@article{aud-han-mes-nin-13-aa-octagon,
  author = {Audet, Charles and Hansen, Pierre and Messine, Fr{\'e}d{\'e}ric and Ninin, Jordan},
  title = {The Small Octagons of Maximal Width},
  journal = {Discrete {\&} Computational Geometry},
  year = 2013,
  volume = {49},
  pages = {589-600},
  month = mar,
  doi = {10.1007/s00454-013-9489-x},
  comment = {AA used to solve a problem of pure mathematics.},
  abstract = {The paper answers an open problem introduced by Bezdek and Fodor (Arch. Math. 74:75–80, 2000). The width of any unit-diameter octagon is shown to be less than or equal to $\frac{1}{4}\sqrt{10+2\sqrt{7}}$ and there are infinitely many small octagons having this optimal width. The proof combines geometric and analytical reasoning as well as the use of a recent version of the deterministic and reliable global optimization code IBBA based on interval and affine arithmetics. The code guarantees a certified numerical accuracy of $1×10^{-7}$.}
}