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https://plus.maths.org/content
enPlus Advent Calendar Door #15: What is general relativity?
https://plus.maths.org/content/plus-advent-calendar-door-15-what-general-relativity
<div class="field field-name-field-abs-img field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="img-responsive" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/icon_15_0.jpg" width="100" height="100" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>When physicists talk about Einstein's equation they don't
usually mean the famous <em>E=mc<sup>2</sup></em>, but another
formula, which encapsulates the celebrated general theory of
relativity, published in
1915. We asked physicist <a href="http://www.damtp.cam.ac.uk/user/tong/">David Tong</a> of the
University of Cambridge to explain what general relativity is and how
Einstein's equation expresses it. You can watch his explanation in the video
below, or read <a href="/content/what-general-relativity">the accompanying article.</a></p>
<iframe width="560" height="315" src="https://www.youtube.com/embed/0MTnfrCdWqY?rel=0" frameborder="0" allowfullscreen></iframe>
<p><em>Return to the <a href="/content/plus-advent-calendar-2017">Plus Advent Calendar</a></em></p></div></div></div>Fri, 15 Dec 2017 14:23:07 +0000Marianne6963 at https://plus.maths.org/contenthttps://plus.maths.org/content/plus-advent-calendar-door-15-what-general-relativity#commentsPlus Advent Calendar Door #14: Complex numbers — insight
https://plus.maths.org/content/plus-advent-calendar-door-14-complex-numbers-insight
<div class="field field-name-field-abs-img field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="img-responsive" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/icon_14_0.jpg" width="100" height="100" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In pure mathematics complex numbers are a great tool to explore dynamical systems. In this video mathematician Holly Krieger gives an example of a dynamical system and how complex numbers come into the picture.</p>
<p>To find out more about complex numbers and their uses, see <a href="/content/complex-numbers-what-do-they-do">this collection of articles and videos</a>. In particular you might want to read <a href="/content/what-mandelbrot-set"><em>What is the Mandelbrot set?</em></a>.</p>
<iframe width="560" height="315" src="https://www.youtube.com/embed/PgjVJ0XpMW8?rel=0" frameborder="0" allowfullscreen></iframe>
<p>Holly Krieger is a lecturer at the <a href="https://www.dpmms.cam.ac.uk">Department of Pure Mathematics and Mathematical Statistics</a>, University of Cambridge, and Fellow and Director of Studies at <a href="https://www.murrayedwards.cam.ac.uk">Murray Edwards College</a>.</p>
<p><em>Return to the <a href="/content/plus-advent-calendar-2017">Plus Advent Calendar</a></em></p></div></div></div>Thu, 14 Dec 2017 14:20:22 +0000Marianne6962 at https://plus.maths.org/contenthttps://plus.maths.org/content/plus-advent-calendar-door-14-complex-numbers-insight#comments'Closing the gap'
https://plus.maths.org/content/closing-gap
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="leftimage" style="width: 150px; border: 1px;"><img src="/content/sites/plus.maths.org/files/reviews/2017/neale_cover.jpg" alt="cover" width="150" height="227" /></div><h2>Closing the gap: The quest to understand prime numbers</h2>
<h3>by Vicky Neale</h3>
<p><em>Closing the gap</em> is among
the clearest popular accounts of maths I've read in
a while. It's about prime numbers, as the title suggests, but it's also a
master piece in the art of weaving. Apart from exploring the mathematics, the book
gives an intimate description of the process of doing maths as
experienced by those who do it every day, and an account of a particularly exciting, and recent, period when prime number theory made some great leaps forward. And it's a look at a completely
new way of doing mathematics: in large online collaborations that
anyone can join. </p>
<p>So many strands are a recipe for a tangled mess (that's personal experience speaking) but Neale has turned the multi-layered nature of
her story into a strong point of the book. Some of
this is anchored in its structure. Chapters alternatingly
look at the actual maths, with no interference from the real world, and at the very real events that unfolded between April 2013 and April 2014, during which some major advances were made. This way of structuring the book isn't a gimmick, as I feared at
first, but probably the best way of getting both parts of the story
across. Adding to the clarity in structure is Neale's calm, unhurried,
and very personal voice, which holds your hand throughout.</p>
<p>Mathematically the book focusses in the famous <em>twin prime
conjecture</em> which asserts that there are infinitely many pairs of primes
whose difference is 2 (you can read more about this conjecture on
<em><a href="/content/tags/twin-prime-conjecture">Plus</a></em>). The fact that the conjecture can be stated in a
sentence illustrates one of the advantages of number theory when it
comes to popular mathematics. Many of its central problems can be easily
explained even to a maths phobe, and pretty much anyone can start playing
with numbers to see how far they get. On some questions, you can get
satisfyingly far with a relatively small mathematical tool kit. But on
others, including the twin prime conjecture, you soon hit a brick
wall. </p>
<p>The tricky nature of prime numbers, which form the building blocks
of number theory, is explored in the chapters that focus on the maths
alone. Neale introduces the subject from scratch and invites the
reader to play. If you like puzzling over maths problems, or feel you
need a break from the author's guiding hand, you can go away and
scribble for a while, until you're ready to get back to the book. The
problems and results are carefully chosen to illustrate the treacherous nature of the
subject, and also to provide some surprisingly deep insights into the
maths used by those at the cutting edge of the field.</p>
<p>If you'd rather give the puzzling a miss, then you can let yourself
be guided through the maths and focus on those chapters that
describe how recent advances on the twin prime conjecture came
about (some of the harder maths can safely be skipped). As hard mathematical problems go, the twin
prime conjecture is unusual in many ways, but in the context of the
book it serves as a great example of how progress in pure maths comes
about: not only through great theoretical leaps, but also through incremental
improvements, the testing of boundaries, blind alleys and
experimentation. Imagination, intuition, the ability to ask good questions and
spot pervasive patterns, and the
courage to get stuck are essential in this.</p>
<p><em>Closing the gap</em> is firmly aimed at a general
audience. A desire to share with non-mathematicians the
pleasure, frustrations and excitement of doing maths, to shed some light on this all
too secretive
process, seems to have been one of Neale's
main motivations for writing the book. She is unapologetic about the maths, so be prepared to think, and think hard in places. If you are already well-versed
in mathematics, the book also has something to offer. It gives some insight
into what's happened in number theory in recent years, at least as far as the
twin prime conjecture is concerned. Above all, it will give you an
interesting insight into the <em>Polymath project</em>, which has seen
mathematicians bare all in public (metaphorically) to see if large
and fast online interaction can bring the subject forward — with very interesting results.</p>
<p>I won't give too much away by saying that the gap between primes
hasn't been closed sufficiently to prove the twin prime conjecture —
not yet. For Neale this
means that writing the book has been a bit of a gamble. Had the conjecture
been proved just as she put the finishing touches to her manuscript,
she would have had a whole lot of rewriting to do. As it stands,
she has left us dangling from a cliff. As progress in mathematics goes, we may stay dangling there for a few decades. But if we're lucky, perhaps by next Christmas Neale will be able to provide us with a concluding sequel.</p>
<dl> <dt><strong>Book details:</strong></dt>
<dd><em>Closing the gap: The quest to understand prime numbers</em></dd> <dd> Vicky Neale</dd> <dd>hardback — 176 pages</dd>
<dd> Oxford University Press (2017)</dd>
<dd> ISBN 9780198788287</dd>
</dl>
</div></div></div><div class="field field-name-field-author field-type-text field-label-inlinec clearfix field-label-inline"><div class="field-label">Review by </div><div class="field-items"><div class="field-item even">Marianne Freiberger</div></div></div>Tue, 12 Dec 2017 19:21:40 +0000Marianne6965 at https://plus.maths.org/contenthttps://plus.maths.org/content/closing-gap#commentsPlus Advent Calendar Door #12: Fighting future pandemics
https://plus.maths.org/content/plus-advent-calendar-door-12-fighting-future-pandemics
<div class="field field-name-field-abs-img field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="img-responsive" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/icon_12_0.jpg" width="100" height="100" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>An influenza pandemic is still one of the greatest threats to humanity. During the pandemic in 2009 over 60 million people caught the H1N1 influenza virus in the United States: over 274,000 of these required hospital and, sadly, over 12,000 people died. Now a groundbreaking project is allowing every person in the UK to contribute to research to combat future pandemics.</p>
<p><a href="http://www.damtp.cam.ac.uk/people/j.r.gog/">Julia Gog</a>, Professor of Mathematical Biology at the University of Cambridge, and her team are working with the BBC on an innovative project, <a href="http://www.bbc.co.uk/programmes/p059y0p1">BBC Pandemic</a>, combining outreach, citizen science and new mathematical research. Find out more in this video.</p>
<iframe width="560" height="315" src="https://www.youtube.com/embed/Cn_ToPamEmA?rel=0" frameborder="0" gesture="media" allow="encrypted-media" allowfullscreen></iframe
<p><em>Return to the <a href="/content/plus-advent-calendar-2017">Plus Advent Calendar</a></em></p></div></div></div>Tue, 12 Dec 2017 14:15:43 +0000Marianne6960 at https://plus.maths.org/contenthttps://plus.maths.org/content/plus-advent-calendar-door-12-fighting-future-pandemics#commentsGraphs and networks
https://plus.maths.org/content/graphs-and-networks
<div class="field field-name-field-abs-img field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="img-responsive" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/network_icon.jpg" width="100" height="100" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>This package brings together all <i>Plus</i> content on graph and network theory. Graphs and networks turn up in many real-life problems, from neuroscience to telecommunications. To start off, you might like to read our brief overview article</p>
<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/5/20_mar_2014_-_0954/icon.png" alt="" width="100" height="100" /></div>
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<p><a href="/content/bridges-networks-0">From bridges to networks</a> — How a cute 18th century puzzle laid the foundations for one of the most modern areas of maths: network theory. This article is also available as a <a href="/content/sites/plus.maths.org/files/posters/bridgeskonigsberg-plus-2014.pdf">poster</a> which you can download and out on your wall.</p>
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<p>We have divided all our other articles into three categories:</p>
<ul>
<li><a href="/content/graphs-and-networks#depth">Graphs and networks in-depth</a>: These articles (and video) give a detailed account of questions relating to graphs and networks and their applications in science, life and other areas of maths.</li>
<li><a href="/content/graphs-and-networks#social">Social networks</a>: Because everyone loves social networks — real and virtual —we have made a special category for them and the mathematical problems connected to them.</li>
<li><a href="/content/graphs-and-networks#news">Network news</a>: This is a collection of news stories relating to networks and graphs and the role they play in the real world.</li>
</ul>
<p>Our sister site <a href="http://nrich.maths.org">NRICH</a> has a beautiful collection of <a href="https://nrich.maths.org/11822">resources</a> designed to give a gentle introduction to the world of graph theory and networks. You don't need any prior knowledge, so jump in, have a play, and see what you can discover!
</p>
<a name="depth"></a>
<h3>Graphs and networks in-depth</h3>
<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/kelly_icon.png" alt="" width="100" height="100" /></div>
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<p><a href="/content/mathematical-moments-frank-kelly">Mathematical moments: Frank Kelly</a> — In this video we talk to the mathematician <a href="http://www.statslab.cam.ac.uk/~frank/">Frank Kelly</a> about his work developing mathematical models to understand large-scale networks.</p>
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<div class="leftimage" style="width: 100px;"><img src="/issue52/package/icon_friends.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/issue16/features/ramsey/index.html">Friends and strangers</a> — This article uses graph colourings to find order in chaos.</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/5/8_nov_2013_-_1206/icon-8.jpg?1383912403" alt="" width="100" height="100" /></div>
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<p><a href="/content/maths-minute-bridges-konigsberg">Maths in a minute: The bridges of Königsberg</a> — This article looks at an problem with an ingenious solution that started off network theory. You can also watch <a href="/content/bridges-konigsberg-movie">Bridges of Königsberg: The movie</a>.</p>
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<div class="leftimage" style="width: 100px;"><img src="/issue52/package/icon_maze.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/issue14/features/budd/index.html">Maths aMazes</a> — Finding your way out of mazes using graphs.</p>
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<div class="leftimage" style="width: 100px;"><img src="/$../../issue37/features/budd/icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/issue37/features/budd/index.html">Crime fighting maths</a> — Using network theory to find out who contaminated the river.</p>
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<div class="leftimage" style="width: 100px;"><img src="/$../../issue43/features/kirk/icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/issue43/features/kirk/index.html">Euler's polyhedron formula</a> — How networks help to pin down polyhedra.</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/5/20_jun_2014_-_1209/icon.jpg?1403262582" alt="" width="100" height="100" /></div>
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<p><a href="/content/art-gallery-problem">The art gallery problem</a> — How would you place guards in an art gallery to make sure nothing gets stolen? The answer comes from graph colouring.</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/map-icon.png" alt="" width="100" height="100" /></div>
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<p><a href="/content/maths-minute-graph-isomorphism-problem">The graph isomorphism problem</a> — How fast can you tell whether two networks are the same?</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/5/4_jan_2013_-_1532/hanoi_icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/content/tower-hanoi-where-maths-meets-psychology">The Tower of Hanoi: Where maths meets psychology</a> — Mathematicians and psychologists don't cross paths that often and when they do you wouldn't expect it to involve an (apparently) unassuming puzzle like the Tower of Hanoi. Yet, the puzzle holds fascination in both fields. </p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/1/1%20Nov%202010%20-%2022%3A00/icon_9e73c839554061411da6c6faa9392b0b.jpeg?1288648830" alt="" width="100" height="100" /></div>
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<p><a href="/content/brain">Wiring up brains</a> — The human brain faces a
difficult trade-off. On the one hand it needs to be complex to ensure high performance, and on the other it needs to minimise "wiring cost". It's a problem well-known to computer scientists. And it seems that market driven human invention and natural selection have come up with similar solutions.</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/tree_icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/content/maths-five-minutes-counting-trees-life">Counting the trees of life</a> — How many possible genetic relationships are there between a collection of different species? The answer is mind-bogglingly large.</p>
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<div class="leftimage" style="width: 100px;"><img src="/$../../issue46/features/phylogenetics/icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/issue46/features/phylogenetics/index.html">Reconstructing the tree of life</a> — Darwin's famous tree of life is of course a mathematical graph. This article looks at some of the mathematical problems facing phylogeneticists.</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/5/3_sep_2014_-_1711/graham_icon.png?1409760685" alt="" width="100" height="100" /></div>
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<p><a href="/content/too-big-write-not-too-big-graham">Too big to write, but not too big for Graham</a> — How a question about the complexity of networks gave rise to a number that's bigger than the observable Universe.</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/4/12_jun_2013_-_0946/icon.jpg?1371026788" alt="" width="100" height="100" /></div>
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<p><a href="/content/exploring-financial-ecosystem">Exploring the financial ecosystem</a> — How models borrowed from biology, and a little network theory, are helping us to manage risk in financial markets .</p>
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<div class="leftimage" style="width: 101px;"><img src="/issue52/package/icon_call.jpg" alt="" width="101" height="101" /></div>
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<p><a href="/issue2/dar/index.html">Call routing in telephone networks</a> — Finding optimal paths through a busy network.</p>
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<div class="leftimage" style="width: 100px;"><img src="/issue52/package/icon_radio.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/issue8/features/phones/index.html">Radio controlled?</a> — This article shows how the mathematics of colouring graphs can help avoid interference on your mobile phone.</p>
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<a name="social"></a>
<h3>Social networks</h3>
<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/5/23_sep_2015_-_1014/internet_icon.png?1442999680" alt="" width="100" height="100" /></div>
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<p><a href="/content/maths-minute-power-networks">Power networks</a> — Why do so many networks exhibit a similar kind of structure? It's because the rich tend to get richer!</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/gossip_fronticon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/content/have-you-heard-maths-rumour-spreading">Have you heard: The maths of rumour spreading</a> — Mathematical models predict how fast a rumour will spread through a social network and how many people it's likely to reach.</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/1/1%20Nov%202010%20-%2022%3A00/icon_9e73c839554061411da6c6faa9392b0b.jpeg?1288648830" alt="" width="100" height="100" /></div>
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<p><a href="/content/big-data">Big data</a> — Everybody's talking about Big Data. But what exactly do they mean and what does it have to do with networks?</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/5/27_may_2016_-_1212/twitter_icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/content/climbing-twitter-ladder">Climbing the Twitter ladder</a> — How popular and successful are you? Not as much as your friends is the sad answer, at least as far as Twitter is concerned. </p>
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<div class="leftimage" style="width: 100px;"><img src="/$../../latestnews/sep-dec05/rappers/icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/latestnews/sep-dec05/rappers/index.html">Rap: rivalry and chivalry</a> — The small world network of rap.</p>
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<div class="leftimage" style="width: 100px;"><img src="/$../../latestnews/may-aug05/networks/icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/latestnews/may-aug05/networks/index.html">Networks: nasty and nice</a> — How to disrupt scale free terrorist networks.</p>
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<p><a href="/latestnews/sep-dec08/complexity/index.html">Catching terrorists with maths</a> — This article contains a section on the small world network formed by the neurons in the brain.</p>
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<a name="news"></a>
<h3>Network news</h3>
<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/4/17_feb_2013_-_2327/icon.jpg?1361143641" alt="" width="100" height="100" /></div>
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<p><a href="/content/disease-moves-ripples-pond">Disease moves like ripples on a pond</a> — Epidemiologists use complex models to predict the spread of diseases. But is there a way to hide all this complexity and draw a simpler picture of how diseases spread, even in today's complex world?</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/5/13%20Jul%202010%20-%2014%3A39/icon.jpg?1279028365" alt="" width="100" height="100" /></div>
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<p><a href="/content/os/latestnews/may-aug10/football/index">Mathematicians rival octopus in World Cup final prediction</a> — A mathematical analysis of team tactics predicted a Spanish win in the last FIFA World Cup final and also shed some light on why England were trashed by Germany.</p>
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<div class="leftimage" style="width: 100px;"><img src="/content/sites/plus.maths.org/files/abstractpics/5/9_jan_2013_-_1356/icon-1.jpg?1357739789" alt="" width="100" height="100" /></div>
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<p><a href="/content/happy-birthday-london-underground">Happy birthday, London Underground!</a> — The famous London tube map is a so-called <em>topological map</em>. It illustrates an important idea in network theory: that two networks can be the same even though they look very different.</p>
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<div class="leftimage" style="width: 100px;"><img src="/$../../latestnews/jan-apr08/road/icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/latestnews/jan-apr08/road/index.html">Country road, take me home</a> — This article looks at the famous <i>road colouring problem</i>.</p>
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<p><a href="/latestnews/may-aug07/sudoku/index.html">Solving sudokus</a> — Using graph colouring to solve sudokus.</p>
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<div class="leftimage" style="width: 100px;"><img src="/$../../latestnews/may-aug07/rubik/icon.jpg" alt="" width="100" height="100" /></div>
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<p><a href="/latestnews/may-aug07/rubik/index.html">Rubik success in twenty-six steps</a> — Using graph theory and group theory to show that you can solve a Rubik's cube in twenty-six moves — theoretically at least.</p>
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<p><a href="/latestnews/jan-apr06/ktn/index.html">Helping business make a crust</a> — Wireless security comes down to graph colourings.</p>
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<p><a href="/content/middle-class-problems">Middle class problems</a> — How quickly can you tell whether two apparently different networks are actually the same? It's a famous question in computer science and it appears to have come closer to an answer.</p>
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<p><a href="/content/neuro-tweets-hashtagging-brain">Neuro-tweets: #hashtagging the brain</a> — As the article above reports, our brain has quite a lot in common with worm brains and information processing systems. But how does it compare to online social networks? </p>
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<p><a href="/issue26/news/programs/index.html">Open wide</a> — Why open-source software is better than its closed counterpart, explained using networks.</p>
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<p><a href="/latestnews/may-aug05/adios/index.html">Machine prose</a> — A sophisticated analysis of the language network teaches machines to talk.</p>
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<p>Don't forget that our sister site <a href="http://nrich.maths.org">NRICH</a> has a beautiful collection of <a href="https://nrich.maths.org/11822">resources</a> designed to give a gentle introduction to the world of graph theory and networks. You don't need any prior knowledge, so jump in, have a play, and see what you can discover!
</p></div></div></div>Tue, 12 Dec 2017 11:58:22 +0000Marianne6967 at https://plus.maths.org/contenthttps://plus.maths.org/content/graphs-and-networks#commentsMathematician advises the Home Office
https://plus.maths.org/content/mathematician-advises-home-office
<div class="field field-name-field-abs-img field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="img-responsive" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/johnaston_icon.jpg" width="100" height="100" alt="" /></div></div></div><div class="field field-name-field-author field-type-text field-label-inlinec clearfix field-label-inline"><div class="field-label">By </div><div class="field-items"><div class="field-item even">Marianne Freiberger</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><a href="http://www.statslab.cam.ac.uk/Dept/People/aston.html">John Aston</a>, Professor of Statistics at the University of Cambridge, has been appointed as the Home Office's new Chief Scientific Adviser.</h2>
<div class="rightimage" style="max-width: 320px;"><img src="/content/sites/plus.maths.org/files/news/2017/aston/Marsham_Street.jpg" alt="Home Office" width="320" height="218" /><p>The Home Office building in London. Image: <a href="https://commons.wikimedia.org/wiki/File:Marsham_Street.jpg">Steve Cadman</a>, <a href="https://creativecommons.org/licenses/by-sa/2.0/deed.en">CC BY-SA 2.0</a>.</div>
<p>"I am honoured and privileged to be joining the Home Office as its Chief Scientific Adviser," Aston said. "I'm looking forward to working with the scientific community to understand the issues facing the Department over the coming years and identify how science, engineering and analysis can help to overcome those challenges."</p>
<p>Aston's role at the Home Office will be to ensure that decisions are informed by scientific evidence wherever possible, and to help ministers and officials assess the quality of evidence and the uncertainties involved. As Chief Scientific Adviser he will offer advice directly to those ministers and officials and work together with the Chief Scientific Advisers' network to advise on issues that cut across government. </p>
<p>Perhaps surprisingly, the Home Office routinely faces challenges that call for scientific analysis involving all parts of the scientific spectrum. An example is the all-pervasive threat of terrorism. Counter terrorism initiatives rely on science and technology, for example to improve aviation security and to safeguard public places. Mathematical techniques are needed to understand the structure of terrorist networks and how to best disable them. Understanding how people become radicalised requires the social sciences and psychology. And since it's impossible to study large samples of terrorists in detail, statistical methods are again needed to quantify the uncertainties involved. (See <a href="/content/search/node/terrorism">here</a> to find out how maths is used in the fight against terrorism.)</p>
<div class="leftimage" style="max-width: 274px;"><img src="/content/sites/plus.maths.org/files/news/2017/aston/johnaston-2.jpg" alt="John Aston" width="274" height="288" /><p>John Aston</div>
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<p>The job of science advisers is to make sure all scientific information is available to ministers (though in the past such advice has not always been welcomed: recall the <a href="http://news.bbc.co.uk/1/hi/8334774.stm"> controversy</a> surrounding Chief Drug Advisor David Nutt's 2009 criticism of the government's stance on cannabis). But in the short time Aston has been in his new post his experience has been positive and he is looking forward to contributing an expert view point. As he <a href="http://data.parliament.uk/writtenevidence/committeeevidence.svc/evidencedocument/science-and-technology-committee/government-office-for-science-annual-report-and-work-of-the-chief-scientific-adviser-network/oral/71596.html" target="_blank">told the Science and Technology Committee in October</a>, "I have certainly found it easy, both with Ministers and with senior officials, to have proactive conversations about what kind of evidence gaps they feel there are and where science can contribute to those evidence gaps."</p>
<p>Aston is well-qualified to deal with statistical and mathematical challenges thrown up by real-world problems.
As well as fulfilling his professorial role at the Statistical Laboratory in Cambridge, he has been a trustee of the <a href="https://www.turing.ac.uk/" target="_blank">Alan Turing Institute</a>, the UK's national centre for data science research and sits on the management board of the <a href="https://www.ccimi.maths.cam.ac.uk/" target="_blank">Cantab Capital Institute for the Mathematics of Information</a> (CCIMI). Both organisation use mathematical and statistical techniques to turn the mass of data that arises in the modern world to our advantage. Their work impinges on areas as diverse as the biomedical sciences, finance, the internet, software and hardware development and security, and the economy. (To find out more about the CCIMI read <a href="/content/uncovering-mathematics-information"><em>Uncovering the mathematics of information</em></a>.)</p>
<p>The remit of the Home Office covers a wide range of social issues and Aston's notes that it's important to take the broadest possible view of what science involves. "People naturally think of science as being physics, chemistry and maths," he told the Committee. "I do not take that view. I think that science spans the entire remit, and I want to be able to be involved in everything, including the arts, humanities and social science implications, which are just as important if not more important than some other things in the Home Office. I want to be involved in the whole spectrum of things."</p>
</div></div></div>Tue, 12 Dec 2017 10:23:37 +0000Marianne6966 at https://plus.maths.org/contenthttps://plus.maths.org/content/mathematician-advises-home-office#commentsPlus Advent Calendar Door #11: Sexual statistics
https://plus.maths.org/content/plus-advent-calendar-door-11-sexual-statistics
<div class="field field-name-field-abs-img field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="img-responsive" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/icon_11_0.jpg" width="100" height="100" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Straight men have had twice as many sexual partners, on average, as straight women. Sounds plausible, seeing that men supposedly think about sex every seven seconds. Except that it's mathematically impossible. To find out more about this and other stories about stats and sex, watch this video featuring <a href="http://www.statslab.cam.ac.uk/Dept/People/Spiegelhalter/davids.html">David Spiegelhalter</a>, Winton
Professor for the Public Understanding of Risk at the University of
Cambridge. (You can also read the <a href="/content/sexual-statistics">accompanying article</a>.)</p>
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<p><em>Return to the <a href="/content/plus-advent-calendar-2017">Plus Advent Calendar</a></em></p></div></div></div>Mon, 11 Dec 2017 14:11:37 +0000Marianne6959 at https://plus.maths.org/contenthttps://plus.maths.org/content/plus-advent-calendar-door-11-sexual-statistics#commentsPlus Advent Calendar Door #10: What is a block universe?
https://plus.maths.org/content/plus-advent-calendar-door-10-what-block-universe
<div class="field field-name-field-abs-img field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="img-responsive" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/icon_10_0.jpg" width="100" height="100" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Could it be that the present, future and past all exist at the same time? According to Einstein's theory of relativity they might well do. In this video Marina Cortês, cosmologist from the Royal Observatory, Edinburgh, explains the concept of a <em>block universe</em>, the arguments for and against this theory, and alternative explanations of the world.</p>
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<p>
You can also watch this interview as a series of shorter clips:
<ul>
<li><a href="https://www.youtube.com/watch?v=d17U0Bgj0lk">What is a block universe?</a></li>
<li><a href="https://www.youtube.com/watch?v=ZdP61lBp46Q">Why do physicists say time is symmetric?</a></li>
<li><a href="https://www.youtube.com/watch?v=cHQ9gmoRtd0">Why do we feel time moves forward in a block universe?</a></li>
<li><a href="https://www.youtube.com/watch?v=eKd_M_aUWIo">How unlikely was the big bang?</a></li>
<li><a href="https://www.youtube.com/watch?v=fM4XqElxT6k"> Why don't you agree with the block universe?</a></li>
<li><a href="https://www.youtube.com/watch?v=9L4I1ldPqbo"> What are the alternatives to the block universe?</a></li>
</ul>
</p>
<p> You can read more in our package of articles <a href="https://plus.maths.org/content/stuff-happens-block-time"><em>Stuff Happens: Time in a Block Universe</em></a>.</p>
<p><em>Return to the <a href="/content/plus-advent-calendar-2017">Plus Advent Calendar</a></em></p></div></div></div>Sun, 10 Dec 2017 14:05:24 +0000Marianne6958 at https://plus.maths.org/contenthttps://plus.maths.org/content/plus-advent-calendar-door-10-what-block-universe#commentsOn the tiles
https://plus.maths.org/content/title-4
<div class="field field-name-field-abs-img field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="img-responsive" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/becky_icon.jpg" width="100" height="100" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Our colleague Becky Warren, who runs the <a href="https://maths.org/roadshow">Hands On Maths Roadshow</a>, has been distracting us with the wonderful puzzles she has been making, both virtually for the <a href="http://mmp.maths.org">Millennium Mathematics Project</a> and also as beautiful hand-made versions to play with in real life.</p>
<p>Here's one example that is particularly satisfying to try for yourself. Start with a dodecagon (you can see how to construct one <a href="https://wild.maths.org/dodecagon-dissection">here</a>, or just print out your own version from <a href="/content/sites/plus.maths.org/files/blog/122017/dodecagon%20dissection.pdf">this PDF</a>) — can you work out the area of this shape? </p>
<p>This might not seem obvious, but there is a clever way of working it out if you first cut the dodecagon up into triangles. The triangles can also be rearranged to form three squares, which quickly lead you to discover the answer, providing a visual proof for a mathematical questions. This kind of problem, where you can rearrange pieces of a puzzle in two ways, is one of Becky's favourite type of puzzles.</p>
<div class="centreimage"><img src="/content/sites/plus.maths.org/files/news/2017/Becky/dodecadon.jpg" alt="Dodecahedron" width="500" height="485" /><p style="max-width: 500px;"></p></div>
<p>Another favourite puzzle of ours involves tiling the plane with pentagons. Impossible you say? You're right, you can't tile the plane with regular pentagons, as we've seen <a href="/content/trouble-five">here</a>. But in 1918 mathematicians discovered that you can tile your bathroom floor with certain irregular pentagons whose sides aren't all the same length. People have been hunting for all the different types of pentagons that can do this, and just <a href="/content/five-fits">two years ago mathematicians discovered the first new tile</a> in 30 years.</p>
<p>New mathematical discoveries like this often inspire Becky, and investigating these
tilings with pentagons led her to a new favourite tiling called the <a href="https://nrich.maths.org/1844">Bow Tie</a>, which you can <a href="https://nrich.maths.org/1844">play with</a> on our sister site NRICH or <a href="https://nrich.maths.org/content/03/07/six5/tile_print.gif">make yourself out of paper</a>. You can arrange the Bow Tie tiles in lots of ways, some have symmetry, some have none, some have different shaped holes, and some neatly fit together to give you a novel tiling idea for your bathroom floor.</p>
<div class="rightimage" style="max-width: 400px;"><img src="/content/sites/plus.maths.org/files/news/2017/Becky/bowtie.jpg" alt="Bowtie tiling" width="400" height="235" /><p> A bow tie tiling.</p></div>
<p>"To construct a puzzle I start with a mathematical idea," says Becky. "At the moment I'm focussed on tessellations. The recent news about pentagons led me to find this particular pentagon — the Bow Tie. It's [one of the ones already known to tile the plane] but I thought it was a particularly interesting one."</p>
<p>There's another recent discovery that has caught Becky's interest. Last year there were breakthroughs in <em>monohedral disc tilings</em>: circles that are cut into equally shaped pieces. "Most people think of it as cutting up a pizza so that all the pieces are the same, but you can also do it with different shapes," says Becky. Again, these tiles can be arranged in many different ways, which led Becky to create some really beautiful sets of tiles you can play with in real life.</p>
<p>
"That's the idea — taking some nice bit of maths, perhaps something that has come up recently, and seeing if you can turn it into a puzzle."</p>
<p>So if you would like some ideas for Christmas gifts you can make yourself, why not check out some of these activities on our sister site NRICH:</p>
<ul><li><a href="https://nrich.maths.org/7026">L-triominoes</a></li>
<li>
<a href=" https://nrich.maths.org/141">Four triangles puzzle</a></li>
<li><a href="https://nrich.maths.org/5945">Putting two and two together</a></li>
<li><a href="https://nrich.maths.org/5944">Repeating patterns</a></li>
<li><a href="https://nrich.maths.org/1052">Making rectangles, making squares</a></li>
<li><a href="https://nrich.maths.org/5908">Equal equilateral triangles.</a></li></ul>
<p>
But if you'd like someone else to do the hard work for you, you can always visit Becky's <a href="https://www.etsy.com/uk/shop/LinesCurvesSpirals">Etsy shop</a>.</p>
<div class="centreimage"><img src="/content/sites/plus.maths.org/files/news/2017/Becky/Becky.jpg" alt="Dodecahedron" width="350" height="287" /><p style="max-width: 500px;">One of Becky's wooden puzzles. The tiles can be arranged in many different ways. You can see (and buy) more <a href="https://www.etsy.com/uk/shop/LinesCurvesSpirals">here</a>.</div>
</div></div></div>Fri, 08 Dec 2017 11:49:44 +0000Marianne6957 at https://plus.maths.org/contenthttps://plus.maths.org/content/title-4#commentsPlus Advent Calendar Door #5: The catenary goes to Wembley with Paul Shephard
https://plus.maths.org/content/plus-advent-calendar-door-5-catenary-goes-wembley-paul-shephard
<div class="field field-name-field-abs-img field-type-image field-label-hidden"><div class="field-items"><div class="field-item even"><img class="img-responsive" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/%5Buid%5D/%5Bsite-date%5D/icon_5_0.jpg" width="100" height="100" alt="" /></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>The most striking feature of Wembley Stadium is the is 133 metre tall steel arch that sits above the north stand. And it's not just any arch — it's an inverted catenary. <a href="http://www.bath.ac.uk/ace/people/shepher">Paul Shepherd</a>, engineer and builder of sports stadiums, explains what makes the catenary so special and why it, as well as eggs, are so important in architecture.</p>
<iframe width="560" height="315" src="https://www.youtube.com/embed/wa1ERcG8WDA" frameborder="0" allowfullscreen></iframe>
<p>You can find out more about the catenary in <a href="/content/matjhs-minute-catenary">this short article</a>. To find out more about Paul Shepherd's work building football stadiums listen to <a href="/content/podcast-5-december-2007-stadium-maths">this podcast</a>.</p>
<p><em>Return to the <a href="/content/plus-advent-calendar-2017">Plus Advent Calendar</a></em></p></div></div></div>Tue, 05 Dec 2017 17:42:04 +0000Rachel6950 at https://plus.maths.org/contenthttps://plus.maths.org/content/plus-advent-calendar-door-5-catenary-goes-wembley-paul-shephard#comments