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Edited by Allyn Jackson, AMS
Contributors: Mike Breen (AMS), Claudia Clark
(freelance science writer), Lisa DeKeukelaere (2004 AMS Media Fellow),
Annette Emerson (AMS)
"Up a Lazy River," by Brian Hayes. American Scientist, November-December 2006, pages 490-494.
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It is well known that water seeks out the shortest route when traveling downhill, so why are there so many---and such large---bends in a river? Why isn't a river's path relatively straight? Hayes examines these questions, focusing on the work of Luna Leopold. Leopold thought an equation describing the direction of a river would be y = µ sin x where y is the angle from the straight down direction, µ is the maximum angle that the river makes with the straight down direction, and x is the distance along the river's centerline. Hayes gives some justification for the equation and investigates work by Hermann von Schelling that used random walks to simulate the meandering of a river. Neither these experiments nor Leopold's theory seem to give a full answer to river-meandering. More basic processes such as sediment transport might offer an answer, yet rivers meander even when they carry no sediment. Hayes is still intrigued by the question and although there may not be a definitive answer at the moment, he believes one does exist. --- Mike Breen
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"Kosakenzipfel." Frankfurter Allgemeine
Zeitung, 5 November 2006;
"Solved: the perfect way to cut a cake", by Amarendra Swarup. New Scientist news
service, 6 November 2006;
"Taart
en land eindelijk eerlijk te delen (Finally an honest way to divide
cake or land)". Der Volkskrant, 6 November 2006;
"Dividere
la torta, la soluzione perfetta (To divide the cake, the perfect
solution)", by Roberto Verrastro. Panorama, 10 November 2006;
"So
kriegt jeder mehr (This way everyone gets more)", by Philipp Berens.
Süddeutsche Zeitung, 8 November 2006;
"Sharing
your cake and eating it too", by Nikhil Swaminathan. Scientific
American Online, 6 November 2006;
"Cientistas
propoem novo método matemático para cortar bolo
(Scientists propose a new method for cutting a cake)", by Carlos
Orsi. Estadao.com.br, 6 November 2006;
"Math
principles can help resolve disputes". United Press
International, 6 November 2006;
"Cutting
the Cake". Quirks and Quarks, hosted by Bob McDonald.
Radio One, Canadian Broadcasting Corporation, 18 November 2006;
"Grazer Forscher als `Weltstar':
Grazer Uni-Professor fand nun zusammen mit US-Kollegen heraus, wie man
Torte richtig teilt (Graz researcher as `World star': Graz
University professor discovers, with US colleagues, how one properly
divides a cake)", by Dieter Demmelmair. Grazer Woche,
November 2006;
"This math theory is a piece of cake", by Kitta Mcpherson. New Jersey Star Ledger, 26
November 2006.
"A Fair Slice," by Julie Rehmeyer. Science News, 16 December
2006, page 390.
"The Kindest Cut," by Steve Mirsky. Scientific American, February 2007, page 94.
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Media outlets around the world ran stories on the research described in "Better Ways to Cut a Cake", an article that appeared in the December 2006 issue of the Notices of the AMS. The article, by Steven Brams, Michael Jones, and Christian Klamer, centers on the mathematics of fair division. The "you cut, I choose" method of dividing a cake between two people has been used since time immemorial. But if the two cake eaters value the cake differently---say Alice prefers the part with chocolate icing, while Bob doesn't care which kind of icing he gets---the cut-and-choose method might leave one person less satisfied than the other. The Brams-Jones-Klamler article describes a method called "Surplus Procedure" that can result in, for example, both cake-eaters feeling that they got 65 percent of what they wanted. The research presented in the article is theoretical, but it could have applications to problems like how to divide land. Moreover, the research shows how a mathematical approach can provide better and more precise ways of resolving disputes. A three-minute clip on the Discovery Channel illustrates the research (if the clip does not come up, do a video search on "cake"). --- Allyn Jackson
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"Students score well with fantasy football," ESPN.com, 9 December 2006;
"San Jose Math Class Lands on ESPN, Thanks to Fantasy
Football." KCBS, 27
November 2006.
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John Hagan at Foothill High School in San Jose, CA, uses fantasy football to help his students learn algebra. The technique has gotten the class excited about algebra. Richard Salazar, one of Hagan's students, says of algebra with fantasy football, "It's not as boring as it used to be. When he connected the fantasy football it kind of had me. I want to be in math class. I wanted to do more work." Bob Creamer's eighth-grade class in Woodbine, NJ, is also using fantasy football math. Creamer is as excited as his students: In just one year, the number of eighth-grade math students judged proficient on the state exam increased from 10 percent to 54 percent. --- Mike Breen
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"Not Just a Pretty Equation": Review of Mathematics and Common Sense: A Case of Creative Tension, by Philip J. Davis. Reviewed by John Ball. New Scientist, 25 November 2006, pages 54-55.
The author of this book, Philip J. Davis, is a mathematician at Brown University and a prolific commentator on many different aspects of mathematics, including how the subject is perceived by the general public. The reviewer is John Ball, a University of Oxford mathematician and president of the International Mathematical Union (IMU). Calling the book "delightful and informative", Ball uses the occasion of the review to present some compelling examples of the impact of mathematics in modern life. He also discusses the story of Grigory Perelman, the only mathematician ever to have declined the Fields Medal, commonly considered the "Nobel Prize" of mathematics. (As IMU president, Ball was the one who announced to the world, at the International Congress of Mathematicians in Madrid in August 2006, that Perelman would not accept the medal. Click here for citations of some of the worldwide media coverage of this historic event.) Ball mentions that one of the many "intelligent and approachable essays" in Davis's book discusses public perceptions of mathematics. The book recounts a story about a television reporter who once came to visit the AMS headquarters office in Providence, Rhode Island. Paraphrasing Davis's story, Ball writes: "[The reporter] had passed the building many times and often wondered what on earth went on inside. `But I really didn't want to know,' he said."
--- Allyn Jackson
"How to End the Math Wars," by Claudia Wallis. Time Online Edition, 19 November 2006.
Claudia Wallis compares educational theory to American politics: red for rote memorization, blue for a more creative, free-thinking approach. In teaching children to read, for example, schools swung from red to blue in the 1980s, then back to red by the end of the 1990s. Wallis predicts that math education, which she sees now as a calculator-pushing, mistake-accepting blue system plagued by an overabundance of disparate state standards, will soon turn back to the red basics. She bases this prediction on a new pared-down list of three basic learning goals for each grade from pre-kindergarten to eighth released by the National Council of Teachers of Mathematics. While she hopes that these new standardized focal points will help bring the mathematical abilities of American children up to the level of their higher-achieving international counterparts, she fears that a joyless overemphasis on the red approach will turn children against math for life. Another article on the topic is "As Math Scores Lag, a New Push for the Basics," by Tamar Lewin, The New York Times, 14 November 2006.
--- Lisa DeKeukelaere
"The Biggest Questions Ever Asked" and "Journey Through Time". Special sections, New Scientist, 18 November 2006.
These special sections were published in celebration of the 50th anniversary of New Scientist magazine. The first one, "The Biggest Questions Ever Asked" does indeed tackle biggies, such as, Do we have free will?, What is Life?, and What happens after you die?. There are articles of several pages, together with short sidebars containing commentaries from an eclectic bunch of thinkers, including some mathematicians. Among the articles, two have a mathematical flavor: "What is reality?" by Roger Penrose, and "Will we ever have a theory of everything?" by Michio Kaku. Among those contributing shorter commentaries are mathematicians Marcus du Sautoy, Timothy Gowers, and, Benoit Mandelbrot. The other section, "Journey Through Time", presents an overview of the past 50 years of science through a selection of New Scientist articles from this period. Judging from this collection of articles, one might conclude that nothing much happened in mathematics during those decades: There are articles on computing, theoretical physics, space exploration, genetics, chemistry, neuroscience, and nuclear power, plus several on aviation---but none exclusively on a mathematical topic.
--- Allyn Jackson
"Dashing Rogues," by Sid Perkins. Science News, 18 November 2006, pages 328-329.
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They have been called "mountains of water" and the troughs that precede them "holes in the sea." These are a few of the phrases used to describe rogue waves, which many scientists define as waves at least 2.2 times the significant wave height---typically the average of the tallest one-third of the waves surrounding it. Some of these waves have damaged and presumably sunk large ocean-going ships. Scientists once assumed that they occurred in any one place only rarely---perhaps once every several thousand years---but "data gathered by instruments on relatively stable platforms and on buoys hint that such big waves occur much more frequently than that," writes Sid Perkins. He describes two studies in which one of the participants was Paul C. Liu, an oceanographer with the National Oceanographic and Atmospheric Administration. In one study, data that Liu and colleague Keith R. MacHutchon gathered over six years from a gas-drilling platform off the southern coast of South Africa showed that "the chance of encountering a rogue wave during any hour spent at this spot was about 3.1 percent." Four of the rogue waves were "more than four times the size of their neighbors," while one older model had suggested that one of these would occur only once every several million years! Why do rogue waves occur? There is no single root cause. For example, Liu points to a number of likely factors for rogue waves off the coast of South Africa: a combination of the Agulhas Current flowing from the northeast, prevailing winds blowing in from the southwest, and the shape of the seafloor and coastline, all of which have an impact on wave formation. In fact, Perkins writes, scientists have "underestimated the frequency of rogue waves for many years because they presumed that real ocean waves behave as mathematically ideal waves do." For example, it was assumed that when two theoretical 1-meter-tall waves cross paths, they briefly form a wave that is 2 meters tall. In fact, this assumption is often wrong. Perkins refers to the recently published work of A. R. Osborne, an oceanographer at the University of Turin in Italy, who describes a condition called "crossing seas" in which rogue waves are more likely to form and to be taller than in a single "wave train"---a large number of waves generated by the same phenomenon that travel in a group. Later computer simulations of crossing seas done by Mattias Marklund of Umeå University in Sweden have shown the rapid generation of rogue waves. Perkins concludes that, "with such mathematical techniques, scientists may predict the conditions that spawn rogue waves." In fact, he reports, rogue-wave forecasts are being issued on an experimental basis by the European Centre for Medium-Range Weather Forecasts. --- Claudia Clark
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"Lottery Strategy Pays Off," by Aisha Labi. The Chronicle of Higher Education, 17 November 2006, page A6.
Seventeen workers at England's Bradford University printing plant, working together, won approximately US$10 million in a recent lottery. Here is their strategy: The team wrote the 49 numbers used in the lottery on separate slips of paper. Each person drew six numbers (the number of numbers chosen in the lottery). After the first 48 slips were drawn, the team used the remaining number and began again with the other 48 numbers. The team felt that using all of the numbers involved in the lottery would increase their chances of winning. Even though the strategy was successful (after four years), is it mathematically any better than choosing numbers at random and perhaps not using all 49 numbers?
--- Mike Breen
"This Academic Life," by Robin Wilson. The Chronicle of Higher Education, 17 November 2006, page A12.
Smith College has been awarded a US$1.5 million grant from the National Science Foundation for a center for women who would like to pursue a graduate degree in mathematics, but whose undergraduate mathematics background is lacking. The college's Center for Women in Mathematics will open next academic year and will provide living expenses and tuition for up to 16 students a year. One of the center's goals is to increase the number of female faculty in mathematics.
--- Mike Breen
"Peloisi shakes capital ... Political Greenhorn: McNerney arrives in D.C. to take Pombo's seat, learn ropes," by Rachel Gordon. San Francisco Chronicle, 14 November 2006.
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Voters in California's 11th Congressional district elected Jerry McNerney, a Ph.D. mathematician and wind-energy expert, to Congress. He won the spot held by a seven-term incumbent. McNerney tells the reporter that he hopes to serve on the Energy and Commerce Committee "to put his professional background to good use," and he would also like to be on the agriculture and transportation committees. The "McNerney for Congress" website posts information about Mcnerney's background, including that he attended the University of New Mexico, where he studied engineering and mathematics, earning a Ph.D. in 1981. He was a contractor to Sandia National Laboratories, where he worked on national security programs. In 1985, he took a senior engineering position with US Windpower and in 1994 began working as an energy consultant utility companies. McNerney will be the only mathematician in Congress. Samuel M. Rankin III, director of the AMS's Washington D.C. office, is quoted as saying: "Obviously we're very excited." --- Annette Emerson
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"Eine fläche für den Poeten (A surface for the poet)". Scienzz web site, 6 November 2006.
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This article reports on the awarding of prizes by the Deutsche Mathematiker Vereinigung (DMV, German Mathematical Society). The renowned German literary figure Hans Magnus Enzensberger got a special prize: He had a mathematical surface named after him, the "Enzensberger Stern" (Enzensberger star), and was presented with a glass model of the six-pointed surface. Other prizewinners were George Szpiro, who received the DMV Media Prize, and Ulf von Rauchhaupt, who received the DMV Journalism Prize. --- Allyn Jackson
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"When god plays dice," by Dana Mackenzie. New Scientist, 4 November 2006, pages 46-49.
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This article discusses renewed interest in twisor theory, a physical theory developed by Roger Penrose in the 1960s, which may help physicists interpret information from experiments to be conducted in 2007 at the Large Hadron Collider. Twistor theory and string theory were both candidates for a "theory of everything" that would unite physical theories about gravity and quantum mechanics. But twistor theory, Mackenzie writes, "made too many predictions that violated reality as we know it, so [the theory] crashed and burnt as a physics theory in the 1970s. Yet it lived on as a mathematical theory." The article includes a sidebar called "Six dimensions with a twist" that discusses the mathematics of twistor theory. In 2003, Edward Witten devised a way to combine string theory and twistor theory, and it is the marriage of the two that may prove relevant for next year's experiments with the Large Hadron Collider. --- Allyn Jackson
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"The Gateway Arch is NOT a Parabola." Interview with Keith Devlin on "Weekend Edition." National Public Radio, 4 November 2006.
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Soon after a commentator on National Public Radio (NPR) identified the St. Louis Gateway arch as a parabola the station received "piles of emails" from listeners pointing out the mistake. NPR's "Math Guy" Keith Devlin was invited to explain why the arch is not a parabola but a catenary curve. Devlin starts by saying that even Galileo got the (parabola) shape wrong and that calculus (which had not yet been invented when Galileo was alive) is needed to figure it out. Devlin explains that the Gateway arch is not exactly a mathematical catenary either, because of its construction. Listen to the segment. --- Annette Emerson
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"Ballot Roulette: Computer Scientists and Mathematicians Look For Better Ways to Vote," by Peter Weiss. Science News Online, 4 November 2006.
This time next year, a mathematician may have helped make sure your vote was counted accurately. The vote-counting scandals of the 2000 election reinvigorated the search for reliable, secure ways to tally ballots. Mathematicians and computer scientists have been working to diagnose vulnerabilities in electronic voting systems and design new voting methods using cryptography. This article provides a look at the present and future of voting systems in America, including recent research by Princeton University computer security experts on ways to load and replicate vote-changing viruses on electronic machines and ideas for ballots with encrypted portions voters can keep as receipts. Author Peter Weiss sets up the vote-counting challenge with a basic description of problems since 2000, questions about the current systems, and alternatives being developed today.
--- Lisa DeKeukelaere
"Beautiful Models": Review of Evolutionary Dynamics: Exploring the Equations of Life, by Martin Nowak. Reviewed by Sean Nee. Nature, 2 November 2006.
The book flows quickly and casually through advanced mathematical concepts, and its author, Martin Nowak, is a successful young Harvard professor. The reviewer did not expect to like the book but was interested and amused by Nowak's research in and explanations of evolutionary dynamics---the mathematical approach to biological phenomena like the human body's response to the AIDS virus. Portions of the book were both funny and exciting, and Nee recommends it to anyone interested in theoretical biology, though some topics and wording seemed geared toward a mathematically knowledgeable audience.
--- Lisa DeKeukelaere
"Coole Mathematiker (Cool Mathematicians)": Review of Bourbaki, A Secret Society of Mathematicians, by Maurice Mashaal. Reviewed by George Szpiro. Neue Zürcher Zeitung, 1 November 2006.
Nicolas Bourbaki was the pseudonym used by a group of mostly French mathematicians who starting in the 1930s wrote mathematics books that had a significant influence on the field. Szpiro writes that the book is written in an entertainingly and refreshingly readable style and contains not just historical but mathematical details.
--- Allyn Jackson
"Fuzzy Math," by Alex Stone. Discover, November 2006, page 18.
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If you are looking for a way to make a profit on your knowledge of conditional probability, then this short article is for you. Three cards are painted as follows: one blue on both sides, one red on both sides, and one has blue on one side and red on the other. The "mark" chooses a card. Suppose that it is blue on one side. Since this is not the red-red card, you reason with the mark that there must be a 50-50 chance that the other side of the drawn card is red. So you wager even money that the other side of the drawn card is blue. It can be shown that this is not an even bet. In fact, you will win 2/3 of the time (the blue could be from the red-blue card or from either of the two sides of the blue-blue card), and thus come out ahead by betting blue. --- Mike Breen
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