9
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<span class="date-display-single">September 1999</span> </div>
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<p>What is the Mandlebrot Set and what are fractals? Why do more numbers in nature start with a 1 than with any other digit? What is Benford's Law? And how were thinkers such as Pythagoras and Newton able to tackle different problems presented to them? This issue explains it all.</p>
9indexTue, 01 Jun 2010 12:18:57 +0000plusadmin5198 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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<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/contentPlus Magazine
http://plus.maths.org/content/plus-magazine-70
<p><a href="http://plus.maths.org/content/plus-magazine-70" target="_blank">read more</a></p>9editorialTue, 31 Aug 1999 23:00:00 +0000plusadmin5174 at http://plus.maths.org/contentLetters
http://plus.maths.org/content/letters-10
<p><a href="http://plus.maths.org/content/letters-10" target="_blank">read more</a></p>9editorialTue, 31 Aug 1999 23:00:00 +0000plusadmin4942 at http://plus.maths.org/contentA student's letter to PASS Maths
http://plus.maths.org/content/students-letter-pass-maths
<p><a href="http://plus.maths.org/content/students-letter-pass-maths" target="_blank">read more</a></p>9staffTue, 31 Aug 1999 23:00:00 +0000plusadmin4857 at http://plus.maths.org/contentCareer interview: Financial modelling
http://plus.maths.org/content/career-interview-financial-modelling
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Mike Pearson </div>
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<p>Was it T.S. Eliot who, asked what advice he would give to an aspiring poet, said "to get a nice steady job in a bank"? David Spaughton works in a bank - but doesn't spend his life behind a counter, explaining why overdrafts can't be exceeded just like that. He works for an Investment Bank - Credit Suisse First Boston - producing and maintaining software for use in futures markets. We
interviewed David in his office at Credit Suisse in London.</p><p><a href="http://plus.maths.org/content/career-interview-financial-modelling" target="_blank">read more</a></p>http://plus.maths.org/content/career-interview-financial-modelling#comments9Black-Scholes equationBusiness & Moneycareer interviewcomputer programmingderivative instrumentfuturemathematical modellingoptionTue, 31 Aug 1999 23:00:00 +0000plusadmin2455 at http://plus.maths.org/contentEditorial
http://plus.maths.org/content/editorial-17
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Robert Hunt </div>
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<li>Ever-increasing standards: a problem of communication?</li>
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<h2>New in this issue</h2>
<p>The PASS Maths <a href="http://plus.maths.org/content/../../%28none%29/index.html">Higher Education Course List</a> has now been fully updated for entry in 2000 by Megan Mills, a sixth-form student at <a href="http://www.impington.cambs.sch.uk/index.html">Impington Village College</a> in Cambridgeshire. This year it includes for each institution a brief description of the mathematics courses offered. We hope you find it
useful.</p><p><a href="http://plus.maths.org/content/editorial-17" target="_blank">read more</a></p>9editorialexaminationsmathematics educationsyllabusTue, 31 Aug 1999 23:00:00 +0000plusadmin4915 at http://plus.maths.org/contentMathematical mysteries: Foucault's pendulum and the eclipse
http://plus.maths.org/content/mathematical-mysteries-foucaults-pendulum-and-eclipse
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<p>You may have seen Foucault's pendulum. There's one in the Science Museum in London (part of the National Museum of Science and Industry), and there are many more in various locations around the UK (for instance, in Glasgow) and the world (including one at the United Nations Headquarters and a famous example at Le Panthéon in Paris).</p>
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<p>You may have seen Foucault's pendulum. There's one in the <a href="http://www.sciencemuseum.org.uk">Science Museum</a> in London (part of the <a href="http://www.nmsi.ac.uk/">National Museum of Science and Industry</a>), and there are many more in various locations around the UK (for instance, in Glasgow) and the world (including one at the <a href="http://www.un.org">United Nations
Headquarters</a> and a famous example at <a href="http://www.paris.org/Monuments/Pantheon/">Le Panthéon</a> in Paris).</p><p><a href="http://plus.maths.org/content/mathematical-mysteries-foucaults-pendulum-and-eclipse" target="_blank">read more</a></p>http://plus.maths.org/content/mathematical-mysteries-foucaults-pendulum-and-eclipse#comments9Mathematical mysteriesTue, 31 Aug 1999 23:00:00 +0000plusadmin4766 at http://plus.maths.org/contentThe origins of proof III: Proof and puzzles through the ages
http://plus.maths.org/content/origins-proof-iii-proof-and-puzzles-through-ages
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Jon Walthoe </div>
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For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. <strong>Jon Walthoe</strong> explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems. </div>
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<p>In the Millennia since Euclid, people's conceptions of mathematical proof have been revolutionised. From the discovery of Calculus and the rise of abstract mathematics, to Gödel's amazing discovery. There have been many changes and a few surprises along the way.</p><p><a href="http://plus.maths.org/content/origins-proof-iii-proof-and-puzzles-through-ages" target="_blank">read more</a></p>http://plus.maths.org/content/origins-proof-iii-proof-and-puzzles-through-ages#comments9axiomcalculusdeductionGödel's Incompleteness Theoreminductionirrational numberparadoxproofrational numberRussell's ParadoxTue, 31 Aug 1999 23:00:00 +0000plusadmin2394 at http://plus.maths.org/contentComputing the Mandelbrot set
http://plus.maths.org/content/computing-mandelbrot-set
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Andrew Williams </div>
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Almost everyone reading this article has no doubt encountered pictures from the Mandelbrot Set. Their appeal is not limited to the mathematician, and their breathtaking beauty has found its way onto posters, T-shirts and computers everywhere. Yet what is a fractal? </div>
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<p align="center"></p><p><a href="http://plus.maths.org/content/computing-mandelbrot-set" target="_blank">read more</a></p>http://plus.maths.org/content/computing-mandelbrot-set#comments9fractalMandelbrot setTue, 31 Aug 1999 23:00:00 +0000plusadmin2393 at http://plus.maths.org/contentExtracting beauty from chaos
http://plus.maths.org/content/extracting-beauty-chaos
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Andy Burbanks </div>
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Images based on Lyapunov Exponent fractals are very striking. <b>Andy Burbanks</b> explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos <em>really</em> is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics. </div>
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<p>There are any number of sites on the World Wide Web dedicated to galleries of computer-generated fractal images. Pictures based on Lyapunov Exponent fractals, such as the one pictured above, are some of the most striking and unusual.</p><p><a href="http://plus.maths.org/content/extracting-beauty-chaos" target="_blank">read more</a></p>http://plus.maths.org/content/extracting-beauty-chaos#comments9bifurcationchaosdynamical systemerrorfractaliterationlogistic mapLyapunov Exponentmathematics and artorbitTue, 31 Aug 1999 23:00:00 +0000plusadmin2392 at http://plus.maths.org/contentLooking out for number one
http://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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<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="http://plus.maths.org/content/looking-out-number-one" target="_blank">read more</a></p>http://plus.maths.org/content/looking-out-number-one#comments9Benford's Lawdistribution of digitsfraud detectionlogarithmrandomnessscale invariancestatisticsuniform distributionTue, 31 Aug 1999 23:00:00 +0000plusadmin2391 at http://plus.maths.org/contentPuzzle page
http://plus.maths.org/content/puzzle-page-102
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<p>From September 1999 onwards, PASS Maths is joining forces with its sister site NRICH to offer many more puzzles changed regularly on the 1st of every month.</p>
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<h2>NRICH: Partners in Puzzles</h2>
<p>From September 1999 onwards, PASS Maths is joining forces with its sister site <a href="http://nrich.maths.org.uk/">NRICH</a> to offer many more puzzles changed regularly on the 1st of every month.</p>
<p>This page will be updated as soon as the new puzzles are published.</p><p><a href="http://plus.maths.org/content/puzzle-page-102" target="_blank">read more</a></p>http://plus.maths.org/content/puzzle-page-102#comments9puzzleTue, 31 Aug 1999 23:00:00 +0000plusadmin2985 at http://plus.maths.org/content