The December 2022 issue of IEEE Spectrum is here!

Close bar

Puzzles by the Drawerful

So why did the chicken cross the Möbius strip?

2 min read
Puzzles by the Drawerful

Professor Stewart’s Cabinet of Mathematical Curiosities

By Ian Stewart; Basic Books, 2008; 256 pp.; US $16.95; ISBN: 978-0-465-01302-9

There’s a lot to be said for a book that transports you back to your childhood. When I was 11, I was given a subscription to Scientific American. Every month, I would turn directly to Martin Gardner’s Mathematical Games column, which Professor Stewart’s Cabinet of Mathematical Curiosities immediately brings to mind.

Open one of the 179 ”drawers” in Professor Stewart’s cabinet, and you might find just a one-liner (”Why did the chicken cross the Möbius band?”) or a seven-page essay on Fermat’s last theorem. Many items, like how to find a fake coin in three weighings and Cantor’s diagonal argument, are likely to be familiar friends, but plenty of others will be new. And Stewart has put a sheen on some of the oldies—Langton’s ant, for example, in which the eponymous insect travels around a checkerboard according to simple rules. I hadn’t imagined some of the strategies that might somehow trap it.

I’m not keen on the book’s shaggy-dog stories nor on its biographies of famous people (do Americans know who Virginia Wade and Carol Vorderman are?). But those parts of the book are more than offset by a variety of knots, magic hexagons, square wheels, and topology tricks in which you pretend to slice off your finger. Answers (but not, unfortunately, a proof of the Goldbach conjecture) are to be found at the back of the book, and many have URLs for further information.

The book can be devoured in one giant gulp or savored, one curiosity at a time. As for the mathematics, the puzzles require at most a bit of algebra. Many should be within the grasp of an intelligent 11-year-old.

About the Author

Clive Feather says that if he had to pick a favorite trick from the book, the one he probably had the most fun with was "learning how to not slice off my fingers with a piece of string." Feather is an Internet regulatory expert and an amateur historian of the London Underground.

Keep Reading ↓Show less

This article is for IEEE members only. Join IEEE to access our full archive.

Join the world’s largest professional organization devoted to engineering and applied sciences and get access to all of Spectrum’s articles, podcasts, and special reports. Learn more →

If you're already an IEEE member, please sign in to continue reading.

Membership includes:

  • Get unlimited access to IEEE Spectrum content
  • Follow your favorite topics to create a personalized feed of IEEE Spectrum content
  • Save Spectrum articles to read later
  • Network with other technology professionals
  • Establish a professional profile
  • Create a group to share and collaborate on projects
  • Discover IEEE events and activities
  • Join and participate in discussions

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
Photo of Jacob Ziv
Photo: Rami Shlush

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.

Keep Reading ↓Show less