**Theorem 4.3**: (Zeitler
[14]) Let an {n/k} star be placed
in a coordinatized plane in such a way that the center of the star is
at the origin and the polar coordinates of one of the points is (r,
90). Let r_{j} be the distance from the points P_{j}
to the center of the circle. Then

r_{j} = rcos(180k/n)sec(180j/n)

The angle at which the P_{j} points are found is

if j is congruent to k mod 2

and

if j is not congruent to k mod 2

i = 1, . . . , n, j = 1, . . . , k

**proof**: The formulas for the angles follow from the fact
that the angles for the points on the {n/k-1} star are halfway
between the angles for the {n/k} stars and iteration.

If P_{j} is a point on the {n/j} star on the line in the
{n/k} star we have the following figure.

Since P_{k} is a point on an {n/k} star, and O is the
center of the circle, it follows that the angle at O is 180j/n, and
the result follows.