Why do Fish Have a “Fish Like Geometryâ€‌?

Abstract

Most fish share a common geometry, a streamlined anterior body and a deep caudal fin, connected to each other at a tailbase neck, where the body almost shrinks to a point. This work attempts to explain the reason that fish exhibit this type of geometry. Assuming that the fishlike geometry is a result of evolution over millions of years, or, that bodies of modernday fish have been optimized in some manner as a result of evolution, this work investigates the optimum geometry for a swimming object through existing mathematical optimization techniques to check whether the result obtained is the same as the naturally observed fishlike geometry. In this analysis, the work done by a swimming object is taken as the objective function of the optimization. It is found that a fishlike geometry is in fact obtained mathematically, provided that the appropriate constraints are imposed on the optimization process, which, in turn, provides some clues that explain the reason that fish have a fishlike geometry.