golden ratio
https://plus.maths.org/content/taxonomy/term/274
enThe life and numbers of Fibonacci
https://plus.maths.org/content/life-and-numbers-fibonacci
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R.Knott and the Plus team </div>
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The Fibonacci sequence – 0, 1, 1, 2, 3, 5, 8, 13, ... – is one of the most famous pieces of mathematics. We see how these numbers appear in multiplying rabbits and bees, in the turns of sea shells and sunflower seeds, and how it all stemmed from a simple example in one of the most important books in Western mathematics. </div>
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<div class="rightshoutout"><a href="https://plus.maths.org/content/fibonacci-sequence-brief-introduction">For a brief introduction to the Fibonacci sequence, see here</a>.</div>
<p>Fibonacci is one of the most famous names in mathematics. This would come as a surprise to Leonardo Pisano, the mathematician we now know by that name. And he might have been equally surprised that he has been immortalised in the famous sequence – 0, 1, 1, 2, 3, 5, 8, 13, ...<p><a href="https://plus.maths.org/content/life-and-numbers-fibonacci" target="_blank">read more</a></p>https://plus.maths.org/content/life-and-numbers-fibonacci#comments3FibonacciFibonacci numbergolden ratiohistory of mathematicslimitsequenceMon, 04 Nov 2013 12:00:00 +0000plusadmin2148 at https://plus.maths.org/contentThe lost mathematicians: Numbers in the (not so) dark ages
https://plus.maths.org/content/lost-mathematicians-numbers-not-so-dark-early-middle-ages
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Charlotte Mulcare </div>
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<p>A commonly held belief about medieval Europe is that academic pursuits had fallen into a dark age. The majority of scholars were churchmen, and their enquiry often related to some principle of church practice. But is there a value to respecting the tenacity of historic mathematicians?</p>
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"Europe had fallen into the dark ages, in which science, mathematics and almost all intellectual endeavor stagnated."</em></br>
From <a href="http://www.storyofmathematics.com/medieval.html">The story of mathematics</a>.
</p><p><a href="https://plus.maths.org/content/lost-mathematicians-numbers-not-so-dark-early-middle-ages" target="_blank">read more</a></p>https://plus.maths.org/content/lost-mathematicians-numbers-not-so-dark-early-middle-ages#commentscomputusgolden ratiohistory of mathematicsThu, 08 Aug 2013 11:30:47 +0000alex5908 at https://plus.maths.org/contentDecoding Da Vinci: Finance, functions and art
https://plus.maths.org/content/decoding-da-vinci
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Tim Johnson </div>
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<p>Dan Brown in his book, <em>The Da Vinci Code</em>, talks about the "divine proportion" as having a "fundamental role in nature". Brown's ideas are not completely without foundation, as the proportion crops up in the mathematics used to describe the formation of natural structures like snail's shells and plants, and even in Alan Turing's work on animal coats. But Dan Brown does not talk about mathematics, he talks about a number. What is so special about this number?</p>
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<div class="rightimage" style="width: 200px;"><img src="https://plus.maths.org/content/sites/plus.maths.org/files/articles/2011/davinci/fibonacci.jpg" alt="Fibonacci" width="200" height="270" /><p>Fibonacci (ca 1170 – ca 1250).</p><p><a href="https://plus.maths.org/content/decoding-da-vinci" target="_blank">read more</a></p>https://plus.maths.org/content/decoding-da-vinci#commentscontinued fractionFibonacciFibonacci numbergolden ratiomathematics and artpower seriesThu, 03 Nov 2011 12:58:56 +0000mf3445576 at https://plus.maths.org/contentEditorial
https://plus.maths.org/content/pluschat-21
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<p>The <em>Plus</em> anniversary year — A word from the editors</p>
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<div class="pub_date">December 2007</div>
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<h2>This issue's <i>Plus</i>chat topics</h2>
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<li><a href="#blurb">The <i>Plus</i> anniversary year</a> — A word from the editors;</li>
<li><a href="#plus10000"><i>Plus</i> 10,000</a> — The best maths ever.</li>
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<h3>The <i>Plus</i> anniversary year — A word from the editors</h3>
<p>This is the last issue of 2007 and, sadly, it's time to wrap up <i>Plus</i>'s tenth birthday party.<p><a href="https://plus.maths.org/content/pluschat-21" target="_blank">read more</a></p>45Al-KhwarizmialgebraeditorialEuclid's ElementsEuclidean geometrygeometrygolden ratiohyperbolic geometryirrational numbernumber systemplus birthdaypythagoras' theoremZeno's paradoxesSat, 01 Dec 2007 00:00:00 +0000plusadmin4901 at https://plus.maths.org/contentMaths and art: the whistlestop tour
https://plus.maths.org/content/maths-and-art-whistlestop-tour
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Lewis Dartnell </div>
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Many people find no beauty and pleasure in maths - but, as <b>Lewis Dartnell</b> explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense. </div>
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<div class="pub_date">January 2005</div>
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<p>The world around us is full of relationships, rhythms, correlations, patterns. And mathematics underlies all of these, and can be used to predict future outcomes. Our brains have evolved to survive in this world: to analyse the information it receives through our senses and spot patterns in the complexity around us. In fact, it's thought that the mathematical structure embedded in the rhythm
and melody of music is what our brains latch on to, and that this is why we enjoy listening to it.<p><a href="https://plus.maths.org/content/maths-and-art-whistlestop-tour" target="_blank">read more</a></p>https://plus.maths.org/content/maths-and-art-whistlestop-tour#comments33escherfractalgeometric abstractiongeometric patternsgolden ratiomathematics and artminimal surfaceorigamiregular polyhedrontessellationSat, 01 Jan 2005 00:00:00 +0000plusadmin2259 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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<div class="pub_date">March 2004</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/contentThe golden ratio and aesthetics
https://plus.maths.org/content/golden-ratio-and-aesthetics
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Mario Livio </div>
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It was Euclid who first defined the <b>Golden Ratio</b>, and ever since people have been fascinated by its extraordinary properties. Find out if beauty is in the eye of the beholder, and how the Golden Ratio crosses from mathematics to the arts. </div>
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<div class="pub_date">November 2002</div>
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<p><i>Mario Livio is a scientist and self-proclaimed "art fanatic" who owns many hundreds of art books. Recently, he combined his passions for science and art in two popular books,</i> The Accelerating Universe<i>, which appeared in 2000, and</i> The Golden Ratio<i>, <a href="/issue22/reviews/book2/index.html">reviewed in this issue of <i>Plus</i></a>. The former book discusses "beauty" as an
essential ingredient in fundamental theories of the universe.<p><a href="https://plus.maths.org/content/golden-ratio-and-aesthetics" target="_blank">read more</a></p>https://plus.maths.org/content/golden-ratio-and-aesthetics#comments22AestheticsFibonacci numbergolden ratioFri, 01 Nov 2002 00:00:00 +0000plusadmin2213 at https://plus.maths.org/contentMaths on the tube
https://plus.maths.org/content/maths-tube
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Keith Moffatt </div>
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<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="https://plus.maths.org/content/sites/plus.maths.org/files/issue17/features/posters/icon.jpg?975628800" /> </div>
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During World Mathematical Year 2000 a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! <b>Keith Moffatt</b> tells us about three of the posters from the series. </div>
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<div class="pub_date">Nov 2001</div>
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<p>Tube travellers may have noticed some of the striking mathematical posters that were designed at the <a href="http://www.newton.cam.ac.uk">Newton Institute</a> for display month-by-month during World Mathematical Year 2000 in trains of the London Underground. Actually, the chance of spotting one in a single tube journey was about one in a hundred, so if you did see one, you could truly say
"This was my lucky day".</p><p><a href="https://plus.maths.org/content/maths-tube" target="_blank">read more</a></p>https://plus.maths.org/content/maths-tube#comments17advection-diffusion equationbutterfly effectchaosdifferential equationFibonacci numberfluid mechanicsgolden ratioLorenz equationsmeteorologystrange attractorFri, 01 Dec 2000 00:00:00 +0000plusadmin2193 at https://plus.maths.org/contentChaos in Numberland: The secret life of continued fractions
https://plus.maths.org/content/chaos-numberland-secret-life-continued-fractions
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John D. Barrow </div>
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One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. <strong>John D. Barrow</strong> explains. </div>
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June 2000
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<p><a href="https://plus.maths.org/content/chaos-numberland-secret-life-continued-fractions" target="_blank">read more</a></p>https://plus.maths.org/content/chaos-numberland-secret-life-continued-fractions#comments11chaoscontinued fractionconvergencegeargolden ratioKhinchin's constantLevy's constantprobability distributionrational approximationWed, 31 May 2000 23:00:00 +0000plusadmin2165 at https://plus.maths.org/contentRectangle triangle problem
https://plus.maths.org/content/rectangle-triangle-problem
<div class="pub_date">September 1997</div>
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<p>You are given a rectangle OABC from which you remove three right-angled triangles leaving a fourth triangle OPQ as shown in the diagram below. <!-- FILE: include/centrefig.html --></p><p><a href="https://plus.maths.org/content/rectangle-triangle-problem" target="_blank">read more</a></p>https://plus.maths.org/content/rectangle-triangle-problem#commentsgolden ratiopuzzleSun, 31 Aug 1997 23:00:00 +0000plusadmin2889 at https://plus.maths.org/content