creativity
https://plus.maths.org/content/category/tags/creativity
enEqual averages
https://plus.maths.org/content/equal-averages
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<p>Exploring the five different notions of average.</p>
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<p>There are several different notions of average: the mean, the median, the mode and the range (see <a href="https://plus.maths.org/content/equal-averages#definitions">below</a> for the definitions). If you work out each of these for the set of numbers 2, 5, 5, 6, 7, you'll notice something interesting — they are all equal to 5!</p><div class="field field-type-number-integer field-field-hidden">
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<p><a href="https://plus.maths.org/content/equal-averages" target="_blank">read more</a></p>https://plus.maths.org/content/equal-averages#commentscreativitypuzzleThu, 24 Sep 2015 10:57:33 +0000mf3446436 at https://plus.maths.org/contentSeven things you need to know about prime numbers
https://plus.maths.org/content/seven-things-you-need-know-about-prime-numbers
<p>In this excellent talk the mathematician <a href="http://people.maths.ox.ac.uk/neale/">Vicky Neale</a> gives a fascinating and easy-to-follow introduction to the prime numbers — from a thorough description of what they are, via the ancient proof that there are infinitely many, to the prime number theorem, the twin prime conjecture and more. By the end of this talk you hopefully agree with us, and Vicky, that the world would be a very boring place without primes.</p><p><a href="https://plus.maths.org/content/seven-things-you-need-know-about-prime-numbers" target="_blank">read more</a></p>https://plus.maths.org/content/seven-things-you-need-know-about-prime-numbers#commentscreativitynumber theoryprime numberprime number distributiontwin prime conjectureUniversity of CambridgevideoTue, 04 Aug 2015 12:55:51 +0000mf3446412 at https://plus.maths.org/contentEinstein and relativity: Part I
https://plus.maths.org/content/einstein-relativity
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David Tong </div>
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<p>Read about the rocky road to one of Einstein's greatest achievements: the general theory of relativity, which celebrates its centenary this year.</p>
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<p><em>This article is an abridged version of a talk David Tong gave at the Southbank Centre in London in 2013. You can listen to a sound recording of the talk on <a href="https://soundcloud.com/southbankcentre/david-tong-on-einsteins-theory/">Soundcloud</a>, or watch a video of a very similar talk, aimed at 16 to 17 year-olds, <a href="https://plus.maths.org/content/stories-einstein">here</a>.</em></p>
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<p>2015 is a special year for physics. It is the 100th
anniversary of Albert Einstein's greatest achievement: the <em>general theory of relativity</em>. </p><p><a href="https://plus.maths.org/content/einstein-relativity" target="_blank">read more</a></p>https://plus.maths.org/content/einstein-relativity#commentscreativityEinsteinFP-carouselgeneral relativityhistory of mathematicsrelativityspecial relativityUniversity of CambridgeThu, 04 Jun 2015 15:56:07 +0000mf3446360 at https://plus.maths.org/contentEinstein and relativity: Part II
https://plus.maths.org/content/einstein-and-relativity-part-ii
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David Tong </div>
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<p>General relativity, Einstein's rise to international stardom, and his legacy.</p>
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<p><em>To read about Einstein's motivation for the general theory of relativity and his struggle to formulate it, read the <a href="https://plus.maths.org/content/einstein-relativity">first part</a> of this article.</em></p>
<h3>General relativity</h3>
<p>Einstein's theory changed our understanding of space and time. Before Einstein people thought of space as stage on which the laws of physics play out. We could throw in some stars or some planets and they would move around on this stage.</p><p><a href="https://plus.maths.org/content/einstein-and-relativity-part-ii" target="_blank">read more</a></p>https://plus.maths.org/content/einstein-and-relativity-part-ii#commentscreativityEinsteingeneral relativityhistory of mathematicsrelativityUniversity of CambridgeThu, 04 Jun 2015 15:15:38 +0000mf3446374 at https://plus.maths.org/contentFolding fractions
https://plus.maths.org/content/folding-numbers
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Rachel Thomas </div>
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<p>Folding a piece of paper in half might be easy, but what about into thirds, fifths, or thirteenths? Here is a simple and exact way for fold any fraction, all thanks to the maths of triangles.</p>
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Can you fold a piece of paper in half? Of course you can, it’s easy, you just match the two corners along one side. But can you fold it in thirds? You might be able to fold it into thirds with a bit of fiddling and guessing, but what about into fifths? Or sevenths? Or thirteenths? Here is a simple way you can fold a piece of paper into any fraction you would like – exactly – no guessing or fiddling needed!
</p><p><a href="https://plus.maths.org/content/folding-numbers" target="_blank">read more</a></p>https://plus.maths.org/content/folding-numbers#commentscreativityHaga's theoremorigamipythagoras' theoremMon, 02 Mar 2015 12:06:28 +0000Rachel6322 at https://plus.maths.org/contentSteady on, Einstein
https://plus.maths.org/content/steady-on-Einstein
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Rachel Thomas </div>
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<p>To celebrate the release of more English translations of Einstein's papers, we revisit one of his previously unknown models of the Universe.</p>
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Albert Einstein's impact on our understanding of the Universe is so widely regarded by both the physics community and the general public, that his name is now a synonym for genius.<p><a href="https://plus.maths.org/content/steady-on-Einstein" target="_blank">read more</a></p>https://plus.maths.org/content/steady-on-Einstein#commentscosmologycreativityEinsteinhistory of mathematicsphilosophy of cosmologysteady state modelMon, 12 Jan 2015 13:50:37 +0000Rachel6297 at https://plus.maths.org/contentTrisecting an angle with origami
https://plus.maths.org/content/trisecting-angle-origami
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Rachel Thomas </div>
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<p>How to solve an ancient problem in a few folds.</p>
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<p>Over 2000 years ago the Greek mathematician <a href="http://www-history.mcs.st-and.ac.uk/Biographies/Euclid.html">Euclid of Alexandria</a> laid down the foundations of geometry. But Euclid's geometry was very different from ours. It was all about the geometric shapes you could produce using just a straightedge (a ruler without markings) and a compass. You can do lots of useful things with these tools. For example, you can such divide an angle into two equal halves:.</p><p><a href="https://plus.maths.org/content/trisecting-angle-origami" target="_blank">read more</a></p>https://plus.maths.org/content/trisecting-angle-origami#commentsangle trisectioncreativitygeometryorigamiFri, 31 Oct 2014 10:42:11 +0000mf3446228 at https://plus.maths.org/contentTic-tac-toe!
https://plus.maths.org/content/tic-tac-toe
<p>We have just learnt a really nice fact about the game of tic-tac-toe. As you may know, tic-tac-toe always results in a draw if both players make the best moves possible at every step of the game. To force a draw you need to follow a particular strategy, which isn't too hard, but tedious to write down (see <a href="http://en.wikipedia.org/wiki/Tic-tac-toe#Strategy">here</a>).</p>
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<p style="width: 289px;"></p><p><a href="https://plus.maths.org/content/tic-tac-toe" target="_blank">read more</a></p>https://plus.maths.org/content/tic-tac-toe#commentscreativitygame theorystrategyThu, 02 Oct 2014 09:21:47 +0000mf3446154 at https://plus.maths.org/contentOrder in disorder
https://plus.maths.org/content/order-disorder
<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? In this video <a href="https://www.dpmms.cam.ac.uk/~leader/">Imre Leader</a> of the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge gives an equation free introduction to a fascinating area of maths called <em>Ramsey theory</em>.
</p><p><a href="https://plus.maths.org/content/order-disorder" target="_blank">read more</a></p>https://plus.maths.org/content/order-disorder#commentscreativityRamsey theoryvideoMon, 29 Sep 2014 12:42:40 +0000mf3446194 at https://plus.maths.org/contentWhy do mathematicians play games?
https://plus.maths.org/content/why-do-mathematicians-play-games
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Marianne Freiberger </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/23_sep_2014_-_1630/games_fronticon.jpg?1411486209" /> </div>
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<p>Why game theory is a serious business.</p>
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<p>The easy answer is "for fun", just like the rest of us. It's obvious
that being good at maths can help you in many difficult games, such as
chess. But there is another reason too. Mathematicians are interested
in games because they can help us understand why we humans (and other
animals) behave as we do. A whole area of mathematics, called <em>game
theory</em>, has been developed to cast some light on our
behaviour, especially the way we make decisions.</p><p><a href="https://plus.maths.org/content/why-do-mathematicians-play-games" target="_blank">read more</a></p>https://plus.maths.org/content/why-do-mathematicians-play-games#commentscreativitygame theoryTue, 23 Sep 2014 11:04:31 +0000mf3446186 at https://plus.maths.org/contentToo big to write but not too big for Graham
https://plus.maths.org/content/too-big-write-not-too-big-graham
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Rachel Thomas and Marianne Freiberger </div>
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<p>Meet the number that's bigger than the observable Universe!</p>
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Recently, when we were writing our book <a href="http://www.amazon.co.uk/Numericon-Journey-through-Hidden-Numbers/dp/1782061541"><em>Numericon</em></a>, we came across what has now become one of our very favourite numbers: <em>Graham's number</em>. One of the reasons we love it is that this number is big. Actually, that's an understatement. Graham's number is mind-bendingly huge.
</p><p><a href="https://plus.maths.org/content/too-big-write-not-too-big-graham" target="_blank">read more</a></p>https://plus.maths.org/content/too-big-write-not-too-big-graham#commentscreativitygraphnetworkRamsey numberRamsey theoryThu, 04 Sep 2014 07:39:12 +0000Rachel6180 at https://plus.maths.org/contentBe creative!
https://plus.maths.org/content/be-creative
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"Ingenuity", "far reaching vision", "unerring sense", "deep
curiosity" — and best of all,
"extraordinary creativity". These are some of the words that have been
used to praise this year's Fields medallists at the <a href="https://plus.maths.org/content/icm-2014">International
Congress of Mathematicians</a> (ICM). These words aren't specific to maths. They
could be used to describe anyone whose work is about discovery and
beauty; writers, poets, or musicians for example. If there has
been one overarching theme at this ICM, it's just how creative a
subject mathematics is.<p><a href="https://plus.maths.org/content/be-creative" target="_blank">read more</a></p>https://plus.maths.org/content/be-creative#commentscreativityICM 2014Wed, 20 Aug 2014 04:18:26 +0000mf3446170 at https://plus.maths.org/contentPlay to win with Nim
https://plus.maths.org/content/play-win-nim
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Marianne Freiberger </div>
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<p>In the game of Nim one player always has a winning strategy — it depends on an unusual way of adding numbers.</p>
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<p>Some games are all about luck. Your winning chance depends on the
roll of a die or the cards you've been dealt. But there are
other games that are only about strategy: if you play cleverly, you're
guaranteed to win. </p>
<p>A great example of this is the ancient game of Nim. Whatever the
state of the game, there is a winning strategy for one of the two
players. And a very cute form of addition tells you which of the two
players it is.</p><p><a href="https://plus.maths.org/content/play-win-nim" target="_blank">read more</a></p>https://plus.maths.org/content/play-win-nim#commentsbinary numbercreativitygame theorynimstrategyMon, 21 Jul 2014 10:18:30 +0000mf3446134 at https://plus.maths.org/contentThe power of good questions
https://plus.maths.org/content/power-good-question
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Marianne Freiberger </div>
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<p>Asking good questions is an important part of doing maths. But what makes a good question?</p>
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<p>What makes a good maths question? If you are a student facing exams,
you might (understandably) say that good means easy. But if
you're doing maths for fun, or are a professional mathematician, your
answer is going to be different. An easy question is boring, but you
also wouldn't want to gnaw your teeth out at something that is
completely inaccessible. What
mathematicians like most are questions that lead to new insights, to
new ways of looking at things, or pose a completely new type of
problem. Asking "good" questions is an important part of doing
maths.<p><a href="https://plus.maths.org/content/power-good-question" target="_blank">read more</a></p>https://plus.maths.org/content/power-good-question#commentsart gallery problemcalculuscreativityFermat's Last Theoremfour-colour theoremgraph theoryTue, 24 Jun 2014 09:03:15 +0000mf3446114 at https://plus.maths.org/contentThe art gallery problem
https://plus.maths.org/content/art-gallery-problem
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Marianne Freiberger </div>
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<p>Sometimes a piece of maths can be so neat and elegant, it makes you want to shout "eureka!" even if you haven't produced it yourself. One of our favourite examples is the art gallery problem.</p>
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<p>The Guggenheim Museum in Bilbao: hard to supervise. Image: <a href="http://commons.wikimedia.org/wiki/User:MykReeve">MykReeve</a>.</p><p><a href="https://plus.maths.org/content/art-gallery-problem" target="_blank">read more</a></p>https://plus.maths.org/content/art-gallery-problem#commentscolouringcreativitygraph theorypolygonSat, 14 Jun 2014 10:23:39 +0000mf3446075 at https://plus.maths.org/content