of a wand.

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