Average pace and horizontal chords
History and Overview
2017-02-23 v2
Abstract
We are motivated by a problem about running: If a race was completed in an average pace of P minutes per mile, is there necessarily some mile of the race that was run in exactly P minutes? The answer is no. We explain why, and describe the history of this celebrated problem, known as the Universal Chord Theorem. We also clarify and streamline the proof of a more powerful result by Heinz Hopf from 1937.
Cite
@article{arxiv.1507.00871,
title = {Average pace and horizontal chords},
author = {Keith Burns and Orit Davidovich and Diana Davis},
journal= {arXiv preprint arXiv:1507.00871},
year = {2017}
}
Comments
16 pages including appendix, 6 figures