creating order in a card deck by shuffling?
Posted on Oct.21, 2011, under math
Persi Diaconis is a Magician turned mathematics professor has written book titled Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks outlining the math behind some of his favorite card tricks. Diaconis was inspired by the work of French mathematician Paul Lévy in the idea of perfect shuffling, taking a standard deck of cards is carefully shuffled eight times and ends up returning precisely to its starting arrangement .
The gaming industry is particularly interested in the efficacy of shuffling as those remaining bits of order in a deck are what card counters use to beat the house.
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Rare Clear View of Alaska
On most days, relentless rivers of clouds wash over Alaska, obscuring most of the state's 6,640 miles (10,690 kilometers) of coastline and 586,000 square miles (1,518,000 square kilometers) of land. The south coast of Alaska even has the dubious distinction of being the cloudiest region of the United States, with some locations averaging more than 340 cloudy days per year. That was certainly not the case on June 17, 2013, the date that the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA's Terra satellite acquired this rare, nearly cloud-free view of the state. The absence of clouds exposed a striking tapestry of water, ice, land, forests, and even wildfires. Snow-covered mountains such as the Alaska Range and Chugach Mountains were visible in southern Alaska, while the arc of mountains that make up the Brooks Range dominated the northern part of the state. The Yukon River -- the longest in Alaska and the third longest in the United States -- wound its way through the green boreal forests that inhabit the interior of the state. Plumes of sediment and glacial dust poured into the Gulf of Alaska from the Copper River. And Iliamna Lake, the largest in Alaska, was ice free. The same ridge of high pressure that cleared Alaska's skies also brought stifling temperatures to many areas accustomed to chilly June days. Talkeetna, a town about 100 miles north of Anchorage, saw temperatures reach 96°F (36°C) on June 17. Other towns in southern Alaska set all-time record highs, including Cordova, Valez, and Seward. The high temperatures also helped fuel wildfires and hastened the breakup of sea ice in the Chukchi Sea.Image Credit: NASA/Jeff Schmaltz, LANCE MODIS Rapid Response Team, NASA GSFCCaption: Adam Voiland
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