Modelling an athletics track
When introducing students to mathematical modelling ideas it is often useful to have them tackle a fairly "well-defined" problem, possibly related to an outside interest, involving the use of traditional mathematical techniques in the solution process. Over the years I have found that such models make them feel "comfortable" and steadily builds up their confidence for participation in the subsequent group discussions about model validity and so on. It is the purpose of this paper to discuss the problem of obtaining measurements to mark out an athletics running track, which I have found to be a very good introductory modelling problem for students. It involves the use of traditional topics in algebra, geometry, trigonometry and, for the 1500-metre race, solving non-linear equations. Parts of the problem could well be suitable for an "investigation" project at A-level or Scottish Higher Grade, the mathematical skills required being at these levels and below. Although at first the problem seems to be well defined, we shall see that there are plenty of discussion points for students in the various model formulations. Some of these points are highlighted and discussed as they arise, whereas others are left for the interested reader to ponder over.