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Audet, Charles; Hansen, Pierre; Messine, Frédéric; Ninin, Jordan
Discrete & computational geometry, 04/2013, Letnik: 49, Številka: 3Journal Article
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 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 .
