Juggling The Numbers Is More A Colorful Science Than An Art
The Age
Tuesday January 11, 2000
As they toss aloft balls, flaming torches and fruit, jugglers are doing more than merely entertaining - they are making an important contribution to mathematical theory, says a maths expert.
From colored balls to colored maps, the Maths 2000 Festival, on in Melbourne this week, heard yesterday how car crashes and countries-by-color could be used to examine mathematical theory.
The festival began shakily when chanting student protesters drove the federal Education Minister, Dr David Kemp, from the stage during his opening speech. But, organisers said, the protest was orderly and Dr Kemp soon returned to the stage.
The festival is part of Unesco's World Mathematical Year celebrations. It aims to simplify mathematics and show those for whom arithmetic is an impenetrable mystery how it can be used in daily life.
Yesterday, Sergeant Peter Bellion of Victoria Police's accident investigation section, discussed mathematical formulae and their importance in reconstructing car crashes. Equipped with illustrations, Sergeant Bellion showed how accident investigators could work out the hows and whys and speed of a crash.
``We use mathematics day in and day out," he said. ``If there's no independent witnesses we can analyse what's left on the roadway and find out what's happened."
Professor Derek Holton, of the University of Otago, New Zealand, challenged festival-goers to guess how many colors were needed to color a map, regardless of its complexity. The answer? Four.
Professor Holton explained the Four Color Theorem and its premise that only four colors are needed to color a world map so that adjacent countries are never the same color.
Later this week, Dr Sandra Britton will discuss how the intricate patterns created by jugglers as they toss chainsaws, flaming torches and fruit have prompted interest in a mathematical idea called swap-site notation.
Dr Britton, a lecturer in mathematics and statistics at Sydney University, will demonstrate that cascades, fountains and showers (juggling techniques, not descriptions of water flow) have a basis in maths, specifically, site-swap notation.
``Site swaps are finite sequences of integers (positive or negative whole numbers) which are used to describe juggling patterns," she said. ``Not only has the notation led to the invention of some new juggling patterns, but site swaps have some very interesting mathematical properties.
``Juggling involves tossing and catching objects in a way that forms a periodic, visually pleasing pattern. Mathematicians are, of course, generally very fond of patterns, and it is these periodic juggling patterns which form the basis of the pure mathematical theory."
Dr Britton said site-swap notation had become a talking point among jugglers. It had helped them wow audiences with their intricate juggling patterns.
© 2000 The Age