Euclid's Muse

Three masses are constrained to lie on the edges of a triangle.  Equal constant force actuators (with force F) are attached to each pair of masses.  When this system finds equilibrium, the potential energy will be at a minimum.  However, the PE in each actuator is simply F times L, where L is the length of the actuator.

Hence minimum PE is achieved when the masses sit at the vertices of the mi…