  Traditionally, the duality between Wilson loops and amplitudes beyond one
loop in N=4 SYM is characterised by the remainder function. Because of the
perturbative origins of the BDS expression, the remainder function is more
natural at weak than at strong coupling. We advocate instead a more direct
approach, based on considering ratios of Wilson loops. This allows us to define
a manifestly finite, regularisation independent, conformally invariant
quantity. It does not make a direct reference to the BDS expression and the
definition is regularisation independent. It is a natural object at weak and at
strong coupling, and in the latter case is directly related to the free energy
of an auxiliary integrable system. We then compute these ratios for continuous
families of regular polygons for 6,8 and 10 points at one and two-loops. These
results are compared to expressions derived recently at strong coupling.
