﻿ Technical Articles

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# Some of our technical (but not too technical) articles

## Online articles

On what day of the week were you born? by Burkard Polster and Marty Ross, Plus Magazine (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.

Ringing the changes by Burkard Polster and Marty Ross, Plus Magazine 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 book.

Juggling, maths and a beautiful mind by Burkard Polster, Plus Magazine 52 (September 2009). Learn about the mathematics of juggling. If you are really keen, check out the book or this survey article.

How to make a perfect plane by Burkard Polster and Marty Ross, Plus Magazine (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.

Marching in squares by Burkard Polster and Marty Ross, preprint (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.

## Printed articles

The intersection game by Burkard Polster, Math Horizons April 2015. In this article Burkard ponders some generalisations of the very mathematical game Spot It!

Kenichi Miura's water wheel, or the dance of the shapes of constant width by Burkard Polster, Math. Intelligencer 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 here.

Viviani à la Kawasaki: Take Two by Burkard Polster, Math. Magazine 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 Mathematica animation isosum.cdf which you can open with either Mathematica or the free Wolfram CDF player.

TracTricks by Burkard Polster, Math Horizons (April 2014), 8-9. Teaching the tractrix and the pseudosphere some new tricks.

The Movies Have Your Number by Burkard Polster and Marty Ross, Vinculum vol. 50 no.3 (2013), 4-8. A fun article about mathematical mess-ups in the movies.

Write Your Own Recipe for Rubik's Cube by Burkard Polster, Math Horizons (April 2013), 24-25. Maybe you learned how to "solve" the Cube-now learn how to solve the Cube.

A case of continuous hangover by Burkard Polster, Marty Ross and David Treeby, American Mathematical Monthly (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 n 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.

The mathematics of juggling by Burkard Polster. This article is a survey of the mathematics that goes into modelling juggling. It appeared, translated into Italian, in La Mathematica: Suoni, forme, parola. C. Bartocci and P. Odifreddi (eds.), Einaudi, Torino, 2011.

Minimizing the footprint of your laptop (on your bedside table) by Burkard Polster, Mathematical Intelligencer (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.

Mathematical Rugby by Burkard Polster and Marty Ross, Mathematical Gazette (UK) (November 2010). An article on planning the optimal conversion shot in rugby football. We started thinking about this topic while researching our Age article Hyperbolic League.

Turning the tables: feasting from a mathsnack by Burkard Polster and Marty Ross, Vinculum, 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 Too hot, too cold, just right is also dedicated to this topic.

Mathematical table turning revisited by Bill Baritompa, Rainer Löwen, Burkard Polster and Marty Ross, Mathematical Intelligencer, 29 (2007), 49-58. In this (much) more technical article, we really do turn the table in any conceivable way, elaborating on the Vinculum 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 here. 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 the clip.

How much is a \$5 betting coupon worth? by Marty Ross, Math Horizons (September 2008). In this article Marty reports on a novel probablility paradox that he stumbled across in the Melbourne Casino. Our Maths Masters article How much is half of a free bet worth? is also dedicated to this topic.

What is the best way to lace your shoes? by Burkard Polster, Nature 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 file that was originally submitted to Nature. 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 here. Our Maths Masters article with the same title is also dedicated to this topic.

Mathematical ambigrams 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 book (Eye Twisters). Our Maths Masters article Angels and Demons is also dedicated to this topic.

Irrational Thoughts by Marty Ross, Mathematical Gazette (March 2004). An introduction to irrational numbers. This article was the Mathematical Gazette's "Article of the Year" in 2004.

Variations on a theme in paper folding by Burkard Polster, American Mathematical Monthly 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.

YEA WHY TRY HER RAW WET HAT by Burkard Polster, Mathematical Intelligencer 21 (June 1999), pp. 38-43. A pictorial tour of the smallest perfect universe.

## And ...

... you may also want to check out our books, or our articles on maths education (and other nonsense), or a fairly complete list of Burkard's publications.