logarithm
https://plus.maths.org/content/taxonomy/term/335
enThe making of the logarithm
https://plus.maths.org/content/dynamic-logarithms
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Marianne Freiberger </div>
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<p>The natural logarithm is intimately related to the number e and that's how we learn about it at school. When it was first invented, though, people hadn't even heard of the number e and they weren't thinking about exponentiation either. How is that possible?</p>
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[maths]Remember the natural logarithm? It's intimately related to one of the most beautiful constants of mathematics, the number $$e = 2.71828182845904523536028747135266249775724709369995...<p><a href="https://plus.maths.org/content/dynamic-logarithms" target="_blank">read more</a></p>https://plus.maths.org/content/dynamic-logarithms#commentshistory of mathematicslogarithmTue, 14 Jan 2014 10:08:29 +0000mf3446014 at https://plus.maths.org/contentHarder, better, faster, stronger
https://plus.maths.org/content/harder-better-faster-stronger
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Modelling Olympic success </div>
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<div class="pub_date">07/08/2008</div>
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<p>After every Olympics, there is speculation about which country performed best. Should we really be surprised when China, with its huge population, and the US, with its combination of high GDP and population, top the medal table? Can we take a look at the medal tables and see which countries did indeed perform better than expected?</p><p><a href="https://plus.maths.org/content/harder-better-faster-stronger" target="_blank">read more</a></p>https://plus.maths.org/content/harder-better-faster-stronger#commentslogarithmmathematical modellingmathematics in sportolympicsstatistical regressionstatisticsWed, 06 Aug 2008 23:00:00 +0000plusadmin2542 at https://plus.maths.org/contentThe prime number lottery
https://plus.maths.org/content/prime-number-lottery
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Marcus du Sautoy </div>
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Marcus du Sautoy begins a two part exploration of the greatest unsolved problem of mathematics: The <b>Riemann Hypothesis</b>. In the first part, we find out how the German mathematician Gauss, aged only 15, discovered the dice that Nature used to chose the primes. </div>
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<div class="pub_date">November 2003</div>
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<p>David Hilbert</p><p><a href="https://plus.maths.org/content/prime-number-lottery" target="_blank">read more</a></p>https://plus.maths.org/content/prime-number-lottery#comments27Fibonacci numberhilbert problemslogarithmprime numberRiemann hypothesisSat, 01 Nov 2003 00:00:00 +0000plusadmin2237 at https://plus.maths.org/contentIn perfect harmony
https://plus.maths.org/content/perfect-harmony
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John Webb </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/issue12/features/harmonic/icon.jpg?967762800" /> </div>
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The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. <b>John Webb</b> applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way. </div>
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<div class="pub_date">September 2000</div>
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<h2>Introduction</h2>
<p>Two elementary series are studied in school mathematics:</p>
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<li>arithmetic series, such as <img src="/MI/3e35c3a6a00638f7c180b293c8e21feb/images/img-0001.png" alt="$1+2+3+\dots +n$" style="vertical-align:-2px;
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<p>and</p><p><a href="https://plus.maths.org/content/perfect-harmony" target="_blank">read more</a></p>https://plus.maths.org/content/perfect-harmony#comments12arithmetic seriesconvergencedivergencegeometric seriesharmonic serieslogarithmThu, 31 Aug 2000 23:00:00 +0000plusadmin2172 at https://plus.maths.org/contentHave we caught your interest?
https://plus.maths.org/content/have-we-caught-your-interest
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John H. Webb </div>
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Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it - or so says a well-known source of financial advice. But what is compound interest, and why is it so important? <strong>John H. Webb</strong> explains. </div>
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<div class="pub_date">June 2000</div>
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<h2>Introduction</h2>
<center><em>"Neither a borrower nor a lender be."</em></center>
<p>Today, nobody heeds the advice of Polonius to his student son Laertes. Everybody borrows and lends all the time.</p><p><a href="https://plus.maths.org/content/have-we-caught-your-interest" target="_blank">read more</a></p>https://plus.maths.org/content/have-we-caught-your-interest#comments11compound interestdifferential equationfuture valuegeometric serieslogarithmMaclaurin seriespresent valuerule of 70Wed, 31 May 2000 23:00:00 +0000plusadmin2166 at https://plus.maths.org/contentFractal expressionism
https://plus.maths.org/content/fractal-expressionism
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Richard P. Taylor, Adam Micolich and David Jonas </div>
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In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. <strong>Richard P. Taylor</strong> explains that Pollock's patterns are really fractals - the fingerprint of Nature. </div>
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<div class="pub_date">June 2000</div>
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<p><i>Can science be used to further our understanding of art? This question triggers reservations from both scientists and artists. However, for the abstract paintings produced by Jackson Pollock in the late 1940s, the answer is a resounding "yes".</i></p><p><a href="https://plus.maths.org/content/fractal-expressionism" target="_blank">read more</a></p>https://plus.maths.org/content/fractal-expressionism#comments11chaosdimensionfractalLevy flightlogarithmmathematics and artscalingWed, 31 May 2000 23:00:00 +0000plusadmin2167 at https://plus.maths.org/contentLooking out for number one
https://plus.maths.org/content/looking-out-number-one
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Jon Walthoe </div>
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You might think that if you collected together a list of naturally-occurring numbers, then as many of them would start with a 1 as with any other digit, but you'd be quite wrong. <b>Jon Walthoe</b> explains why Benford's Law says otherwise, and why tax inspectors are taking an interest. </div>
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<div class="pub_date">September 1999</div>
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<p>So, here's a challenge. Go and look up some numbers. A whole variety of naturally-occuring numbers will do. Try the lengths of some of the world's rivers, or the cost of gas bills in Moldova; try the population sizes in Peruvian provinces, or even the figures in Bill Clinton's tax return. Then, when you have a sample of numbers, look at their first digits (ignoring any leading zeroes). Count
how many numbers begin with 1, how many begin with 2, how many begin with 3, and so on - what do you find?</p><p><a href="https://plus.maths.org/content/looking-out-number-one" target="_blank">read more</a></p>https://plus.maths.org/content/looking-out-number-one#comments9Benford's Lawdistribution of digitsfraud detectionlogarithmrandomnessscale invariancestatisticsuniform distributionTue, 31 Aug 1999 23:00:00 +0000plusadmin2391 at https://plus.maths.org/contentJackson's fractals
https://plus.maths.org/content/jacksons-fractals
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<p>Combining the computational powers of modern digital computers with the complex beauty of mathematical fractals has produced some entrancing artwork during the past two decades. Intriguingly, recent research at the University of New South Wales, Australia, has suggested that some works by the American artist Jackson Pollock also reflect a fractal structure.</p>
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<div class="pub_date">September 1999</div>
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<p>As recent articles in PASS Maths have shown, combining the computational powers of modern digital computers with the complex beauty of mathematical fractals has produced some entrancing artwork during the past two decades.</p>
<p>Intriguingly, recent research at the Physics Department of the University of New South Wales, Australia, has suggested that some works by the American artist Jackson Pollock also reflect a fractal structure.</p><p><a href="https://plus.maths.org/content/jacksons-fractals" target="_blank">read more</a></p>https://plus.maths.org/content/jacksons-fractals#commentsdimensionfractallogarithmmathematics and artvon Koch curveTue, 31 Aug 1999 23:00:00 +0000plusadmin2675 at https://plus.maths.org/content