MathDB

Let

A_1

A_2

A_3

be three points in the plane, and for convenience, let

A_4= A_1

A_5 = A_2

. For

n = 1

2

, and

3

, suppose that

B_n

is the midpoint of

A_n A_{n+1}

, and suppose that

C_n

is the midpoint of

A_n B_n

. Suppose that

A_n C_{n+1}

and

B_n A_{n+2}

meet at

D_n

, and that

A_n B_{n+1}

and

C_n A_{n+2}

meet at

E_n

. Calculate the ratio of the area of triangle

D_1 D_2 D_3

to the area of triangle

E_1 E_2 E_3

3