A small square is constructed inside a square of area 1 by dividing each side of the unit square into n equal parts, and then connecting the vertices to the division points closest to the opposite vertices. Find the value of n if the the area of the small square is exactly 1/1985.
[asy]
size(200);
pair A=(0,1), B=(1,1), C=(1,0), D=origin;
draw(A--B--C--D--A--(1,1/6));
draw(C--(0,5/6)^^B--(1/6,0)^^D--(5/6,1));
pair point=( 0.5 , 0.5 );
//label("A", A, dir(point--A));
//label("B", B, dir(point--B));
//label("C", C, dir(point--C));
//label("D", D, dir(point--D));
label("1/n", (11/12,1), N, fontsize(9));[/asy] geometryquadraticstrapezoidtrigonometrysimilar triangles