ABSTRACT
Often, algebraic inequalities can be interpreted as potential energy of a system. In this case, the constant in the right-hand side of the inequality effectively represents the system state of stable equilibrium which corresponds to a minimum potential energy. From the equilibrium conditions that correspond to the stable equilibrium, a number of useful relationships can be derived and the unknown lower bound determined without resorting to complex models. The meaningful interpretation in terms of potential energy is based on the concepts ‘potential energy of a constant-tension spring’ and ‘potential energy of a non-linear spring’. Among the presented results from this type of interpretation are (i) a general necessary condition for minimising the sum of powers of distances to a fixed number of points in space, (ii) a necessary condition for minimising the sum of distances to various geometrical objects and (iii) a necessary condition for determining the lower bound of the sum of squares of two quantities.
Finally, a treatment based on potential energy has been discussed, of a general case involving a monotonic convex function.
