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Number 428, May 14, 1999 by Phillip F. Schewe and Ben Stein
PI AND RANDOM NUMBERS. Pi is a "quark" of mathematics: it is one of the basic building blocks out of which various geometrical and algebraic relations are built. Normally thought of as the ratio of a circle's circumference to its diameter, pi keeps turning up in odd places. For example, Georges Leclerc, Count de Buffon, was the first to show a connection between pi and the occurrence of random events. In 1777 he performed an experiment in which needles are randomly dropped onto a surface covered with ruled lines spaced apart by an amount equal to the size of the needle; the fraction of times the needle comes down astride a line is related to pi. Mathematicians have exploited this relation to make random number generators. Sylvan Bloch (813-961-0778), of the University of South Florida does the converse of this. He and Robert Dressler developed software (for the classroom) for using random numbers to generate a statistical estimation of pi. By the way, in warped spacetime pi is not necessarily equal to the ratio of a circle's circumference to its diameter. As an appendix to his article in the April issue of the American Journal of Physics, Bloch shows how "pi" varies as space becomes increasingly curved. (As usual science journalists can obtain copies of articles from AIP public information. For pi lore, see http://forum.swarthmore.edu/dr.math/faq/faq.pi.html.)
ATOMIC STEERING COMMITTEE. Even the smoothest-looking coatings are very rough on the atomic scale, with islands of atoms peppered abundantly across the microscopic landscape. Depositing copper atoms on a Cu surface, researchers (Sebastiaan van Dijken, University of Twente, the Netherlands, s.vandijken@tn.utwente.nl) have identified a largely ignored mechanism which contributes to introducing roughness in films of atoms being deposited onto surfaces. Known as steering, it arises when surface atoms, including already deposited ones, exert chemical forces on incoming atoms and cause them to veer towards the surface. This is reminiscent of how static electricity can cause some of the milk poured from a glass to drip down the sides rather than fall freely from the glass. Steering causes incoming atoms, especially those approaching the surface at grazing angles, to arrive preferentially on the top of protruding islands of atoms. Therefore, steering can make already rough surfaces even rougher. Besides providing insights into the causes of roughness, understanding this effect may help researchers to prepare arrays of surface ridges, which could serve as templates for making magnetic nanowires and other customized materials. (S. van Dijken et al., Physical Review Letters, 17 May 1999; see figure at Physics News Graphics)
KING EDWARD III of England (1312-1377) has, back to the time of Charlemagne, about 1000 perches on his family tree. Of course in the relatively closed world of medieval royalty, many names on that tree appear more than once; indeed the repetition of ancestors conforms to a predictable pattern. A new study of the statistical properties of genealogical trees, using Edward III's pedigree as a case history, concludes that by going about 30 generations into your past, you and all your contemporaries will be related to everyone who lived then, at least to those who had offspring and who lived within that particular geographical or cultural realm. Bernard Derrida of the Ecole Normale Superieure in Paris (bernard.derrida@lps.ens.fr), Susanna Manrubia of the Max Planck Institute in Berlin, and Damian Zanette (Barlioche, Argentina), have discovered that the factors shaping the patterns of repetitions of individuals in family trees have traits in common with the forces that govern the behavior of granular materials and can, furthermore, be understood using the mathematical tools applied to a variety of phase transitions in physics. They expect their work to have applications in the study of population genetics and evolutionary biology. Derrida et. al., Physical Review Letters, 1 March 1999; view Edward's family tree at http://uts.cc.utexas.edu/~churchh/edw3chrt.html; see figure at Physics News Graphics )
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