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POPSAwesome research/ Homework resource I only found this the other day and mostly I'm clipping it for my own uses; however, it's a great resource and I thought I'd share. The site itself has pretty cool info too. 'Hope you guys like the clip.
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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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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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POPSA New Kind of Science - Stephen Wolfram (Lecture) worth watching, on cellular automata, complexity, randomness, nature, mathematics, science, biology, natural selection, networks, space-time, physics, causality, relativity, determinism, quantum mechanics, computational irreducibility, ... (not necessarily in that order) His book is freely available online: http://www.wolframscience.com/nksonline/toc.html (see also The Nature of Code )
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POPSSeeing in four dimensions The videos are all available free at www.dimensions-math.org. The videos go on to show how we can visualize imaginary numbers geometrically, how fractal patterns emerge in the Mandelbrot set and Julia sets, and how beautiful and complex shapes can be built up from circles.
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POPSFuture 'Top 10' Hot Careers in 2012 5) Simulation Engineering By 2012, an increase in processing power and rich data will make simulations more realistic, and user-friendly. Simulation engineers will be working on bringing us closer to “Star Trek’s” Holodecks—the ultimate total immersion simulation. Simulations will be in every industry and every engineering field, 6) Boomer Caregiving 7) Genetic Counseling 8) Brain Analysts 9) Space Tourism 10) Roboticists
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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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POPSMusic Reduced to Beautiful Math "You can use these geometrical spaces to provide ways of visualizing musical pieces," Tymoczko told LiveScience. "These spaces give us a much better and comprehensive picture of the space of all possible chords."
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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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POPSGirls Make History At Science Contest More: Dr. Hopkins helped start a national discussion about girls and science two years ago when she walked out of a talk by Harvard University’s president, Lawrence H. Summers, after he suggested that innate differences between men and women might be one reason that fewer women than men succeed in math and science careers. Dr. Summers apologized during the ensuing furor; he announced his resignation as Harvard’s president 13 months later James Whaley, president of the Siemens Foundation, which oversees the competition for Siemens AG, a global electronics and engineering company, said the competition results send a great message to young women Alicia Darnell, 17, a senior at Pelham Memorial High School in Pelham, N.Y., won second place and a $50,000 scholarship in the individual category for research that identified genetic defects that could play a role in the development of Lou Gehrig’s disease Pretty good for 16 and 17 year olds don't ya think?
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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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