Ramsey theory
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enFriends and strangers
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Imre Leader </div>
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<p>Can we always find order in systems that are disordered? If so, just how large does a system have to be to contain a certain amount of order?</p>
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Can we always find order in systems that are disordered? If so, just how
large does a system have to be to contain a certain amount of order?
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Let's consider a concrete example. Suppose there is a
room with six people in it. We are interested in whether
people in this room know each other or not. Let's call two
people friends if they know each other, strangers if they
don't.
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<p><a href="http://plus.maths.org/content/friends-and-strangers-0" target="_blank">read more</a></p>http://plus.maths.org/content/friends-and-strangers-0#commentscombinatoricsgraph theoryRamsey theoryThu, 27 Mar 2014 15:01:00 +0000Rachel6062 at http://plus.maths.org/contentMathematical mysteries: Painting the Plane
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Helen Joyce </div>
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<p>Suppose you have an infinitely large sheet of paper (mathematicians refer to this hypothetical object as the plane). You also have a number of different colours - pots of paint, perhaps. Your aim is to colour every point on the plane using the colours available. That is, each point must be assigned one colour.</p>
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<div class="pub_date">May 2001</div>
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<p>Suppose you have an infinitely large sheet of paper (mathematicians refer to this hypothetical object as the <i>plane</i>). You also have a number of different colours - pots of paint, perhaps. Your aim is to colour every point on the plane using the colours available. That is, each point must be assigned one colour.</p>
<p>Can you do this so that, for any two points on the plane which are exactly 1cm apart, they are given different colours?</p><p><a href="http://plus.maths.org/content/mathematical-mysteries-painting-plane" target="_blank">read more</a></p>http://plus.maths.org/content/mathematical-mysteries-painting-plane#comments15Mathematical mysteriesplane colouringRamsey theoryMon, 30 Apr 2001 23:00:00 +0000plusadmin4750 at http://plus.maths.org/contentFriends and strangers
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Imre Leader </div>
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Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. <b>Imre Leader</b> looks at the colourful world of Ramsey Theory. </div>
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<div class="pub_date">Sep 2001</div>
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<p>In 1928, <a href="http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Ramsey.html">Frank Ramsey</a> was wrestling with a problem in mathematical logic. To solve it, it seemed to him, he needed to show that the mathematical systems he was studying would always have a certain amount of order in them.<p><a href="http://plus.maths.org/content/friends-and-strangers" target="_blank">read more</a></p>http://plus.maths.org/content/friends-and-strangers#comments16chaoscolouringgraph theoryRamsey numberRamsey theoryFri, 01 Dec 2000 00:00:00 +0000plusadmin2190 at http://plus.maths.org/content