Rogers's proof of Vaaler's theorem

TL;DR

This paper discusses Rogers's 1958 proof of Vaaler's 1979 theorem on cube sections, highlighting its implications and potential for generalizations in geometric analysis.

Contribution

It reveals that Rogers's argument provides a valid proof of Vaaler's theorem and enables new generalizations of the theorem.

Findings

Rogers's proof confirms Vaaler's theorem.

The approach allows for generalizations of the original theorem.

The paper clarifies the connection between Rogers's argument and Vaaler's results.

Abstract

We note that an argument by Rogers (1958) gives a proof of Vaaler's theorem (1979) about sections of the cube and allows certain generalizations of the theorem.