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The equilateral small octagon of maximal width
- Source :
- Mathematics of Computation. 91:2027-2040
- Publication Year :
- 2022
- Publisher :
- American Mathematical Society (AMS), 2022.
-
Abstract
- A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with n = 2 s n=2^s vertices is not known when s ≥ 3 s \ge 3 . This paper solves the first open case and finds the optimal equilateral small octagon. Its width is approximately 3.24 3.24% larger than the width of the regular octagon: cos ( π / 8 ) \cos (\pi /8) . In addition, the paper proposes a family of equilateral small n n -gons, for n = 2 s n=2^s with s ≥ 4 s\ge 4 , whose widths are within O ( 1 / n 4 ) O(1/n^4) of the maximal width.
- Subjects :
- Computational Mathematics
Algebra and Number Theory
Mathematics - Metric Geometry
Optimization and Control (math.OC)
Applied Mathematics
FOS: Mathematics
Mathematics - Combinatorics
Metric Geometry (math.MG)
Combinatorics (math.CO)
52A40, 52A10, 52B55
Mathematics - Optimization and Control
Subjects
Details
- ISSN :
- 10886842 and 00255718
- Volume :
- 91
- Database :
- OpenAIRE
- Journal :
- Mathematics of Computation
- Accession number :
- edsair.doi.dedup.....173e16916fe128e4303f7fffeafc6034