MathDB

The convex polygon

A_1A_2...A_n

is given in the plane. Denote by

T_k

(k \le n)

the convex

k

-gon of the largest area, with vertices at the points

A_1, A_2, ..., A_n

and by

T_k(A+1)

the convex k-gon of the largest area with vertices at the points

A_1, A_2, ..., A_n

in which one of the vertices is in

A_1

. Set the relationship between the order of arrangement in the sequence

A_1, A_2, ..., A_n

vertices: 1)

T_3

and

T_3 (A_2)

T_k

and

T_k (A_1)

T_k

and

T_{k+1}

VI.18