Billiards, invisibility, and perfectly streamlining objects

Abstract

In this paper we shall describe recent applications of billiards in aerodynamics and optics. More precisely, we shall explain how to construct perfectly streamlining bodies in the framework of Newtonian aerodynamics and invisible objects in geometric optics. The methods we shall use are quite elementary and accessible to students of the high school; they include focal properties of curves of the second order and unfolding of a billiard trajectory.