topology
https://plus.maths.org/content/taxonomy/term/613
en

Introducing the Klein bottle
https://plus.maths.org/content/introducingkleinbottle
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Marianne Freiberger </div>
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<img class="imagefield imagefieldfield_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/5_jan_2015__1744/kleinbottle_icon.jpg?1420479898" /> </div>
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<p>A Klein bottle can't hold any liquid because it doesn't have an inside. How do you construct this strange thing and why would you want to?</p>
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<p>If you like a drink, then a Klein bottle is <em>not</em> a recommended receptacle. It may look vaguely like a bottle, but it doesn't enclose any volume, which means that it can't actually hold any liquid. Whatever you pour "in" will just come back out again.</p><p><a href="https://plus.maths.org/content/introducingkleinbottle" target="_blank">read more</a></p>
https://plus.maths.org/content/introducingkleinbottle#comments
klein bottle
mobius strip
orient ability
surface
topology
Tue, 06 Jan 2015 10:37:52 +0000
mf344
6292 at https://plus.maths.org/content

John Milnor: A conversation with a mathematical legend
https://plus.maths.org/content/mathematicallegendourinterviewjohnmilnor
<div class="rightimage" style="width: 250px;"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/news/2011/abel/milnor.jpg" alt="" width="250" height="264" /><p>John Milnor</p><p><a href='http://plus.maths.org/content/sites/plus.maths.org/files/podcast/milnor_edit.mp3'>Listen to our conversation with John Milnor</a></p><p><a href="https://plus.maths.org/content/mathematicallegendourinterviewjohnmilnor" target="_blank">read more</a></p>
https://plus.maths.org/content/mathematicallegendourinterviewjohnmilnor#comments
dynamical system
ICM 2014
topology
Mon, 18 Aug 2014 04:25:24 +0000
mf344
6167 at https://plus.maths.org/content

Maryam Mirzakhani: counting curves
https://plus.maths.org/content/mm
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<p>Maryam Mirzakhani is being honoured for her "rare combination of superb technical ability, bold ambition, farreaching vision, and deep curiosity".</p>
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<p><em> Maryam Mirzakhani has been awarded the <a href="http://www.mathunion.org/general/prizes/fields/details/">Fields Medal</a>, the most prestigious prize in maths, at this year's <a href="http://www.icm2014.org">International Congress of Mathematicians</a> in Seoul.</em></p>
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<img src="https://plus.maths.org/content/sites/plus.maths.org/files/news/2014/Seoul/f1.jpg" width="300" height="331" alt="MM"/>
<p></p><p><a href="https://plus.maths.org/content/mm" target="_blank">read more</a></p>
https://plus.maths.org/content/mm#comments
fields medal
Fields Medal 2014
geometry
ICM 2014
topology
Wed, 13 Aug 2014 00:24:46 +0000
mf344
6156 at https://plus.maths.org/content

Playing billiards on doughnuts
https://plus.maths.org/content/billiardsdonuts
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Marianne Freiberger </div>
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<p>The paths of billiard balls on a table can be long and complicated. To understand them mathematicians use a beautiful trick, turning tables into surfaces.</p>
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<p><em>Thanks to <a href="http://www.maths.bris.ac.uk/~maxcu/">Corinna Ulcigrai</a> of the University of Bristol for her help with this article.</em></p><p><a href="https://plus.maths.org/content/billiardsdonuts" target="_blank">read more</a></p>
https://plus.maths.org/content/billiardsdonuts#comments
BMC2014
chaos
dynamical system
geodesic
topology
torus
Tue, 27 May 2014 09:40:45 +0000
mf344
6083 at https://plus.maths.org/content

Maths in a minute: The bridges of Königsberg
https://plus.maths.org/content/mathsminutebridgeskonigsberg
<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="https://plus.maths.org/content/mathsminutebridgeskonigsberg" target="_blank">read more</a></p>
https://plus.maths.org/content/mathsminutebridgeskonigsberg#comments
Bridges of Konigsberg
creativity
graph theory
topology
Wed, 20 Nov 2013 09:05:11 +0000
mf344
5969 at https://plus.maths.org/content

Happy birthday, London Underground!
https://plus.maths.org/content/happybirthdaylondonunderground
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<p>The London Underground turns 150 today! It's probably the most famous rail network in the world and much of that fame is due to the iconic London Underground map. But what makes this map so special?</p>
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<div class="rightimage"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/news/2012/rubber/tube.jpg" width="300" height="199" alt="Tube map"/><p style="width:300px;"> Part of the London Underground map. See the full map <a href="http://www.tfl.gov.uk/assets/downloads/standardtubemap.pdf">here</a>.</p><p><a href="https://plus.maths.org/content/happybirthdaylondonunderground" target="_blank">read more</a></p>
https://plus.maths.org/content/happybirthdaylondonunderground#comments
Bridges of Konigsberg
graph theory
topology
Wed, 09 Jan 2013 13:55:38 +0000
mf344
5853 at https://plus.maths.org/content

The shape of things to come
https://plus.maths.org/content/shapethingscome
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The Plus Team </div>
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Progress in pure mathematics has its own tempo. Major questions may remain open for decades, even centuries, and once an answer has been found, it can take a collaborative effort of many mathematicians in the field to check
that it is correct. The <em>New Contexts for Stable Homotopy Theory</em> programme, held at the Institute in 2002, is a prime example of how its research programmes can benefit researchers and its lead to landmark results. </div>
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<p><em>This article is part of a <a href="https://plus.maths.org/content/isaacnewtoninstitute">series</a> celebrating the 20th birthday of the <a href="http://www.newton.ac.uk/">Isaac Newton Institute</a> in Cambridge. The Institute is a place where leading mathematicians from around the world can come together for weeks or months at a time to indulge in what they like doing best: thinking about maths and exchanging ideas without the distractions and duties that come with their normal working lives.<p><a href="https://plus.maths.org/content/shapethingscome" target="_blank">read more</a></p>
https://plus.maths.org/content/shapethingscome#comments
homotopy
Newton Institute
topology
Thu, 19 Jul 2012 08:20:32 +0000
mf344
5439 at https://plus.maths.org/content

Rubber data
https://plus.maths.org/content/rubberdata
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Data, data, data — 21st century life provides tons of it. It's paradise for researchers, or at least it would be if we knew how to make sense of it all. This year's AAAS annual meeting in Vancouver
devoted plenty of time to the question of how to understand large amounts of data. And there's one method we
particularly liked. It's based on the kind of idea that gave us the London tube map. </div>
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<p>Data, data, data — 21st century life provides tonnes of it. It's paradise for researchers, or at least it would be if we knew how to make sense of it all. This year's <a href="http://www.aaas.org/meetings/2012/">AAAS annual meeting in Vancouver</a>
devoted plenty of time to the question of how to understand large amounts of data. And there's one method we
particularly liked.</p>
<div class="rightimage"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/news/2012/rubber/tube.jpg" width="300" height="199" alt="Tube map"/><p style="width:300px;"> The London Underground map.</p><p><a href="https://plus.maths.org/content/rubberdata" target="_blank">read more</a></p>
https://plus.maths.org/content/rubberdata#comments
data analysis
data mining
topology
Wed, 07 Mar 2012 10:36:30 +0000
mf344
5669 at https://plus.maths.org/content

Maths in a minute: The fundamental group
https://plus.maths.org/content/mathsminutefundamentalgroup
<p>Topologists famously think that a doughnut is the same as a coffee cup because one can be deformed into the other without tearing or cutting. In other words, topology doesn't care about exact measurements of quantities like lengths, angles and areas. Instead, it looks only at the overall shape of an object, considering two objects to be the same as long as you can morph one into the other without breaking it. But how do you work with such a slippery concept?</p><p><a href="https://plus.maths.org/content/mathsminutefundamentalgroup" target="_blank">read more</a></p>
https://plus.maths.org/content/mathsminutefundamentalgroup#comments
fundamental group
group theory
topology
Mon, 11 Apr 2011 09:18:34 +0000
mf344
5465 at https://plus.maths.org/content

The Abel Prize 2011 goes to John Milnor
https://plus.maths.org/content/abelprize2011goesjohnmilnor
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<p>The Abel Prize 2011 goes to John Willard Milnor of Stony Brook University, New York for "pioneering discoveries in topology, geometry and algebra".</p>
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<p>The Abel Prize 2011 goes to <a href="http://www.math.sunysb.edu/~jack/">John Willard Milnor</a> of Stony Brook University, New York for "pioneering discoveries in topology, geometry and algebra". The Abel Prize is one of the most important international prizes in mathematics. It's awarded annually by the <a href="http://english.dnva.no/">Norwegian Academy of Science and Letters</a> and carries a prize money of around £650,000.</p><p><a href="https://plus.maths.org/content/abelprize2011goesjohnmilnor" target="_blank">read more</a></p>
https://plus.maths.org/content/abelprize2011goesjohnmilnor#comments
mathematical reality
Abel prize
differential topology
dynamical system
Julia set
knot
knot theory
Mandelbrot set
topology
Wed, 23 Mar 2011 11:05:49 +0000
mf344
5456 at https://plus.maths.org/content

Winding numbers: Topography and topology II
https://plus.maths.org/content/windingnumberstopographyandtopologyii
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Ian Short </div>
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<p>This is the second in a series of two articles in which Ian Short looks at topology using topographical features of maps. Find out about Jordan curves and winding numbers with the help of hermits, lighthouses and drunken sailors.</p>
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<p><em>This is the second in a series of two articles in which we look at topology using topographical features of maps. You may wish to read the <a href="https://plus.maths.org/content/dividingwallstopologyandtopographyi">first article</a> on dividing walls, although the two articles are largely independent.</em></p>
<h3>The Jordan Curve Theorem</h3>
<p>A hermit hires some builders to construct a wall around his house. The wall they construct is shown in figure 1. Does the wall actually surround the house?</p><p><a href="https://plus.maths.org/content/windingnumberstopographyandtopologyii" target="_blank">read more</a></p>
https://plus.maths.org/content/windingnumberstopographyandtopologyii#comments
jordan curve
topology
winding number
Wed, 23 Mar 2011 10:00:00 +0000
mf344
5449 at https://plus.maths.org/content

Dividing Walls: Topology and topography I
https://plus.maths.org/content/dividingwallstopologyandtopographyi
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Ian Short </div>
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<p>Journey to distant islands to discover if topology can overcome topography and bring peace to rival towns.</p>
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<p><em>Topography is a branch of geography concerned with the natural and constructed features on the surface of land, such as mountains, lakes, roads, and buildings. Topology is a branch of mathematics concerned with the distortion of shapes. In this, the first of two articles, Ian Short explores topological problems using topography.</em></p><p><a href="https://plus.maths.org/content/dividingwallstopologyandtopographyi" target="_blank">read more</a></p>
https://plus.maths.org/content/dividingwallstopologyandtopographyi#comments
topography
topology
Thu, 24 Feb 2011 15:43:26 +0000
Rachel
5423 at https://plus.maths.org/content

Exotic spheres, or why 4dimensional space is a crazy place
https://plus.maths.org/content/richardelwes
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Richard Elwes </div>
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<p>The world we live in is strictly 3dimensional: up/down, left/right, and forwards/backwards, these are the only ways to move. For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4 or 5dimensional universe look like? Or might it even be true that we already inhabit such a space, that our 3dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3dimensional cube produces a 2dimensional square?</p> </div>
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<p>The world we live in is strictly 3dimensional: up/down, left/right, and forwards/backwards, these are the only ways to move. For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4 or 5dimensional universe look like? Or might it even be true, as some have suggested, that we already inhabit such a space, that our 3dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3dimensional cube produces a 2dimensional square?</p><p><a href="https://plus.maths.org/content/richardelwes" target="_blank">read more</a></p>
https://plus.maths.org/content/richardelwes#comments
mathematical reality
differential topology
fractal
geometry
Poincare Conjecture
smooth Poincare conjecture
topology
Wed, 12 Jan 2011 11:03:17 +0000
mf344
5399 at https://plus.maths.org/content

Knitting by numbers
https://plus.maths.org/content/knittingnumbers
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Lucinda Mathews </div>
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<b>Lucinda Mathews</b> visualises tricky surfaces </div>
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<div class="pub_date">June 2009</div>
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<p><i>This article is the runnerup in the general public category of the <a href="https://plus.maths.org/content/iplusinewwritersaward2009"><i>Plus</i> new writers award 2009</a>.</i></p>
<p>Recently I became friends with a keen knitter. She makes such beautiful creations, and knitting looked so meditative, that I decided to take it up myself. What I hadn't expected to end up thinking about during my new hobby was mathematics.</p><p><a href="https://plus.maths.org/content/knittingnumbers" target="_blank">read more</a></p>
https://plus.maths.org/content/knittingnumbers#comments
hyperbolic geometry
klein bottle
mobius strip
permutation
Plus new writers award 2009
topology
Sun, 31 May 2009 23:00:00 +0000
plusadmin
2365 at https://plus.maths.org/content

2008 Crafoord Prize
https://plus.maths.org/content/2008crafoordprize
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One of science's biggest prizes awarded for research into strings and knots </div>
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<div class="pub_date">23/01/2008</div>
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<p>Edward Witten receiving the US National Medal of Science from President Bush. Photo © <a href='http://www.nsf.gov/'>National Science Foundation</a>.</p><p><a href="https://plus.maths.org/content/2008crafoordprize" target="_blank">read more</a></p>
https://plus.maths.org/content/2008crafoordprize#comments
cosmology
knot theory
Poincare Conjecture
string theory
topology
Wed, 23 Jan 2008 00:00:00 +0000
plusadmin
2619 at https://plus.maths.org/content