Ivars Peterson's MathTrek
Organized and hosted by Tom Rodgers, Mark Setteducati, and Elwyn Berlekamp, G4G7 was the seventh in this series of biannual meetings. Attendance at these events is by invitation only. See http://www.plambeck.org/oldhtml/journal/g4g6.htm.
This year's gathering featured 4 days of illuminating presentations and amazing performances. Packed with wonderful treats and startling surprises, it provided one "aha!" moment after another.
Here are some highlights.
Mathematician Daina Taimina of Cornell University described how her crocheting skills turn a hyperbolic plane into an intriguingly crinkled blossom of yarn. Her skirt was itself a graceful rendering of the same form in wool. Examples of her work can be seen in an online exhibition sponsored by the Institute for Figuring.
Hungarian inventor Dániel Erdély introduced spidronsisosceles triangles assembled into spiral arms, which then provide the basis for an wide array of fascinating structures. Spidrons have been used to create novel tilings, variants of regular polygons and polyhedra, pyramids and prisms, and more.
Lou Zocchi of North Biloxi, Miss., not only performed brilliantly on the nose flute, playing-card harmonica, saw, and other unusual "musical" instruments but also had for sale the widest assortment of polyhedral dice that I have ever seen. I couldn't resist adding his patented version of a 100-sided die, the Zocchihedron, to my collection. Zocchi's one-man company, Gamescience, sells an incredible array of precision randomizers.
Artist Tony Robbin explained how a book about four-dimensional geometry influenced Pablo Picasso and led to the style of art known as cubism. See http://tonyrobbin.home.att.net/shadows.html.
Puzzle designer and software engineer Wei-Hwa Huang of Google recounted his experiences at the first World Sudoku Championship, held in Italy, where he finished third. He also outlined an ingenious method for solving Sudoku puzzles.
Bob Hearn of the Massachusetts Institute of Technology described how various games, such as Rush Hour, TIPOVER, and Konane, provide useful insights into computation.
Puzzle creator Dick Hess of Rancho Palos Verdes, Calif., introduced an ingenious strategy for solving coin-weighing brainteasers that involve using a scale or balance to identify which one of a set of coins is counterfeit, when the counterfeit coin weighs a little less or a little more than the others.
Mathematician and math puzzle historian David Singmaster described his search for the roots of the monkey-and-coconuts brainteaser.
Ann Schwartz demonstrated the hexa-dodeca-flexagona new type of folded-paper strip that can be "flexed" into various configurations. Flexagons were the topic of Martin Gardner's first article in Scientific American, which led to his famous "Mathematical Games" columns.
Known for his triangulated egg, Ron Resch described how origami patterns have proved useful for designing devices that must unfold to operate properly—such as stents to prop open arteries and sails to collect light for solar-powered spacecraft. The algorithm for folding airbags into a flat configuration came out of origami recipes for folding paper insects.
Following on from his work on alphamagic squares, Lee Sallows introduced "geomagic" squares, in which geometric figures play the same role that numbers do in ordinary magic squares.
There was much, much more. Even the hallway outside the meeting room became a venue for card tricks, toy demos, impromptu presentations, art displays, and much excited conversation. Where else would you find John Conway demonstrating a card trick or Roger Penrose pondering a puzzle?
I'll conclude with a new coin-weighing puzzle from Dick Hess.
Of 2006 coins, two are counterfeit, one lighter and one heavier than a true coin. With four weighings on a simple two-pan balance, determine if the two false coins weigh less, the same, or more than two true coins.
Copyright © 2006 by Ivars Peterson
Peterson, I. 2006. Martin Gardner's puzzles and problems. Science News Online (Feb. 27). Available at http://blog.sciencenews.org/2006/02/martin_gardners_puzzles_and_pr_1.html.
______. 2005. Sliding around. MAA Online (Oct. 24).
______. 2005. Magic squares of squares. MAA Online (June 27).
______. 2005. Sudoku math. Science News Online (June 18). Available at http://www.sciencenews.org/articles/20050618/mathtrek.asp.
______. 2005. Divisibility by seven. MAA Online (May 23).
______. 2003. Alphamagic squares. MAA Online (July 7).
______. 2002. Testing for divisibility. MAA Online (Aug. 19).
______. 2002. Logic in the blocks. Science News 162(Aug. 17):106-107. Available at http://www.sciencenews.org/articles/20020817/bob10.asp.
______. 1998. Calculus made easy. MAA Online (Sept. 21).
______. 1998. The counterfeit coin. MAA Online (Feb. 16).
______. 1997. Martin Gardner's lucky number. MAA Online (Sept. 8).
______. 1997. Hankies, snarks, and triangles. MAA Online (Jan. 11).