  Despite being a major component in the teaching of special relativity, the
twin `paradox' is generally not examined in courses on general relativity. Due
to the complexity of analytical solutions to the problem, the paradox is often
neglected entirely, and students are left with an incomplete understanding of
the relativistic behaviour of time. This article outlines a project, undertaken
by undergraduate physics students at the University of Sydney, in which a novel
computational method was derived in order to predict the time experienced by a
twin following a number of paths between two given spacetime coordinates. By
utilising this method, it is possible to make clear to students that following
a geodesic in curved spacetime does not always result in the greatest
experienced proper time.
