A note on the affine plank conjecture

TL;DR

This paper advances the understanding of the affine plank conjecture by establishing a new lower bound on the total relative width of planks covering a convex body in -dimensional space, improving upon previous bounds.

Contribution

The paper provides a new lower bound of 2/(1+sqrt(d)) for the total relative width in the affine plank conjecture, enhancing previous results.

Findings

New lower bound of 2/(1+sqrt(d)) for the affine plank conjecture

Improved upon the previous bound of 2/(1+d)

Progress towards resolving the affine plank conjecture

Abstract

In 1951, Bang posed the affine plank conjecture, which remains open: If a convex body in $\mathbb{R}^d$ is covered by planks, then the total relative width of the planks is at least one. We prove a lower bound of $2/(1+\sqrt{d})$ for this total relative width. The best previously known lower bound was $2/(1+d)$.