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POPSAncient Blueprints of Calculus Uncovered in Archimedes Text Details have been released from the nine-year-long reconstruction project to recover the Greek mathematician's writings from this one-of-a-kind find and the results are fascinating. Buried beneath the surface of this gilded palimpsest, researchers discovered more extensive demonstrations of concepts such as infinite series, approximations, limits, and integral calculus than had been known to exist in ancient times. Archimedes wrote The Method almost two thousand years before Isaac Newton and Gottfried Wilhelm von Leibniz developed calculus in the 1700s. Reviel Netz, an historian of mathematics at Stanford University who transcribed the text, says that the examination of Archimedes' work has revealed "a new twist on the entire trajectory of Western mathematics."
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POPSNo Shortcuts to First-World Wealth New cluster-analysis of the world's product export space reveals the differences in connectivity and diversity between nations' production capacities as well as the very sizable developmental gaps in this network that keep poorer countries on the industrial fringes. The rich countries of the industrialized world tend to have broad portfolios of industries, and accordingly occupy large areas of the product space, usually including much of the network's core. Fast-growing developing countries such as China, Thailand, and Hungary are strong in some of those central, well-connected regions. The poorest countries, especially those in sub-Saharan Africa, tend to specialize in a few of the peripheral products—such as oil for Nigeria and copper for Zambia. EDIT :My first title was too generic ("Mapping the Wealth of Nations.")
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POPSNew Math Theory Explains Toddler's "Word Spurt" A bell-shaped word distribution and a steady child learning rate turn out to be enough to bring about the extraordinary explosion seen in children's vocabularies around this age. McMurray notes that languages have only a small number of very easy-to-learn words and many more intermediate words. So when a baby has been exposed to enough language to learn the easy words, she will acquire just a few words. As she is exposed to more language, she begins to learn the medium words. And because there are a lot of medium words, she is likely to pick up a lot of words at this stage. This, McMurray says, is the vocabulary explosion.
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POPSMath as a Civil Right The ubiquity of computers makes abstract, quantitative reasoning skills critical to a wide range of job opportunities. "Information age technology put math on the table as a literacy requirement in the same way that industrialism made reading literacy a requirement," says Moses. For that reason, he says, the country needs to raise math education standards for all students.
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POPSNew Math For Analyzing Evolutionary Trees "What this tells me is that you don't know what kind of mathematics is going to be useful to biology," Billera says. "It wasn't clear before this that geometry and topology would be useful to biology. Who would think they had anything to do with each other?" Ernst Haeckel's classic hand-drawn diagram is just for fun—it's one of those wonderful diagrams that functions as both science and art.
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POPSThe Mathematical Lives of Plants The seeds of a sunflower, the spines of a cactus, and the bracts of a pine cone all grow in whirling spiral patterns. Remarkable for their complexity and beauty, they also show consistent mathematical patterns that scientists have been striving to understand. ... Scientists have puzzled over this pattern of plant growth for hundreds of years. Why would plants prefer the golden angle to any other? And how can plants possibly "know" anything about Fibonacci numbers? For the first time, scientists have found convincing biochemical mechanisms responsible for the interlocking spiral growth patterns seen in many plants. (The Romanesco broccoli plant is a striking example.) The video of the experiment with magnetized liquid iron droplets demonstrates how the geometry of such growth could occur in nature.
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POPS248-Dimensional Mathematical Map Calculated "The calculation was known to be possible in principle, but it was thought to be hopeless in practice," says Adams. "But four years ago a group of us said let's really try to do it. We're pretty sure we've got it right, but it's hard to be 100% sure." "It's probably one of the most complicated pure mathematical calculations anyone's ever done," says Stewart. "Each entry is difficult to calculate — it's amazing they managed to do this."
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POPSInventor of Fortran, John W. Backus, Dies Not only did Backus give the world the first high-level (and highly-successful) programming language, but he had the genius in 1959 to develop Backus–Naur form , the meta-language used to define all possible programming languages, past, present and future. Our digital world wouldn't be the same without him. Shortly before he graduated, Mr. Backus wandered by the I.B.M. headquarters on Madison Avenue in New York, where one of its room-size electronic calculators was on display. When a tour guide inquired, Mr. Backus mentioned that he was a graduate student in math; he was whisked upstairs and asked a series of questions Mr. Backus described as math “brain teasers.” It was an informal oral exam, with no recorded score. He was hired on the spot. As what? “As a programmer,” Mr. Backus replied, shrugging. “That was the way it was done in those days.”
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POPS80-Year-Old Indian Math Mystery Solved A few months into 2007 and already another long-standing mathematical mystery has been more-or-less put to rest. It will be hard to top Perelman's stunning proof of the legendary Poincaré Conjecture from last year, but in math and science, you never know when the next breakthrough will come. (If you haven't already, read up on some of the incredible anecdotes about the life of the Indian genius, Ramanujan. He was truly one of a kind.)
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POPSMath Behind Ancient Islamic Tile Patterns Decoded When Peter J. Lu traveled to Uzbekistan, he had no idea of the mathematical journey that he was about to embark on as well. See the full research article as published in Science . It's a wonderful example of original, multidisciplinary academic research bridging history and mathematics that happens to force us to re-think the sophistication of ancient geometrical knowledge. When Lu looked at photographs of Islamic buildings, he found that he could break the patterns on their surfaces up into the same shapes, even though the shapes often weren't immediately visible. "I couldn't sleep for days," he said. "I skipped Christmas break to work on it."
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POPSFractal Food: Self-Similarity on the Supermarket Shelf This great article on computational self-similarity in nature provided the author with an excuse to take a series of spectacular close-up photos of the incredible Romanesco broccoli plant. Fractals never looked so delicious! (Click pictures for high-resolution images.) Nearly exact self-similar fractal forms occur do in nature, but I'd never seen such a beautiful and perfect example until, some time after moving to Switzerland, I came across a chou Romanesco like the one above in a grocery store. This is so visually stunning an object that on first encounter it's hard to imagine you're looking at a garden vegetable rather than an alien artefact created with molecular nanotechnology. But of course, then you realise that vegetables are created with molecular nanotechnology, albeit the product of earthly evolution, not extraterrestrial engineering.
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POPSArt of the Tetrahedron, Revisited Wonderfully angular sculptures. And what an inspiring story! Until age 50, Silverman had been a highly successful surgeon, practicing medicine with considerable enthusiasm and skill. Then he encountered an ailing colleague near death, who advised Silverman that if there were anything he might really want to do, then he ought to do it right away, before the chance slips away. The encounter changed Silverman's life. He returned to interests that had captured his attention when he was a teenager. He had visited museums to gaze at statues, and he had tried his hand at carving wood. Later, when studying medicine at Tulane University, he had met a sculpture teacher who had invited him to classes and taught him to see, in the artistic sense.
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POPSWhat Did Descartes Really Know? (Book Review) Great review of two new Descartes biographies that set some of the records straight on the great naturalist's works. Despite his current reputation, the man himself seems to have been less interested in metaphysics than in applying algebra to geometry and delving into the innards of cows. He turned to philosophy relatively late in life, and out of fear that the Catholic Church would condemn his science. He would have been surprised at how he is remembered. Most of all, he would have been aghast at the way in which “I think, therefore I am” has been ripped from its context, inflated into a one-sentence summary of his ideas, and turned into something absurd. The rot set in at the start of the nineteenth century, when Hegel made heavy weather of “I think, therefore I am” and took it to mean that thought and being are fundamentally the same thing.
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POPSSt. Louis Arch Couldn't Exist According to Its Own Description It turns out that for more than 40 years, there's been a blatant mathematical error etched into the plaque at the base of the Gateway Arch and apparently the mistake has only been caught now! The Arch is a giant inverted catenary, a curve with a precise mathematical equation. One of the geometric equations at the arch turns out to be meaningless. If the Arch were actually built to satisfy these equations, it wouldn't even exist! This could be some kind of national embarrassment, given the prominence of this mistake's locale.
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POPSThe Exanding Mathematical Universe of Spidrons A field of triangles crumples and twists into a wavy crystalline sea. A crystal ball sprouts spiraling, labyrinthine passages. Faceted bricks stack snugly into a tidy, compact structure. Underlying each of these objects is a remarkable geometric shape made up of a sequence of triangles—a spiral polygon that resembles a seahorse's tail. The result is beautiful to behold.
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POPSExploding the Charter School Myth My own 2¢: I've taught and tutored math and science in a variety of public, private, and charter schools. I went to several non-standard schools myself, so I thought positively of charter schools in general...until I had to teach students there. I always felt less productive in these situations for frustrating reasons like this: Free-standing charter schools often bite off more than they can chew. The presumption is that without the bureaucratic restraints of the public school system and the teacher unions, charter schools can provide better education at lower cost. But the problem with failing public schools is that they often lack both resources and skilled, experienced teachers. While there are obvious exceptions, some charter schools embark on a path that simply recreates the failures of the schools they were developed to replace.
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POPS"Perelman's Song" - A Mathematical-Fiction Short Story The audience for "Math-Fi" may not be large, but author Tina Chang obviously had a lot of fun with this cute story and managed to elucidate some of the topological ideas involved in Perelman's recent landmark proof of the longstanding Poincaré conjecture. For background see Rob's clip: Elusive Proof, Elusive Prover: A New Mathematical Mystery .
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POPSThe Number Spiral It looks as though primes tend to concentrate in certain curves that swoop away to the northwest and southwest, like the curve marked by the blue arrow. (The numbers on that curve are of the form x ( x +1) + 41, the famous prime-generating formula discovered by Euler in 1774.) Some clips from a wonderfully-done exploration of this curious mathematical construct (also known as the Ulam Spiral ). To date, it is not fully understood exactly why more primes tend to fall along certain "curves" in the spiral than others, but the elusive quest for a simple prime-generating formula keeps the deceptively-simple spiral intriguing to number theorists.
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