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Smallest sum of length of edges and diagonals of an integer polygon with n vertices.
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%I #12 Apr 06 2016 09:09:22

%S 3,19,60,90

%N Smallest sum of length of edges and diagonals of an integer polygon with n vertices.

%C An integer polygon is a convex polygon such that the distance between every pair of vertices is an integer (in some length units).

%H B. E. Peterson and J. H. Jordan, <a href="http://www.jstor.org/stable/3618764">Integer geometry: some examples and construction</a>, The Mathematical Gazette, Volume 81, Number 490, 1997, pages 18-28.

%e An equilateral triangle with sides of length 1 has the smallest perimeter. Hence a(3)=3.

%e The integer quadrilateral with the smallest sum of lengths of edges and diagonals is a trapezium with bases of length 3 and 4, legs of length 2 and diagonals of length 4. Hence a(4)=19.

%Y Cf. A096872 for minimum diameter.

%K nonn,more

%O 3,1

%A _Dmitry Kamenetsky_, Feb 20 2016