
05671724
j
2010b.00545
Griffiths, Martin
The immortal ant and the expanding balloon.
Teach. Math. Appl. 28, No. 3, 150158 (2009).
2009
Oxford University Press, Oxford; Institute of Mathematics and its Applications (IMA), Southendonsea, Essex
EN
I54
I55
M14
M15
calculus
mathematical applications
mathematical models
spheres
integral calculus
doi:10.1093/teamat/hrp009
Summary: In this article we consider, via a specific modelling example, the educational benefits to be gained from running mathematical activities with our sixthform and undergraduate students that, in modern parlance, might be termed `rich tasks'. The idea for this modelling activity arose while the author was reading a popularscience book on cosmology (in particular, on the possible shapes of the universe). Light travelling around the universe was likened to an ant crawling around a balloon. A statement in the book regarding the ant's progress around the balloon did not entirely ring true with the author, and his subsequent investigations led to the activity described here. We explore several scenarios associated with the model in order both to preempt possible paths taken by the students and to be able to provide some guidance when necessary. Suggestions are given as to how the activity may be extended, and then, after highlighting the numerous educational benefits, we consider the potential pitfalls and difficulties associated with the delivery of tasks such as these.