Why does your headphone cable get tangled?
How might we prevent this with better cable design?
This is a project about applying maths to solve real world problems.
Real world problems of a certain broad type.
(Not necessarily headphone cable tangles, but perhaps something analogous;
or something related, like how to achieve good washing results
by a good design for a washing machine ...)
So, the first question is, what kind of challenge are we going to try
to apply maths to?
-- For definiteness let's think about the cable design problem.
In which case the _aim_ is to design a better (less tangly) cable.
(The project need not actually achieve this aim, but it should try to
take a helpful step in the right direction.)
This challenge is going to start with the problem of understanding _why_ the
cable tangles.
And perhaps even before that, the problem of establishing exactly what
it means to say that the cable tangles!
(It might be a good idea
for a project student or team working in this area
to begin by getting some quantitative
information on real cable tangling -- that is, by doing some
controlled experiments with real cables.
The exact details of the experiment are not
so important here.
The idea is just to get a feel for what really
happens when a cable tangles.)
The next question is: how do we apply maths to help us with this challenge?!
This is the problem of ``mathematical modelling''.
A good place to look for clues is in the way maths already models
knots and tangles -- in the Theory of Knots and Tangles (which
already exists!
See e.g. the book
Introduction to Knot Theory by R H Crowell and R H Fox).
Then we can see if this existing maths can be adjusted to suit our
cable modelling problem.