trigonometry
http://plus.maths.org/content/taxonomy/term/342
enLost but lovely: The haversine
http://plus.maths.org/content/lost-lovely-haversine
<p>Sine, cosine, and tangent — we do love our trigonometric functions! So imagine our bliss when we recently came across a function we had never even heard of before. It's called the <em>haversine</em> and it's defined in terms of the sine function:</p><p><a href="http://plus.maths.org/content/lost-lovely-haversine" target="_blank">read more</a></p>http://plus.maths.org/content/lost-lovely-haversine#commentsnavigationtrigonometryFri, 04 Jul 2014 09:44:56 +0000mf3446127 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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<img class="imagefield imagefield-field_abs_img" width="100" height="100" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/11_oct_2011_-_1710/icon.jpg?1318349428" /> </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/contentCan triangles help spot a bomb?
http://plus.maths.org/content/maths-inside-guns-knives
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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/5/5_jul_2011_-_1023/icon-4.jpg?1309857808" /> </div>
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<p>Airport security staff have a daunting task. With impatient queues looming over them they need to search x-ray scans of cluttered suitcases for several items at once: knives, guns and bombs. How can we ease their task and make sure they don't miss a crucial item? To find out, scientists are trying to understand how we humans take in visual information. The humble triangle plays a crucial role in the experiments they perform.</p>
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<div style="position: relative; left: 60%; width: 40%"><font size="2"><em>Back to the <a href="http://plus.maths.org/content/maths-inside-2011">Maths inside 2011 page </a></em></font></div><br style="brclear"/>
<p>Airport security staff have a daunting task. With impatient queues
looming over them they need to search x-ray scans of cluttered
suitcases for several items at once: knives, guns and bombs. How can we ease their task and make sure they don't miss a crucial item? To find out, scientists at the University of Southampton are trying to understand how we humans take in visual information.<p><a href="http://plus.maths.org/content/maths-inside-guns-knives" target="_blank">read more</a></p>http://plus.maths.org/content/maths-inside-guns-knives#commentsmaths insidepublic understanding of mathematicstrigonometryvisual angleTue, 05 Jul 2011 08:00:20 +0000mf3445514 at http://plus.maths.org/contentTeacher package: Trigonometry
http://plus.maths.org/content/os/issue55/package/index
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<img class="imagefield imagefield-field_abs_img" width="101" height="101" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/abstractpics/5/12%20Jul%202010%20-%2016%3A31/icon-8.jpg?1278948689" /> </div>
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<p>This teacher package brings together our material on trigonometry, from problems about simple triangles to the wavy behaviour of trig functions.</p>
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<br clear="all"></br><p>The <i>Plus</i> teacher packages are designed to give teachers (and students) easy access to <i>Plus</i> content on a particular subject area. Most
<i>Plus</i> articles go far beyond the explicit
maths taught at school, while still being accessible to someone doing A level maths.<p><a href="http://plus.maths.org/content/os/issue55/package/index" target="_blank">read more</a></p>http://plus.maths.org/content/os/issue55/package/index#comments55teacher packagetrigonometryMon, 12 Jul 2010 15:50:49 +0000mf3445226 at http://plus.maths.org/contentDefying gravity: The uphill roller
http://plus.maths.org/content/defying-gravity-uphill-roller
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Julian Havil </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/issue40/features/uphill/icon.jpg?1157065200" /> </div>
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What goes up must come down — or does it? Find out how to cheat gravity with <b>Julian Havil</b>. </div>
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<div class="pub_date">September 2006</div> <p><em>"Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics."</em></p> <p align="right"><strong>Leonardo da Vinci</strong></p><p><a href="http://plus.maths.org/content/defying-gravity-uphill-roller" target="_blank">read more</a></p>http://plus.maths.org/content/defying-gravity-uphill-roller#comments40gravitymechanicstrigonometryThu, 31 Aug 2006 23:00:00 +0000plusadmin2289 at http://plus.maths.org/contentMathematical mysteries: Strange Geometries
http://plus.maths.org/content/mathematical-mysteries-strange-geometries
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Helen Joyce </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/5/30%20Jun%202010%20-%2016%3A30/mystery.gif?1277911831" /> </div>
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<p>The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.</p>
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<div class="pub_date">Jan 2002</div>
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<h2>Euclidean Geometry</h2>
<p>The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics. Euclid's work is discussed in detail in <a href="/issue7/features/proof1/index.html">The Origins
of Proof</a>, from Issue 7 of <i>Plus</i>.</p><p><a href="http://plus.maths.org/content/mathematical-mysteries-strange-geometries" target="_blank">read more</a></p>http://plus.maths.org/content/mathematical-mysteries-strange-geometries#comments18curvaturecurvature of spaceescherEuclid's ElementsEuclidean geometryflatnesshyperbolic geometryMathematical mysteriesMercator projectionspherical geometrytrigonometrySat, 01 Dec 2001 00:00:00 +0000plusadmin4754 at http://plus.maths.org/contentAnalemmatic sundials: How to build one and why they work
http://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="http://plus.maths.org/content/analemmatic-sundials-how-build-one-and-why-they-work" target="_blank">read more</a></p>http://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 http://plus.maths.org/contentA postcard from Italy
http://plus.maths.org/content/postcard-italy
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Eugen Jost </div>
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<strong>Eugen Jost</strong> is a Swiss artist whose work is strongly influenced by mathematics. He sent us this Postcard from Italy, telling us about his work and the important roles that nature and numbers play in it. </div>
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<div class="pub_date">September 1999</div>
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<p><em><a href="http://www.datacomm.ch/jostechk/">Eugen Jost</a> is a Swiss artist, born in Zürich, whose work is strongly influenced by mathematics.</em></p>
<p><em>His early career was a technical one: after taking an apprenticeship with Siemens-Albis Telecommunications and working as a technical designer at Bobst et fils in Lausanne, he went on to Teacher Training College in Bern, later becoming a teacher and an instructor in Matten/Interlaken and Spiez.</em></p><p><a href="http://plus.maths.org/content/postcard-italy" target="_blank">read more</a></p>http://plus.maths.org/content/postcard-italy#comments9Fibonacci numberinfinitypalindromeparadoxpuzzlesundialsymmetrytrigonometryTue, 31 Aug 1999 23:00:00 +0000plusadmin2390 at http://plus.maths.org/content