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Marcus du Sautoy: Symmetry, reality's riddle

Marcus du Sautoy: Symmetry, reality's riddle

BBC: Slideshow: The art of mathematics To the untrained eye, these vivid images might appear to be random sets of colourful swirls and circles. But they are in fact precise visual representations of mathematical theory known as dynamical systems. Some of the images - created by mathematicians from across the world - have gone on display at the University of Liverpool. Here, mathematician Lasse Rempe explains how they are made - and considers their artistic merits. <table cellspacing="0" cellpadding="0" border="0" width="352" align="center"><tr><td><table cellspacing="1" cellpadding="30" border="0" bgcolor="#cccccc" width="100%" height="33"><tr><td bgcolor="#fafafa"><div class="font-family:Verdana;color:#666666;font-size:11px;"><span style="font-family:Verdana;color:#333333;font-size:18px;font-weight:800;"><strong>Javascript and Flash plug-in required</strong></span><P>Either the Flash plugin was not detected on your computer or the JavaScript features of your brower have been disabled.

JimBobJenkins's Channel Game Theory 101: The Complete Textbook on Amazon: Two prisoners are locked into separate interrogation rooms. The cops know they were trespassing and believe they were planning on robbing a store, but they lack sufficient evidence to charge them with the latter crime. Thus, they offer the prisoners the following deal: If no one confesses, both will only be charged with trespassing and receive a sentence of one month. If each prisoner only want to minimize the amount of time he spends in jail, what should they do? This lesson introduces the concept of strict dominance, which is a very useful tool for a game theorist.

The story of the Gömböc September 2009 Play this movie to see the Gömböc wriggle. This article is also available as a podcast. A Gömböc is a strange thing. It looks like an egg with sharp edges, and when you put it down it starts wriggling and rolling around with an apparent will of its own. Until quite recently, no-one knew whether Gömböcs even existed. Balancing act The defining feature of a Gömböc is the fact that it's got just two points of equilibrium: one is stable and the other is unstable. A Gömböc made from plexiglass. "It's a bit like putting a ball on a hilly landscape," says Domokos, "if you put the ball down at a generic point, it will always roll off in the same direction, down into the valley. To give it its full mathematical description, a Gömböc is a three-dimensional, convex and homogeneous object with exactly one stable point of equilibrium and one unstable point of equilibrium. Doubtful existence An ellipse has two stable and two unstable points of equilibrium. A geometric stem cell Gábor Domokos

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