The largest small octagon is the
octagon
In geometry, an octagon (from the Greek ὀκτάγωνον ''oktágōnon'', "eight angles") is an eight-sided polygon or 8-gon.
A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, whi ...
that has the largest
area among all
convex octagons with unit
diameter. The diameter of a
polygon is the length of the longest segment joining two of its
vertices. 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. The optimal
hexagon was found in 1975 by finding the roots of a degree-10
polynomial.
See also
*
Biggest little polygon
References
External links
2010 Toulouse Global Optimization Workshopat
Wolfram MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science D ...
Combinatorics
Types of polygons
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