creativity
http://plus.maths.org/content/category/tags/creativity
enTrisecting an angle with origami
http://plus.maths.org/content/trisecting-angle-origami
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Rachel Thomas </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/31_oct_2014_-_1120/origami_icon.png?1414754459" /> </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="http://plus.maths.org/content/trisecting-angle-origami" target="_blank">read more</a></p>http://plus.maths.org/content/trisecting-angle-origami#commentsangle trisectioncreativityFP-carouselgeometryorigamiFri, 31 Oct 2014 10:42:11 +0000mf3446228 at http://plus.maths.org/contentTic-tac-toe!
http://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="http://plus.maths.org/content/tic-tac-toe" target="_blank">read more</a></p>http://plus.maths.org/content/tic-tac-toe#commentscreativitygame theorystrategyThu, 02 Oct 2014 09:21:47 +0000mf3446154 at http://plus.maths.org/contentWhy do mathematicians play games?
http://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="http://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="http://plus.maths.org/content/why-do-mathematicians-play-games" target="_blank">read more</a></p>http://plus.maths.org/content/why-do-mathematicians-play-games#commentscreativitygame theoryTue, 23 Sep 2014 11:04:31 +0000mf3446186 at http://plus.maths.org/contentBe creative!
http://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="http://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="http://plus.maths.org/content/be-creative" target="_blank">read more</a></p>http://plus.maths.org/content/be-creative#commentscreativityICM 2014Wed, 20 Aug 2014 04:18:26 +0000mf3446170 at http://plus.maths.org/contentPlay to win with Nim
http://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 gam 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="http://plus.maths.org/content/play-win-nim" target="_blank">read more</a></p>http://plus.maths.org/content/play-win-nim#commentsbinary numbercreativitygame theorynimstrategyMon, 21 Jul 2014 10:18:30 +0000mf3446134 at http://plus.maths.org/contentThe power of good questions
http://plus.maths.org/content/power-good-question
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Marianne Freiberger </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/20_jun_2014_-_1337/icob_questions.jpg?1403267859" /> </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="http://plus.maths.org/content/power-good-question" target="_blank">read more</a></p>http://plus.maths.org/content/power-good-question#commentsart gallery problemcalculuscreativityFermat's Last Theoremfour-colour theoremgraph theoryTue, 24 Jun 2014 09:03:15 +0000mf3446114 at http://plus.maths.org/contentThe art gallery problem
http://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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<div class="rightimage" style="width: 300px;"><img src="http://plus.maths.org/content/sites/plus.maths.org/files/articles/2014/gallery/guggenheim-bilbao-jan05.jpg" alt="Gallery" width="300" height="152" />
<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="http://plus.maths.org/content/art-gallery-problem" target="_blank">read more</a></p>http://plus.maths.org/content/art-gallery-problem#commentscolouringcreativitygraph theorypolygonSat, 14 Jun 2014 10:23:39 +0000mf3446075 at http://plus.maths.org/contentPatterns and structures
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Rachel Thomas </div>
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<p>Patterns and structures lie at the heart of mathematics, some even say they are mathematics. But how do they help us do mathematics?</p>
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"A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." This much quoted line is from British mathematician G. H. Hardy's famous book, <em>A mathematician's apology</em>, written in 1940. And any mathematician, from the ancient Greeks to those working today, would agree.
</p><p><a href="http://plus.maths.org/content/patterns-and-structures" target="_blank">read more</a></p>http://plus.maths.org/content/patterns-and-structures#commentscreativityFibonacciFibonacci numberThu, 29 May 2014 09:00:08 +0000Rachel6091 at http://plus.maths.org/contentWhat is creativity?
http://plus.maths.org/content/what-creativity
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Where were your most creative experiences at school? In art class? In music? English? In your maths lesson? That last one might not be the obvious choice for many of us, unless you were lucky enough to have a really inspiring maths teacher. But that is exactly the type of opportunity we are hoping to create for maths students aged 7-16 as part of the project, <em>Developing Mathematical Creativity</em>, with our sister site, <a href="http://nrich.maths.org">NRICH</a>.
</p><p><a href="http://plus.maths.org/content/what-creativity" target="_blank">read more</a></p>http://plus.maths.org/content/what-creativity#commentscreativityThu, 24 Apr 2014 15:32:10 +0000Rachel6090 at http://plus.maths.org/contentBuilding a bridge to maths
http://plus.maths.org/content/hands-maths-masses
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<p>At last month's Cambridge Science Festival we had great fun trying out a hands-on (or rather feet-on) activity based on one of our favourite puzzles – the bridges of Königsberg. We were really pleased with how it went, so we thought we'd share our game for others to put on at their own science or maths event.</p>
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<p>At last month's <a href="http://mmp.maths.org/news/CSF14maths-people">Cambridge Science Festival</a> we decided to try and bring maths to the masses using one of our favourite puzzles. Our aim was to deliver a hands-on (or rather feet-on) activity that's fun and brings across the
creative aspects of maths, but also links up to cutting edge mathematical research. We were really pleased with how it went, so we thought we'd share our game for others to put on at their own science or maths event.</p><p><a href="http://plus.maths.org/content/hands-maths-masses" target="_blank">read more</a></p>http://plus.maths.org/content/hands-maths-masses#commentscreativityFri, 04 Apr 2014 13:23:37 +0000mf3446077 at http://plus.maths.org/contentFriends and strangers
http://plus.maths.org/content/friends-and-strangers-0
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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.
</p><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#commentscombinatoricscreativitygraph theoryRamsey theoryThu, 27 Mar 2014 15:01:00 +0000Rachel6062 at http://plus.maths.org/contentThe Gömböc: The object that shouldn't exist
http://plus.maths.org/content/gomboc-object-barely-exists
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Marianne Freiberger </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/8_nov_2013_-_1528/icon-3.jpg?1383924513" /> </div>
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<p>A Gömböc is a strange thing. It wriggles and rolls around with an apparent will of its own. Until quite recently, no-one knew whether Gömböcs even existed. Even now, Gábor Domokos, one of their discoverers, reckons that in some sense they barely exists at all.</p>
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<center>What's this? Read on to find out.</center></div><p><a href="http://plus.maths.org/content/gomboc-object-barely-exists" target="_blank">read more</a></p>http://plus.maths.org/content/gomboc-object-barely-exists#commentscreativityWed, 12 Mar 2014 15:26:50 +0000mf3445971 at http://plus.maths.org/contentBridges of Königsberg: The movie
http://plus.maths.org/content/bridges-konigsberg-movie
<p>We've read the book. We've bought the T-shirt. And now, finally, here it is: the movie of one of our favourite maths problems, the bridges of Königsberg. Though admittedly, we made it ourselves. We learnt several interesting lessons in the process. For example that a bin doesn't make a good supporting character and that people who shouldn't be in the frame should get out of it. But other than that, we're well on course for an Oscar this weekend!</p><p><a href="http://plus.maths.org/content/bridges-konigsberg-movie" target="_blank">read more</a></p>http://plus.maths.org/content/bridges-konigsberg-movie#commentsBridges of Konigsbergcreativitygraph theoryThu, 27 Feb 2014 13:00:27 +0000mf3446053 at http://plus.maths.org/contentMaths in a minute: The bridges of Königsberg
http://plus.maths.org/content/maths-minute-bridges-konigsberg
<p>In the eighteenth century the city we now know as Kaliningrad was
called Königsberg and it was part of Prussia. Like many other great
cities Königsberg was divided by a river, called the Pregel. It contained two
islands and there were seven bridges linking the various land masses. A
famous
puzzle at the time was to find a walk through
the city that crossed every bridge exactly once. Many people claimed
they had found such a walk but when asked to reproduce it no one was able to.<p><a href="http://plus.maths.org/content/maths-minute-bridges-konigsberg" target="_blank">read more</a></p>http://plus.maths.org/content/maths-minute-bridges-konigsberg#commentsBridges of Konigsbergcreativitygraph theorytopologyWed, 20 Nov 2013 09:05:11 +0000mf3445969 at http://plus.maths.org/content