# Proof of L\'aszl\'o Fejes T\'oth's zone conjecture

## TL;DR

This paper proves that the total width of any collection of zones covering the unit sphere must be at least π, resolving a long-standing question posed by Fejes Tóth in 1973.

## Contribution

It provides a rigorous proof of Fejes Tóth's zone conjecture, establishing a lower bound on the total width of covering zones on the sphere.

## Key findings

- Total width of covering zones on the sphere is at least π
- Answer to Fejes Tóth's 1973 question
- Completes the understanding of spherical zone coverings

## Abstract

A zone of width $\omega$ on the unit sphere is the set of points within spherical distance $\omega/2$ of a given great circle. We show that the total width of any collection of zones covering the unit sphere is at least $\pi$, answering a question of Fejes T\'oth from 1973.