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The Gordian unknot. Alexander the Great cut the knot in 333 BC, and thereby destroyed important mathematical evidence. What was this knot that no one could untie? Keith Delvin reports in the September 13, 2001 Guardian that ``A Polish physicist [Piotr Pieranski of Poznan] and a Swiss biologist [Andrzej Stasiak of Lausanne] have used computer simulation to recreate what might have been the Gordian knot.'' His piece is entitled ``Unravelling the myth.'' Pieranski and Stasiak argue that the knot could not have had any free ends, so the cord was actually a circle. But if the circle had been topologically knotted, the problem would have been mathematically impossible, and therefore not a fair challenge. So the circle itself was tied into what had to be an unknot, and only the thickness of the cord made it impossible to loosen it. For example, the knot might have been tied in a wet cord which was then allowed to dry, and perhaps to shrink itself into an impossible configuration. Pieranski and Stasiak, motivated by interest in string theory and in the knotting of biological molecules, respectively, used a computer program to simulate the manipulation of such knots, and have found one so obdurate that maybe it has the structure of the original puzzle that Alexander ``solved.'' Devlin's article is available online. Pieranski's home page has animations of the computer program in action.
Answering an Age-Old Cry: When Will I Use This Math? is the title of a piece by Timothy Jack Ward in the House and Home section of the September 6, 2001 New York Times. The answer is found in the work of Jhane Barnes, a designer of menswear, carpets, textiles, furniture and throws. The math gets used in the designs, and Ward's enthusiasm is over Barnes' use of fractals. These are not your run-of-the-mill Julia sets, but rather a harnessing of fractal rythm into the succession of graphic elements. Wired Online also has a piece on Jhana Barnes, ``Fashion Nerd,'' by Michael Sand: ``Using a host of computer programs to incorporate symmetry, mathematics, and fractal geometry into her work, she's the only major fashion designer out there who's using technology as a true creative tool.''
The Abel prize is the name of a new ``top maths prize,'' as Nature puts it in their September 13 2001 ``News in brief.'' The prize is being set up by the Norwegian government in honor of that country's greatest mathematician. The prize reportedly is aimed at bringing recognition of research achievements in mathematics up to the Nobel level. It will be given every year (starting in 2003) and the money is good: NKr 5 million (approx US$ 550,000).
Photo Solitons. Solitons are solutions to a non-linear wave equation. They have been observed in nature since 1844, when John Scott Russell chased a ``solitary wave'' as it sped down the Edinburgh to Glascow canal without losing its shape. This phenomenon in another context turned out to be the key to understanding a strange phenomenon called ``Fermi-Pasta-Ulam recurrence'' (1953). In the computer simulation of the oscillations of a string consisting of 64 particles with non-linear interaction, the initial shape of the string dissolved as expected into a superposition of non-coherent modes, but after a certain time the modes magically reassembled into the original configuration. This was the ``recurrence.'' In a News and Views piece (``Déjà vu in optics'') in the September 20, 2001 Nature, Nail Akhmediev explains how the phomenon was initially understood theoretically as a a solitary wave in the solutions of the Korteweg-de Vries equation, the mathematical model for the original system, and how it is now understood that ``essentially the Fermi-Pasta-Ulam recurrence is a periodic solution of the non-linear Schrödinger equation.'' Now this phenomenon has been observed in a real physical system, using light beams in an optical fibre. The experiment was reported this year in Physical Review Letters by Van Simaeys, Emplit and Haelterman. ``Because they took great care when setting up the initial conditions, the recurrence they saw was almost perfect.''
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