Exploring a planet, revisited

TL;DR

This paper simplifies Ortega-Moreno's proof of Fejes Tóth's conjecture, which states that evenly spaced great circles passing through poles minimize the maximum distance from any point on a sphere to the nearest circle.

Contribution

It provides a concise simplification of an existing proof confirming the optimal placement of great circles on a sphere.

Findings

Fejes Tóth's conjecture is proven to be true.

Evenly spaced great circles passing through poles are optimal.

The proof is simplified compared to previous versions.

Abstract

How should we place $n$ great circles on a sphere to minimize the furthest distance between a point on the sphere and its nearest great circle? Fejes T\'oth conjectured that the optimum is attained by placing $n$ circles evenly spaced all passing through the north and south poles. This conjecture was recently proved by Jiang and Polyanskii. We present a short simplification of Ortega-Moreno's alternate proof of this conjecture.