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Article Dans Une Revue Discrete and Computational Geometry Année : 2013

The Small Octagons of MaximalWidth


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 .

Dates et versions

hal-00847250 , version 1 (23-07-2013)



Charles Audet, Pierre Hansen, Frédéric Messine, Jordan Ninin. The Small Octagons of MaximalWidth. Discrete and Computational Geometry, 2013, 49 (3), pp.589-600. ⟨10.1007/s00454-013-9489-x⟩. ⟨hal-00847250⟩
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