Newton's problem of the body of minimal resistance in the class of convex developable functions

We investigate the minimization of Newton's functional for the problem of t he body of minimal resistance with maximal height M > 0 [4] in the class of convex developable functions defined in a disc. This class is a natural ca ndidate to find a (non-radial) minimizer in accordance with the results of [9]. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with n sides centered in the disc, and numerical experime nts indicate that the natural number n greater than or equal to 2 is a non- decreasing function of M. The corresponding functions all achieve a lower v alue of the functional than the optimal radially symmetric function with th e same height M.