Largest Small Polygon nco LANCELOT AMPL short 0; set I := 1..N; param pi := 4*atan(1.); var rho{i in I} <= 1, >= 0 # polar radius (distance to fixed vertex) := 4*i*(N + 1 - i)/(N+1)**2; var the{i in I} >= 0 # polar angle (measured from fixed direction) := pi*i/N; s.t. cd{i in I, j in i+1 .. N}: rho[i]**2 + rho[j]**2 - 2*rho[i]*rho[j]*cos(the[j]-the[i]) <= 1; s.t. ac{i in 2..N}: the[i] >= the[i-1]; s.t. fix_theta: the[N] = pi; s.t. fix_rho: rho[N] = 0; maximize area: .5*sum{i in 2..N} rho[i]*rho[i-1]*sin(the[i]-the[i-1]); ]]> data; param N := 6; This model is based on pgon.mod available from http://www.netlib.org/ampl/models/ The model computes the maximum area for unit-diameter polygon of N sides. The model started as a GAMS model by Francisco J. Prieto.