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The Small Octagons of MaximalWidth
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 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 .
https://hal.archives-ouvertes.fr/hal-00847250
Contributeur : Annick Billon-Coat <>
Soumis le : mardi 23 juillet 2013 - 10:45:15
Dernière modification le : vendredi 27 novembre 2020 - 09:34:05
Contributeur : Annick Billon-Coat <>
Soumis le : mardi 23 juillet 2013 - 10:45:15
Dernière modification le : vendredi 27 novembre 2020 - 09:34:05
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