Monday, March 17, 2014

Polishing off that pizza



I know that I said I wouldn't be posting the solution to Sicilian Solution III: Pepperoni Protocol, but I think there have been enough developments to warrant one more post....

Reader jeff worked through a few approaches, including finding the solution shown below. The picture of the solution comes to us from Harold Jacobs---it works because the cut goes through the center of the rectangle; goes through the center of one of the circles; and separates the other two circles.



By the way, I should say that Harold was also a colleague of Martin Gardner's, and he reminded me about the nice problems in Gardner's book Penrose Tiles to Trapdoor Ciphers. For example, how do you bisect both halves of a yin-yang symbol with a single cut? This problem dates back to at least 1917.

The "Penrose" of Gardner's book title is of course Sir Roger Penrose. It was both a privilege and a pleasure to be one of Roger's research students during the 1990s. In addition to his researches in physics and mathematics, Roger is widely read in the history of mathematics and knows a lot about mathematical games. He has held the W.W. Rouse Ball Professorship in Mathematics at Oxford, which is named for another mathematician with a historical sensibility and a taste for puzzles.

This morning, my wife found herself facing two hungry little girls, both of them eyeing the last chocolate-chip pancake. She kept the peace with this Solomonic cut:



Google "pancake theorem" for some results along these lines. Some other references you might want to check out:

Hope you enjoyed these forays into bisection! Lately I've been thinking about a physics puzzle...if I get anywhere with it, I'll post. :-)

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