The minimum diameter octagon with unit-length sides: Vincze's wife's octagon is suboptimal

@article{Audet2004TheMD,
  title={The minimum diameter octagon with unit-length sides: Vincze's wife's octagon is suboptimal},
  author={Charles Audet and Pierre Hansen and Fr{\'e}d{\'e}ric Messine and Sylvain Perron},
  journal={J. Comb. Theory, Ser. A},
  year={2004},
  volume={108},
  pages={63-75}
}
This paper answers a query of S. Vincze (Acta Univ. Szeged, Sect. Sci. Math. 12 A (1950) 136–142): find the convex octagon with unit-length sides and minimum diameter. It also shows that the solution is -unique. The proof uses geometric arguments and a global optimization algorithm to solve a nonconvex quadratic program. 
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References

Publications referenced by this paper.
Showing 1-10 of 10 references

On a geometrical extremum problem

  • S. Vincze
  • Acta Sci. Math. Szeged, 12(Leopoldo Fejer et…
  • 1950
Highly Influential
14 Excerpts

The decomposition of the n-sphere and the boundaries of plane convex domains. In Convexity and graph theory (Jerusalem, 1981), volume 87 of North-Holland Math. Stud., pages 209–214

  • D. G. Larman, N. K. Tamvakis
  • 1984
1 Excerpt

Geometrical extrema suggested by a lemma of Besicovitch

  • P. Bateman, P. Erdös
  • Amer. Math. Monthly,
  • 1951
2 Excerpts

Extremale polygone gegebenen durchmessers

  • K. Reinhardt
  • Jahresber. Deutsch. Math. Verein,
  • 1922
1 Excerpt

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