MathDB

Given a natural number

n> 3

. On the plane are considered convex

n

- gons

F_1

and

F_2

such that on each side of

F_1

lies one vertex of

F_2

and no two vertices

F_1

and

F_2

coincide. For each

n

, determine the limits of the ratio of the areas of the polygons

F_1

and

F_2

. For each

n

, determine the range of the areas of the polygons

F_1

and

F_2

, if

F_1

is a regular

n

-gon. Determine the set of values of this value for other partial cases of the polygon

F_1

Problem Statement