geometry
http://plus.maths.org/content/taxonomy/term/674
enPolar power
http://plus.maths.org/content/polar-power
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Marianne Freiberger </div>
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<p>Like spirals and flowers? Then you'll love polar coordinates and the pretty pictures they allow you to draw!</p>
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<p>Cartesian coordinates. </p><div class="field field-type-number-integer field-field-hidden">
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<p><a href="http://plus.maths.org/content/polar-power" target="_blank">read more</a></p>http://plus.maths.org/content/polar-power#commentsArchimedean spiralgeometrylogarithmic spiralpolar coordinatessystemThu, 03 Apr 2014 15:46:05 +0000mf3446072 at http://plus.maths.org/contentMaths in a minute: Triangle central
http://plus.maths.org/content/maths-minute-triangle-central
<p>How do you balance a cardboard cut-out of a triangle on a pencil? Trial and error is one way, but maths can save you lots of bending down and picking it up. Take the pencil and a ruler and connect the mid-point of each side to the opposite corner. You'll find that the three lines intersect in a single point, which lies exactly a third of the way from the midpoint of each side to the opposite vertex. That point, called the <em>centroid</em>, is the centre of mass of the triangle.<p><a href="http://plus.maths.org/content/maths-minute-triangle-central" target="_blank">read more</a></p>http://plus.maths.org/content/maths-minute-triangle-central#commentsgeometryWed, 06 Nov 2013 09:46:11 +0000Rachel5967 at http://plus.maths.org/content3D printing mathematics
http://plus.maths.org/content/3d-printing
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Saul Schleimer and Henry Segerman </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/5/13_sep_2013_-_1234/print_icon.jpg?1379072049" /> </div>
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<p>Saul Schleimer and Henry Segerman show off some of their beautiful 3D printed mathematical structures.</p>
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<p>When learning about existing mathematics, and especially when trying
to produce new mathematics, we spend a lot of time thinking about
examples. How do parts of the example interact with each other? What
are the regularities and symmetries? Does it come in a family of
examples, or does it live on its own? In many cases, the first thing
to do is to try and draw a picture. We are both geometric topologists,
working mostly with two and three-dimensional objects. As such, two-dimensional pictures are important currency in our field.<div class="field field-type-number-integer field-field-hidden">
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<p><a href="http://plus.maths.org/content/3d-printing" target="_blank">read more</a></p>http://plus.maths.org/content/3d-printing#commentscreativitygeometrymathematics and artmobius strippolytopevisualisationWed, 23 Oct 2013 08:18:02 +0000mf3445939 at http://plus.maths.org/contentMaths in a minute: Not always 180
http://plus.maths.org/content/maths-minute-strange-geometries
<p>Over 2000 years ago the Greek mathematician <a href="http://www-history.mcs.st-and.ac.uk/Mathematicians/Euclid.html">Euclid</a> came up with a list of five postulates on which he thought geometry should be built. One of them, the fifth, was equivalent to a statement we are all familiar with: that the angles in a triangle add up to 180 degrees. However, this postulate did not seem as obvious as the other four on Euclid's list, so mathematicians attempted to deduce it from them: to show that a geometry obeying the first four postulates would necessarily obey the fifth.<p><a href="http://plus.maths.org/content/maths-minute-strange-geometries" target="_blank">read more</a></p>http://plus.maths.org/content/maths-minute-strange-geometries#commentsEuclidean geometrygeometryhyperbolic geometryspherical geometryWed, 03 Jul 2013 12:47:01 +0000mf3445921 at http://plus.maths.org/contentWatch out, it's behind you!
http://plus.maths.org/content/watch-out-its-behind-you
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<p>The <em>Plus</em> team's vehicle of choice is the bicycle, so we're particularly pleased about an announcement that hit the news this month: a clever car mirror that eliminates the dreaded blind spot has been given a patent in the US. The mirror was designed by the mathematician Andrew Hicks, of Drexel University, after years of puzzling over the problem.</p>
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<p>The <em>Plus</em> team's vehicle of choice is the bicycle, so we're intrigued by an announcement that hit the news this month: a clever car mirror that eliminates the dreaded blind spot has been given a patent in the US. The mirror was designed by the mathematician <a href="http://www.drexel.edu/math/contact/facultyDirectory/AndrewHicks/">Andrew Hicks</a>, of Drexel University, after years of puzzling over the problem.</p><p><a href="http://plus.maths.org/content/watch-out-its-behind-you" target="_blank">read more</a></p>http://plus.maths.org/content/watch-out-its-behind-you#commentsgeometryopticsreflectionFri, 29 Jun 2012 15:12:41 +0000mf3445725 at http://plus.maths.org/contentBridges, string art and Bézier curves
http://plus.maths.org/content/bridges-string-art-and-bezier-curves
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Renan Gross </div>
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The Jerusalem Chords Bridge, Israel, was built to make way for the city's light rail train
system. Its design took into consideration more than just utility — it is a work of
art, designed as a monument. Its beauty rests not only in the visual appearance of its criss-cross
cables, but also in the mathematics that lies behind it. So let's take a deeper look at it. </div>
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<h3>The Jerusalem Chords Bridge</h3>
<p>The Jerusalem Chords Bridge, Israel, was built to make way for the city's light rail train
system. However, its design took into consideration more than just utility — it is a work of
art, designed as a monument. Its beauty rests not only in the visual appearance of its criss-cross
cables, but also in the mathematics that lies behind it. Let us take a deeper look into these
chords.</p><p><a href="http://plus.maths.org/content/bridges-string-art-and-bezier-curves" target="_blank">read more</a></p>http://plus.maths.org/content/bridges-string-art-and-bezier-curves#commentsarchitectureBezier curveengineeringgeometrymathematics and artparabolaMon, 05 Mar 2012 09:31:51 +0000mf3445654 at http://plus.maths.org/contentMaths behind the rainbow
http://plus.maths.org/content/rainbows
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Marianne Freiberger </div>
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<p>The only good thing about a wash-out summer is that you get to see lots of rainbows. Keats complained that a mathematical explanation of these marvels of nature robs them of their magic, conquering "all mysteries by rule and line". But rainbow geometry is just as elegant as the rainbows themselves.</p>
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<p>When the great mathematician <a href="http://www.gap-system.org/~history/Biographies/Newton.html">Isaac Newton</a> explained the <a href="http://en.wikipedia.org/wiki/Isaac_Newton#Optics">colours of the rainbow</a> with refraction the poet <a href="http://en.wikipedia.org/wiki/John_Keats">John Keats</a> was horrified. Keats complained (through poetry of course) that a mathematical explanation robbed these marvels of nature of their magic, conquering <a href="http://en.wikipedia.org/wiki/Rainbow#Literature">"all mysteries by rule and line"</a>.<p><a href="http://plus.maths.org/content/rainbows" target="_blank">read more</a></p>http://plus.maths.org/content/rainbows#commentsEuclidean geometrygeometryrefractionrefractive indexsnell's lawtrigonometryFri, 21 Oct 2011 08:34:47 +0000mf3445558 at http://plus.maths.org/contentMeet the gyroid
http://plus.maths.org/content/meet-gyroid
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Adam G. Weyhaupt </div>
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What do butterflies, ketchup, microcellular structures, and plastics have in common? It's a curious minimal surface called the <em>gyroid</em>. </div>
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<p>What do butterflies, ketchup, microcellular structures, and plastics have in common?
It's a curious minimal surface called the <em>gyroid</em>. </p>
<div class="centreimage"><img src="http://plus.maths.org/content/sites/plus.maths.org/files/articles/2011/gyroid/gyroid_2views_0.jpg" width="600" height="275" alt="Gyroid"/><p style="width: 600px; margin: auto">Figure 1: Two views of a section of the gyroid surface. </p><p><a href="http://plus.maths.org/content/meet-gyroid" target="_blank">read more</a></p>http://plus.maths.org/content/meet-gyroid#commentsgeometrygyroidminimal surfaceMon, 12 Sep 2011 10:39:33 +0000mf3445547 at http://plus.maths.org/contentLeaning into 2012
http://plus.maths.org/content/leaning-2012
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<p>Rising like a giant pringle from the Olympic Park construction site, the Velodrome is the first of the 2012 London Olympic venues to be completed. With its sweeping curved roof and beautiful cedar clad exterior the Velodrome is a stunning building. But what most of the athletes are excited about is the elegant wooden cycle track enclosed inside, the medals that will be won, and the records that might be broken, in the summer of 2012.</p>
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<div class="packagebacklink">Back to the <a href="http://plus.maths.org/content/ingenious-constructing-our-lives">Constructing our lives package</a></div><br clear="all"><p>Rising like a giant pringle from the Olympic Park construction site, the Velodrome is the first of the 2012 London Olympic venues to be completed.</p>
<div class="rightimage" style="width: 400px"><img src="http://plus.maths.org/content/sites/plus.maths.org/files/news/2011/velo/velo_exterior.jpg" width="350" height="233" alt="The London velodrome"><p>The London Velodrome.</p><p><a href="http://plus.maths.org/content/leaning-2012" target="_blank">read more</a></p>http://plus.maths.org/content/leaning-2012#commentsgeometrymathematics in sportolympicsTue, 15 Mar 2011 14:00:12 +0000mf3445447 at http://plus.maths.org/contentExotic spheres, or why 4-dimensional space is a crazy place
http://plus.maths.org/content/richard-elwes
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Richard Elwes </div>
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<p>The world we live in is strictly 3-dimensional: 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 5-dimensional universe look like? Or might it even be true that we already inhabit such a space, that our 3-dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3-dimensional cube produces a 2-dimensional square?</p> </div>
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<p>The world we live in is strictly 3-dimensional: 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 5-dimensional universe look like? Or might it even be true, as some have suggested, that we already inhabit such a space, that our 3-dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3-dimensional cube produces a 2-dimensional square?</p><p><a href="http://plus.maths.org/content/richard-elwes" target="_blank">read more</a></p>http://plus.maths.org/content/richard-elwes#commentsmathematical realitydifferential topologyfractalgeometryPoincare Conjecturesmooth Poincare conjecturetopologyWed, 12 Jan 2011 11:03:17 +0000mf3445399 at http://plus.maths.org/contentVisual curiosities and mathematical paradoxes
http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes
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Linda Becerra and Ron Barnes </div>
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<p>When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions, which we call paradoxes. This article looks at examples of geometric optical illusions and paradoxes and gives explanations of what's really going on.</p>
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<p>When your eyes see a picture they send an image to your brain, which your brain then has to make sense of. But sometimes your brain gets it wrong. The result is an optical illusion. Similarly in logic, statements or figures can lead to contradictory conclusions; appear to be true but in actual fact are self-contradictory; or appear contradictory, even absurd, but in fact may be true. Here again it is up to your brain to make sense of these situations. Again, your brain may get it wrong. These situations are referred to as paradoxes.<p><a href="http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes" target="_blank">read more</a></p>http://plus.maths.org/content/visual-curiosities-and-mathematical-paradoxes#commentsarchitectureBanach-Tarski paradoxBarber's Paradoxeschergeometryimpossible objectoptical illusionparadoxPenrose staircasePenrose triangleperspectiveRussell's ParadoxWed, 17 Nov 2010 14:06:13 +0000mf3445337 at http://plus.maths.org/contentUncovering the cause of cholera
http://plus.maths.org/content/uncovering-cause-cholera
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<p>London, September, 1853. A cholera outbreak has decimated Soho, killing 10% of the population and wiping out entire families in days. Current medical theories assert that the disease is spread by "bad air" emanating from the stinking open sewers. But one physician, John Snow, has a different theory: that cholera is spread through contaminated water. And he is just about to use mathematics to prove that he is right.</p>
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<div style="position: relative; left: 50%; width: 70%"><font size="2"><i>Back to the <a href="http://plus.maths.org/content/do-you-know-whats-good-you-maths-next-microscope">Next microscope package </a><br>Back to the <a href="http://plus.maths.org/content/do-you-know-whats-good-you-0">Do you know what's good for you package</a></li></ul></i></font></div><br clear="all">
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<p>The John Snow memorial and pub in London</p><p><a href="http://plus.maths.org/content/uncovering-cause-cholera" target="_blank">read more</a></p>http://plus.maths.org/content/uncovering-cause-cholera#commentsepidemiologygeometryjohn snowmedicine and healthvoronoi diagramFri, 10 Sep 2010 15:52:52 +0000Rachel5307 at http://plus.maths.org/contentHow to make a perfect plane
http://plus.maths.org/content/projective-geometry-projective-plane-geometry
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Burkard Polster and Marty Ross </div>
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Two lines in a plane always intersect in a single point ... <i>unless</i> the lines are parallel. This annoying exception is constantly inserting itself into otherwise simple mathematical statements. <b>Burkard Polster</b> and <b>Marty Ross</b> explain how to get around the problem. </div>
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<p>Two lines in a plane always intersect in a single point ... <i>unless</i> the lines are parallel. This annoying exception is constantly inserting itself into otherwise simple mathematical statements. Here is an example.</p>
<h3>Parallel lines never meet</h3>
<p>You may have heard of <i>Desargues' Theorem</i>. Draw any three lines through a point, and draw two triangles with corners on the lines, choosing three colours for corresponding edges, like this:</p><p><a href="http://plus.maths.org/content/projective-geometry-projective-plane-geometry" target="_blank">read more</a></p>http://plus.maths.org/content/projective-geometry-projective-plane-geometry#commentsgeometryprojective geometryprojective planeFri, 16 Jul 2010 14:00:14 +0000mf3445258 at http://plus.maths.org/contentThe power of origami
http://plus.maths.org/content/power-origami
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Liz Newton </div>
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We've all heard of origami. It's all about making paper birds and pretty boxes, and is really just a game invented by Japanese kids, right? Prepare to be surprised as <b>Liz Newton</b> takes you on a journey of origami, maths and science. </div>
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<p><i>Allosaurus skeleton</i> made by Robert J. Lang from 16 uncut squares of Wyndstone 'Marble' paper. Size: 24 inches.<div class="field field-type-number-integer field-field-hidden">
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<p><a href="http://plus.maths.org/content/power-origami" target="_blank">read more</a></p>http://plus.maths.org/content/power-origami#comments53angle trisectionbifurcationcreativitydoubling the cubegeometryorigamiTue, 01 Dec 2009 00:00:00 +0000plusadmin2375 at http://plus.maths.org/contentHow long is a day?
http://plus.maths.org/content/how-long-day
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Nicholas Mee </div>
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The obvious answer is 24 hours, but, as <b>Nicholas Mee</b> discovers, that would be far too simple. In fact, the length of a day varies throughout the year. If you plot the position of the Sun in the sky at the same time every day, you get a strange figure of eight which has provided one artist with a source for inspiration. </div>
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<p><i>This article was part of a <A href="http://plus.maths.org/content/seven-things-everyone-wants-know-about-universe">project</a> we ran to celebrate the <a href="http://www.astronomy2009.co.uk/">International Year of Astronomy 2009</a>. The project asked you to nominate the questions about the Universe you'd most like to have answered, and this is one of them. We took it to the physicist <a href="http://www.nicholasmee.com">Nicholas Mee</a> and here is his answer.</i></p><p><a href="http://plus.maths.org/content/how-long-day" target="_blank">read more</a></p>http://plus.maths.org/content/how-long-day#comments53analemmaastronomygeometryinternational year of astronomy 2009Kepler's three laws of planetary motionTue, 01 Dec 2009 00:00:00 +0000plusadmin2374 at http://plus.maths.org/content