The Small Octagons of Maximal Width

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 $$\frac{1}{4}\sqrt{10 + 2\sqrt{7}}$$ 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 $$1\times 10^{-7}$$.

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