Abstract: | On an arc L of length h, of class Cn, and in Euclidean En, the set of n+1 points (the partition of the arc) P={0, 1 h, , n–1h, h}, 0<1<<n–1<1 determines a simplex Sh(P) inscribed in the arc. For its volume Vh(P) we evaluate lim
and prove that its greatest value is obtained for a unique choice of P=Pcr. The exact values for i from Pcr are found for n=2, 3, 4, 5, 6.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 114–120, 1990. |