A. Zirakzadeh (1) has determined for n = 3 the minimal value of the perimeter length of a polygon A1 A2 … An, where A1, A2, … , An–1, and An divide the perimeter of a convex curve C, of perimeter length l, into n parts of equal length; further he has stated a conjecture concerning the general case. In the following a simpler proof for the case n = 3 is given; the minimum for even values of n, which confirms the conjecture of A. Zirakzadeh, is determined; and a fairly precise estimation for odd values of n, which refutes the conjecture of A. Zirakzadeh, is given. For n = 3 we have the following theorem.