ellipse
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enTwo-faced conic sections
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Marianne Freiberger </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="99" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/13_jan_2015_-_1415/conics_icon-1.png?1421158507" /> </div>
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<p>Play with our applets to explore the conic sections and their different definitions.</p>
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<p>What do the circle, the ellipse, the parabola and the hyperbola have in common? They are all shapes you get when you slice through a cone. You get a <strong>circle</strong> when you intersect a cone and a plane that is perpendicular to the cone's axis. When you tilt the plane slightly the circle turns into an <strong>ellipse</strong>. As you tilt the plane further, it will eventually become parallel to one of the <em>generating lines</em> of the cone — that's a straight line lying on the cone and emanating from the apex. When this happens the intersection is a <strong>parabola</strong>.<p><a href="https://plus.maths.org/content/conic-sections" target="_blank">read more</a></p>https://plus.maths.org/content/conic-sections#commentsconic sectionsellipsehyperbolaparabolaTue, 13 Jan 2015 12:25:48 +0000mf3446301 at https://plus.maths.org/contentThe story of the Gömböc
https://plus.maths.org/content/story-goumlmboumlc
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Marianne Freiberger </div>
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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue52/features/gomboc/icon.jpg?1251759600" /> </div>
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A Gömböc is a strange thing. It looks like an egg with sharp edges, and when you put it down it starts wriggling and rolling around as if it were alive. Until quite recently, no-one knew whether Gömböcs even existed. Even now, <b>Gábor Domokos</b>, one of their discoverers, reckons that in some sense they barely exists at all. So what are Gömböcs and what makes them special? </div>
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<center>Play this movie to see the Gömböc wriggle.</center></div><br>
<p><i>This article is also available as a <a href="/podcasts/PlusPodcastSep09.mp3">podcast.</a></i></p><p><a href="https://plus.maths.org/content/story-goumlmboumlc" target="_blank">read more</a></p>https://plus.maths.org/content/story-goumlmboumlc#comments52ellipseequilibriumgeometrygömböcmechanicsMon, 31 Aug 2009 23:00:00 +0000plusadmin2370 at https://plus.maths.org/contentHow to dodge a very big bullet
https://plus.maths.org/content/how-dodge-very-big-bullet
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Adding weight helps Earth dodge killer asteroids </div>
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<div class="pub_date">23/04/2009</div>
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<p>On Friday the 13th, in April 2029, the asteroid Apophis will pass close enough to the Earth to be viewed with the naked eye. This will be an exciting event for stargazers, but for a short time in 2004 there was concern that this event would be cataclysmic.<p><a href="https://plus.maths.org/content/how-dodge-very-big-bullet" target="_blank">read more</a></p>https://plus.maths.org/content/how-dodge-very-big-bullet#commentsasteroidasteroid collisionastronomyellipsegeometryWed, 22 Apr 2009 23:00:00 +0000plusadmin2610 at https://plus.maths.org/contentCareer interview: Systems engineer
https://plus.maths.org/content/career-interview-systems-engineer
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Marianne Freiberger </div>
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<div class="pub_date">September 2008</div>
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<div style="position: relative; left: 50%; width: 70%"><font size="2"><i>Back to the <a href="https://plus.maths.org/content/ingenious-constructing-our-lives">Constructing our lives package</a></i></font></div><br clear="all">
<p><i>A version of this interview is also available as a <a href="/podcasts/PlusCareersPodcastSep08.mp3">podcast</a>.</i></p><p><a href="https://plus.maths.org/content/career-interview-systems-engineer" target="_blank">read more</a></p>https://plus.maths.org/content/career-interview-systems-engineer#comments48aerodynamicscareer interviewdifferential equationellipseengineeringheat diffusion equationKepler's three laws of planetary motionmathematical modellingpartial differential equationphysicssatelliteScience & Engineeringspace explorationstatisticsuncertaintySun, 31 Aug 2008 23:00:00 +0000plusadmin2437 at https://plus.maths.org/contentDrinking coffee in the Klein Café
https://plus.maths.org/content/drinking-coffee-klein-cafeacute
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Jonathan Tims </div>
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<b>Runner up in the schools category</b>. Dusty books, chalky blackboards and checked shirts are all things usually associated with maths. But according to <b>Jonathan Tims</b>, pubs, hot chocolate and cats can be far more inspirational. Join him on a trip through shadow land. </div>
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<div class="pub_date">December 2006</div>
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<p style="color:purple;"><b><i>This article is a runner-up of the schools category of the Plus new writers award 2006.</i></b></p>
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<p>Dry and impenetrable?</p><p><a href="https://plus.maths.org/content/drinking-coffee-klein-cafeacute" target="_blank">read more</a></p>https://plus.maths.org/content/drinking-coffee-klein-cafeacute#comments41conic sectionsellipsegeometryhyperbolaPappus's theoremparabolaprojective geometrySat, 09 Dec 2006 00:00:00 +0000plusadmin2297 at https://plus.maths.org/content1089 and all that
https://plus.maths.org/content/1089-and-all
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David Acheson </div>
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Why do so many people say they hate mathematics, asks <b>David Acheson</b>? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best. </div>
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<h2>The element of surprise in mathematics</h2>
<p><i>Why do so many people say they hate mathematics?</i></p>
<p>All too often, the real truth is that they have never been allowed anywhere near it, and I believe that mathematicians like myself could do more, if we wanted, to bring some of the ideas and pleasures of our subject to a wide public.</p>
<p>And one way of doing this might be to emphasise the element of <i>surprise</i> that often accompanies mathematics at its best.</p><p><a href="https://plus.maths.org/content/1089-and-all" target="_blank">read more</a></p>https://plus.maths.org/content/1089-and-all#comments31ellipseFermat's Last Theoremfocalpointsgeometrykeplerleibnizmathematics and magicpendulumPiproofTue, 31 Aug 2004 23:00:00 +0000plusadmin2250 at https://plus.maths.org/content101 uses of a quadratic equation: Part II
https://plus.maths.org/content/101-uses-quadratic-equation-part-ii
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Chris Budd and Chris Sangwin </div>
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In issue 29 of <i>Plus</i>, we heard how a simple mathematical equation became the subject of a debate in the UK parliament. <b>Chris Budd</b> and <b>Chris Sangwin</b> continue the story of the mighty quadratic equation. </div>
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<div class="pub_date">May 2004</div>
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<p><i>In <a href="/issue29/features/quadratic/index.html">101 uses of a quadratic equation: Part I</a> in issue 29 of Plus we took a look at quadratic equations and saw how they arose naturally in various simple problems. In this second part we continue our journey. We shall soon see how the humble quadratic makes its appearance in many different and important applications.</i></p><p><a href="https://plus.maths.org/content/101-uses-quadratic-equation-part-ii" target="_blank">read more</a></p>https://plus.maths.org/content/101-uses-quadratic-equation-part-ii#comments30accelerationbernoulli equationchaosdifferential equationellipsegravitynavier-stokes equationsNewtonian mechanicsparabolapublic understanding of mathematicsquadratic equationFri, 30 Apr 2004 23:00:00 +0000plusadmin2248 at https://plus.maths.org/content101 uses of a quadratic equation
https://plus.maths.org/content/101-uses-quadratic-equation
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Chris Budd and Chris Sangwin </div>
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It isn't often that a mathematical equation makes the national press, far less popular radio, or most astonishingly of all, is the subject of a debate in the UK parliament. However, as <b>Chris Budd</b> and <b>Chris Sangwin</b> tell us, in 2003 the good old quadratic equation, which we all learned about in school, reached these dizzy pinnacles of fame. </div>
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<p><i>It isn't often that a mathematical equation makes the national press, far less popular radio, or most astonishingly of all, is the subject of a debate in the UK parliament. However, in 2003 the good old quadratic equation, which we all learned about in school, was all of those things.</i></p>
<h3>Where we begin</h3>
<p><!-- FILE: include/rightfig.html --></p><p><a href="https://plus.maths.org/content/101-uses-quadratic-equation" target="_blank">read more</a></p>https://plus.maths.org/content/101-uses-quadratic-equation#comments29Babylonian mathematicscompleting the squareellipseFibonaccigolden ratioNewton-Raphson methodpublic understanding of mathematicspythagoras' theoremquadratic equationMon, 01 Mar 2004 00:00:00 +0000plusadmin2245 at https://plus.maths.org/contentMission to Mars
https://plus.maths.org/content/mission-mars
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The geometry says that now is the right time for a mission to Mars. </div>
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<p>The race for Mars is on. The European Space Agency's <a href="http://www.esa.int/SPECIALS/Mars_Express/index.html">Mars Express</a> mission and the first of two US <a href="http://mars.jpl.nasa.gov/mer/">Mars Exploration Rovers</a> launched by NASA are currently hurtling toward the red planet, each hunting for water and possible signs of life. But why this flurry of activity? Is it simply the
spirit of competition that has driven the parallel missions?</p><p><a href="https://plus.maths.org/content/mission-mars" target="_blank">read more</a></p>https://plus.maths.org/content/mission-mars#commentsaphelionellipseEuropean Space AgencykeplerKepler's three laws of planetary motionMarsNASANewtonorbitperihelionSun, 15 Jun 2003 23:00:00 +0000plusadmin2717 at https://plus.maths.org/contentAnalemmatic sundials: How to build one and why they work
https://plus.maths.org/content/analemmatic-sundials-how-build-one-and-why-they-work
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Chris Sangwin and Chris Budd </div>
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We've all seen a traditional sundial, where a triangular wedge is used to cast a shadow onto a marked-out dial - but did you know that there is another kind? In this article, <strong>Chris Sangwin</strong> and <strong>Chris Budd</strong> tell us about a different kind of sundial, the analemmatic design, where you can use your own shadow to tell the time. </div>
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<div class="pub_date">June 2000</div>
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<h2>Introduction</h2>
<p>Imagine that you have just got the latest in digital watches, with a stop watch, date, times from all over the world, and the ability to function at 4000 fathoms. There is just one small problem: the batteries have gone flat. However, if the sun is shining you don't need to use a watch at all, because the sun makes an excellent clock which (fortunately) doesn't need batteries that can run
down.<p><a href="https://plus.maths.org/content/analemmatic-sundials-how-build-one-and-why-they-work" target="_blank">read more</a></p>https://plus.maths.org/content/analemmatic-sundials-how-build-one-and-why-they-work#comments11angular distancedeclination of the sunellipseProjectionsundialtrigonometryWed, 31 May 2000 23:00:00 +0000plusadmin2168 at https://plus.maths.org/contentThe origins of proof II : Kepler's proofs
https://plus.maths.org/content/origins-proof-ii-keplers-proofs
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J.V. Field </div>
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Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. <b>J.V. Field</b> continues our series on the origins of proof with an examination of Kepler's astronomy. </div>
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<div class="pub_date">May 1999</div>
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<p>As we explained in <a href="/issue7/features/proof1/index.html">The Origins of Proof, Part I</a> in <a href="https://plus.maths.org/content/issue/7">Issue 7</a> of PASS Maths, the concept of a "proof" was developed in the field of geometry by the Greeks. The Pythagoreans and Euclid were among the mathematicians who developed the idea of abstract deduction. But during the Renaissance the philosophy
of nature increasingly came to rely upon mathematics to help to explain the Universe and its workings.</p><p><a href="https://plus.maths.org/content/origins-proof-ii-keplers-proofs" target="_blank">read more</a></p>https://plus.maths.org/content/origins-proof-ii-keplers-proofs#comments8astronomyellipseerrorgeometrygravityhistory of mathematicsKepler's three laws of planetary motionproofFri, 30 Apr 1999 23:00:00 +0000plusadmin2389 at https://plus.maths.org/content