Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The equilateral small octagon of maximal width
HTML articles powered by AMS MathViewer

by Christian Bingane and Charles Audet HTML | PDF
Math. Comp. 91 (2022), 2027-2040 Request permission

Abstract:

A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with $n=2^s$ vertices is not known when $s \ge 3$. This paper solves the first open case and finds the optimal equilateral small octagon. Its width is approximately $3.24%$ larger than the width of the regular octagon: $\cos (\pi /8)$. In addition, the paper proposes a family of equilateral small $n$-gons, for $n=2^s$ with $s\ge 4$, whose widths are within $O(1/n^4)$ of the maximal width.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2020): 52A40, 52A10, 52B55
  • Retrieve articles in all journals with MSC (2020): 52A40, 52A10, 52B55
Additional Information
  • Christian Bingane
  • Affiliation: Département de mathématiques et de génie industriel, Polytechnique Montréal, Montreal, Quebec H3C 3A7, Canada
  • ORCID: 0000-0002-1980-5146
  • Email: christian.bingane@polymtl.ca
  • Charles Audet
  • Affiliation: Département de mathématiques et de génie industriel, Polytechnique Montréal, Montreal, Quebec H3C 3A7, Canada
  • MR Author ID: 619525
  • ORCID: 0000-0002-3043-5393
  • Email: charles.audet@polymtl.ca
  • Received by editor(s): August 12, 2021
  • Received by editor(s) in revised form: January 5, 2022
  • Published electronically: March 30, 2022
  • Additional Notes: This work was financed by the IVADO Fundamental Research Projects Grant PRF-2019-8079623546
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 2027-2040
  • MSC (2020): Primary 52A40, 52A10, 52B55
  • DOI: https://doi.org/10.1090/mcom/3733
  • MathSciNet review: 4435955