  A parallel flow of non-interacting point particles is incident on a body at
rest. When hitting the body's surface, the particles are reflected elastically.
Assume that each particle hits the body at most once (SIC condition); then the
force of resistance of the body along the flow direction can be written down in
a simple analytical form.
  The problem of minimal resistance within this model was first considered by
Newton (1687) in the class of bodies with a fixed length M along the flow
direction and with a fixed maximum orthogonal cross section, under the
additional conditions that the body is convex and rotationally symmetric. Here
we solve the problem (first stated by Ferone, Buttazzo, and Kawohl in 1995) for
the wider class of bodies satisfying SIC and with the additional conditions
removed. The scheme of solution is inspired by Besicovitch's method of solving
the Kakeya problem. If the maximum cross section is a disc, the decrease of
resistance as compared with the original Newton problem is more than twofold;
the ratio tends to 2 as M goes to 0 and to 81/4 as M goes to infinity. We also
prove that the infimum of resistance is 0 for a wider class of bodies with both
single and double impacts allowed.
