@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 $1×10^{-7}$.} }