New numerical solutions to Newton's problem of least resistance via a convex hull approach

TL;DR

This paper introduces a convex hull-based numerical method to solve Newton's least resistance problem, revealing symmetric solutions with extremal points on specific curves, enabling highly accurate results.

Contribution

The paper develops a novel convex hull approach for numerically solving Newton's problem, highlighting the structure and symmetry of solutions.

Findings

Solutions exhibit symmetry and extremal points on specific curves

The method achieves high accuracy in solutions

Solutions' structure supports conjectured symmetry

Abstract

We present a numerical method for the solution of Newton's problem of least resistance in the class of convex functions using a convex hull approach. We observe that the numerically computed solutions possess some symmetry. Further, their extremal points lie on several curves. By exploiting this conjectured structure, we are able to compute highly accurate solutions to Newton's problem.