The Small Octagon with Longest Perimeter

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BibTeX reference

The convex octagon with unit diameter and maximum perimeter is determined. This answers an open question dating from 1922. The proof uses geometric reasoning and an interval arithmetic based global optimization algorithm to solve a series of non-linear and non-convex programs involving trigonometric functions.

, 24 pages

Research Axis


The small octagon with longest perimeter
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Journal of Combinatorial Theory, 114(1), 135–150, 2007 BibTeX reference