  A micelle consists of monolayer of lipid molecules containing hydrophilic
head and hydrophobic tail. These amphiphilic molecules in aqueous environment
aggregate spontaneously into monomolecular layer held together due to
hydrophobic effect by weak non-covalent forces. Micelles are flexible surfaces
that show variety of shapes of different topology, but remarkably in mechanical
equilibrium conditions they are spherical in shape. The shape and size of a
micelle are functions of many variables such as lipid concentration,
temperature, ionic strength, etc. Addressing the question, why the shape of
micelles is sphere in mechanical equilibrium conditions, analytically proved to
be a difficult problem. In the following paper we offer the shortest and
elegant analytical proof of micelles spheroidal nature when they are
thermodynamically equilibrated with solvent. The formalism presented in this
paper can be readily extended to any homogenous surfaces, such are vesicles and
membranes.
