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A monthly survey of math news
Math on Broadway. The May 24, 2000 New York Times carries Bruce Weber's review of a new play called "Proof," "an exhilarating and assured new play that turns the esoteric world of higher mathematics literally into a back porch drama, one that is as accessible and compelling as a detective story." The work, by David Auburn, is the latest in a series of successful plays with a mathematical flavor. The ground-breaker was Hugh Whitemore's 1986 "Breaking the Code," about Alan Turing's exploits and sorry end (which occurred in Manchester, now the setting for "Queer as Folk"!). Andrew Hodges, whose biography of Turing was the basis for the play, tells us (on his comprehensive Turing site) how risky it was to put such stuff on stage. "Facing the audience with a full-frontal description of Gödel's Theorem was probably breaking an even greater taboo than claiming a gay man as a war hero." The next big success in this genre was Tom Stoppards "Arcadia" in 1997. It was reviewed by Tim Beardsley in the Scientific American ("Scientists tired of being represented either as Faust figures or as clowns should applaud the value of this achievement."), it is the subject of a video in which the author is interviewed by MSRI Special Projects Director Robert Osserman, and it is the focus of a wonderful webpage assembled by students at the Eden Prairie High School.
Honeybee Calculus and Analytic Geometry. It is known that a honeybee that has found food returns to the hive and performs a dance to tell her hivemates the location of her find. For longer distances from the hive (over 50m), the dance is the "waggle dance" which gives the location in apian polar coordinates. The orientation of the dancer's body ("waggle axis") tells the direction (with respect to the direction of the sun) and the duration of waggling tells the distance (very close to 1.88ms of waggle for each meter of distance). These facts come from a report, Honeybee Navigation: Nature and Calibration of the "Odometer", in the 4 Feb 2000 Science, picked up by the e-journal ScienceWeek for May 12. The report, by an Australian-German team led by M. V. Srinivasan of the Australian National University, addresses the question: how does the honeybee know how far she has gone? The answer, teased out by an elegant series of experiments, is that she integrates the speed of movement of images across her eyes. In one of the experiments the bees flew through narrow tunnels (much more rapid visual movement) and reported much longer distances.
Euler's Spinning Penny. A nice piece of mathematical mechanics was reported in the 20 April 2000 Nature. The problem is the realistic analysis of the motion of a penny spinning on a table (one of the references is to Euler himself, who posed the problem back in the 18th century). The author, H. W. Moffatt of the Newton Institute at Cambridge University, starts off quite classically ("It is a fact of common experience that ...") but shows how in fact classical mechanics alone cannot account for the phenomenon, and that the correct solution depends on a subtle interplay between gravity (which keeps the coin on the table) and energy dissipation by air, which by itself would go to infinity as the angle between the coin and the table goes to zero.
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