ABSTRACT
However, there are many problems of extremisation that cannot be framed in terms of maximising or minimising a function of finitely many variables. Indeed the extremisation problem and its variants that we considered above are simple special cases of a more general problem known as the Isoperimetric Problem. This asks the following question. Amongst all closed curves one could draw on a plane, of fixed total perimeter, which is the one of maximal area. We can see that by no longer restricting oneself to a restricted class of curves (namely, rectangles/parallelograms/quadrilaterals) we have significantly complicated the question. In the former case we had a finite set of variables which characterised the most general member of the class. Hence the problem of extremising the area was one of computing the area as a function of these variables and taking partial derivatives and setting them equal to zero. The solution of the resulting equations gave the answer to the question.
