Retour

G-2012-22

The Small Octagons of Maximal Width

, , et

référence BibTeX

The paper answers an open problem introduced by Bezdek and Fodor in 2000. The width of any unit-diameter octagon is shown to be less than or equal to \(\frac{1}{4}\sqrt{10 + 2\sqrt7}\) 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 \(1\times10^{-7}\).

, 14 pages

Axe de recherche

Publication

, , et
Discrete & Computational Geometry, 49(3), 589–600, 2013 référence BibTeX