The Small Octagons of MaximalWidth
Résumé
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 1 4 10+27 √ − − − − − − − √ 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 .