The exact value of the area of the largest small octagon lies between 0.72686845 and 0.72686849, and is approximately 2.8% larger than the area of the regular octagon. This octagon was found in 2002 using global optimization algorithms.
Abstract. Thrackleation of graphs and global optimization for quadratically constrained quadratic programming are used to find the octagon with unit diameter ...
Geometry · Computational Geometry · General Computational Geometry · Applied Mathematics · Optimization. Largest Small Octagon. See. Biggest Little Polygon.
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The convex octagon with unit diameter and maximum perimeter is determined. This answers an open question dating from 1922. The proof uses geometric ...
Thrackleation of graphs and global optimization for quadratically constrained quadratic programming are used to find the octagon with unit diameter and ...
Feb 11, 2002 · of the octagon. The largest small octagon is 2.78% larger than the regular octagon. This percentage is less than the case of the hexagon (4 ...
This paper solves the first open case and finds the optimal equilateral small octagon. Its width is approximately 3.24% larger than the width of the regular ...
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Graham's biggest little hexagon is the largest possible (not necessarily regular) convex hexagon with polygon diameter 1 (i.e., for which no two of the ...
The aim of this paper is the determination of the largest $n$-dimensional polytope with $n+3$ vertices of unit diameter. This is a special case of a more ...