<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <title>Technical Articles</title> <link rel="shortcut icon" href="qed1.png"> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> </head> <body> <p>Back to <a href="http://www.qedcat.com">www.qedcat.com.</a></p> <h1> Some of our technical (but not too technical) articles</h1> <p><font face="Verdana"> <p> <h2> Online articles</a></h2> <p><a href="http://plus.maths.org/issue54/features/polsteross/index.html">On what day of the week were you born?</a> by Burkard Polster and Marty Ross, <i>Plus Magazine</i> (March 2010). Recently we learnt a very impressive trick: tell us the date you were born and we will almost immediately tell you what day of the week that was. In this articles we show you how this is done. This article includes some nice Java applets that you can use for practicing. </p> <p> <a href="http://plus.maths.org/issue53/features/polsteross/">Ringing the changes</a> by Burkard Polster and Marty Ross, <i>Plus Magazine</i> 53 (December 2009). Do you prefer your maths in exotic locations? Then perhaps you should join a band of bell ringers, engaged in the grand old practice of ringing the changes. But what does bell ringing have to do with maths? As we explain in this article, a lot! If you are really keen on the maths involved, there is a fairly technical chapter about mathematical change ringing in Burkard's maths of juggling book <a href="../books.html">book.</a></p><p> <a href="http://plus.maths.org/issue52/features/polster/index.html">Juggling, maths and a beautiful mind</a> by Burkard Polster, <i>Plus Magazine</i> 52 (September 2009). Learn about the mathematics of juggling. If you are really keen, check out the <a href="../books.html">book</a> or this <a href="juggling_survey.pdf">survey article.</a></p> <p><a href="http://plus.maths.org/content/projective-geometry-projective-plane-geometry">How to make a perfect plane</a> by Burkard Polster and Marty Ross, <i>Plus Magazine</i> (August 2010). Two lines in a plane always intersect in a single point ... unless the lines are parallel. This annoying exception is constantly inserting itself into otherwise simple mathematical statements. We explain how to get around the problem. </p> <p><a href="http://arxiv.org/abs/1503.04658">Marching in squares</a> by Burkard Polster and Marty Ross, <i>preprint</i> (March 2015). We put ourselves in the shoes of someone who choreographs routines for bands of marchers and in the process discover a lot of nice mathematics. </p> <h2> Printed articles</h2> <p> <a href="intersectiongame.pdf">The intersection game</a> by Burkard Polster, <i> Math Horizons</i> April 2015. In this article Burkard ponders some generalisations of the very mathematical game <i>Spot It!</i></p> <p> <a href="waterwheel1.pdf">Kenichi Miura's water wheel, or the dance of the shapes of constant width</a> by Burkard Polster, <i> Math. Intelligencer</i> 36 (2014), 30-36. In this article we teach those old shapes of constant width some great new tricks. Comes with some fun animations which live <a href="www.qedcat.com/water_wheel.html">here</a>. </p> <p> <a href="viviani.pdf">Viviani &agrave; la Kawasaki: Take Two</a> by Burkard Polster, <i>Math. Magazine</i> 87 (2014), 280-283. A new take on a great "proof without words" of Viviani's theorem (In an equilateral triangle the sum of the distances from any interior point of the triangle to its three sides is equal to the height of the triangle.) Comes with a nice <i>Mathematica</i> animation <a href="isosum.cdf">isosum.cdf</a> which you can open with either <i>Mathematica</i> or the free Wolfram CDF player. </p> <p><a href="http://www.jstor.org/discover/10.4169/mathhorizons.21.4.18?uid=3737536&uid=2129&uid=2&uid=70&uid=4&sid=21105519232283">TracTricks</a> by Burkard Polster, <i>Math Horizons</i> (April 2014), 8-9. Teaching the tractrix and the pseudosphere some new tricks. </p> <p><a href="vinculum.pdf">The Movies Have Your Number</a> by Burkard Polster and Marty Ross, <i>Vinculum</i> vol. 50 no.3 (2013), 4-8. A fun article about mathematical mess-ups in the movies. </p> <p><a href="http://www.qedcat.com/rubiks_cube/">Write Your Own Recipe for Rubik's Cube</a> by Burkard Polster, <i>Math Horizons</i> (April 2013), 24-25. Maybe you learned how to "solve" the Cube-now learn how to solve the Cube. </p> <p><a href="monthly2.pdf">A case of continuous hangover</a> by Burkard Polster, Marty Ross and David Treeby, <i>American Mathematical Monthly</i> (February 2012). How much of an overhang can we produce by stacking identical rectangular blocks, one on top of the other, at the edge of a table? Most mathematicians know that with <i>n</i> blocks of length 2 we can build a staircase of maximal overhang equal to 1+1/2+1/3+1/4+...+1/n. Since the harmonic series diverges, it follows that this overhang can be arranged to be as large as desired, simply by using a suitably large number of blocks. In this article we consider a continuous analogue of these paradoxical staircases. </p> <p><a href="juggling_survey.pdf">The mathematics of juggling</a> by Burkard Polster. This article is a survey of the mathematics that goes into modelling juggling. It appeared, translated into Italian, in <i>La Mathematica: Suoni, forme, parola. C. Bartocci and P. Odifreddi (eds.), Einaudi, Torino, 2011.</i> <p><a href="http://arxiv.org/abs/0906.0809">Minimizing the footprint of your laptop (on your bedside table)</a> by Burkard Polster, <i>Mathematical Intelligencer</i> (July 2011). Burkard often works on his laptop in bed. When needed, he parks the laptop on the bedside table, where the computer has to share the small available space with a lamp, books, notes, and heaven knows what else; it often gets quite squeezy. Being regularly faced with this tricky situation, it finally occurred to him to determine once and for all how to place the laptop on the bedside table so that its ``footprint'' - the area in which the laptop coincides with the bedside table - is minimal. In this note he gives the solution of this problem, using some very pretty and elementary mathematics. </p> <p><a href="rugby.pdf">Mathematical Rugby</a> by Burkard Polster and Marty Ross, <i>Mathematical Gazette (UK)</i> (November 2010). An article on planning the optimal conversion shot in rugby football. We started thinking about this topic while researching our <i>Age</i> article <a href="http://www.qedcat.com/archive/10.html">Hyperbolic League</a>.</p> </p> <p><a href="http://www.qedcat.com/mathsnacks/table_turning.pdf" target="_blank">Turning the tables: feasting from a mathsnack</a> by Burkard Polster and Marty Ross, <i>Vinculum</i>, 42 (2005), 6-9. We investigate under which conditions a regular rectangular table can be turned on the spot to result in all four feet touching the ground. It turns out that under normal circumstances (continuous, not too slopy ground), this is always possible. So, the next time you are faced with a table or a chair that wobbles, you might try just turning it on the spot to stabilize it. Our Maths Masters article <a href="http://www.qedcat.com/archive/toohot.html">Too hot, too cold, just right</a> is also dedicated to this topic.</p> <p><a href="http://arxiv.org/abs/math/0511490">Mathematical table turning revisited</a> by Bill Baritompa, Rainer L&ouml;wen, Burkard Polster and Marty Ross, <i>Mathematical Intelligencer</i>, 29 (2007), 49-58. In this (much) more technical article, we really do turn the table in any conceivable way, elaborating on the <i>Vinculum</i> article above. This research was reported on TV, radio, and in newspapers around the world. You can watch a video clip of Marty being interviewed on the ABC news <a href="../media.html">here.</a> There was also a movie of a turning table referred to in the article. Since the original link is dead now, here is a new link to <a href="table.mov">the clip</a>. </p> <p><a href="coupon.pdf" target="_blank">How much is a $5 betting coupon worth?</a> by Marty Ross, <i>Math Horizons</i> (September 2008). In this article Marty reports on a novel probablility paradox that he stumbled across in the Melbourne Casino. Our Maths Masters article <a href="http://www.qedcat.com/archive/137.html">How much is half of a free bet worth?</a> is also dedicated to this topic.</p> <p><a href="http://www.nature.com/nature/journal/v420/n6915/abs/420476a.html">What is the best way to lace your shoes?</a> by Burkard Polster, <i>Nature</i> 420, 476 (5 December 2002). The two most popular ways to lace shoes have historically been to use "criss-cross" or "straight" lacing - but are these the most efficient? Burkard demonstrates mathematically that the shortest lacing is neither of these, but instead is a rarely used and unexpected type of lacing known as "bowtie" lacing. However, the traditional favourite lacings are still the strongest. Here is the <a href="lacing.pdf" target="_blank">file</a> that was</i> originally submitted to <i>Nature</i>. This paper was reported on TV, radio, and in newspapers around the world. You can watch a video clip of Burkard being interviewed on the ABC news <a href="../media.html">here</a>. Our Maths Masters article <a href="http://www.qedcat.com/archive/31.html">with the same title</a> is also dedicated to this topic.</p> <p><a href="ambigram.pdf" target="_blank">Mathematical ambigrams</a> by Burkard Polster, Proceedings of the Mathematics and Art Conference 2000, Bond University, 10-12 December 2000, pp. 21-32. A brief introduction into the art of writing words such they can be read in serveral different ways. If you are really keen, check out the <a href="../books.html">book</a> (Eye Twisters). Our Maths Masters article <a href="http://www.qedcat.com/archive/11.html">Angels and Demons</a> is also dedicated to this topic.</p> <p><a href="http://www.m-a.org.uk/resources/tmg/irrational_thoughts.doc" target="_blank">Irrational Thoughts</a> by Marty Ross, <i>Mathematical Gazette</i> (March 2004). An introduction to irrational numbers. This article was the Mathematical Gazette's "Article of the Year" in 2004.</p> <p><a href="paperfolding.pdf" target="_blank">Variations on a theme in paper folding</a> by Burkard Polster, <i>American Mathematical Monthly</i> 111 (January 2004), pp. 39-47. In this article Burkard explores some simple variations on a really neat trick, to approximate rational angles by folding a strip of paper.</p> <p><a href="yea.pdf" target="_blank">YEA WHY TRY HER RAW WET HAT</a> by Burkard Polster, <i>Mathematical Intelligencer</i> 21 (June 1999), pp. 38-43. A pictorial tour of the smallest perfect universe. </p> <h2> And ...</h2> <p>... you may also want to check out <a href="../books.html">our books</a>, or our articles on <a href="http://www.qedcat.com/misc/index.html">maths education (and other nonsense)</a>, or a fairly complete list of <a href="pubs.html">Burkard's publications</a>. </p> <p">Copyright 2004-&#8734; <img src="qed.jpg" width="47" height="46"> All rights reserved. </p> </body> </html>