G-2012-22
The Small Octagons of Maximal Width
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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 \(1\times10^{-7}\)
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Published May 2012 , 14 pages
Research Axis
Publication
Apr 2013
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Discrete & Computational Geometry, 49(3), 589–600, 2013
BibTeX reference