MathDB

In rhombus ABCD,

\angle A = 60^\circ

. Rhombus

BEFG

is constructed, where

E

and

G

are the midpoints of

BC

and

AB

, respectively. Rhombus

BHIJ

is constructed, where

H

and

J

are the midpoints of

BE

and

BG

, respectively. This process is repeated forever. If the area of

ABCD

and the sum of the areas of all of the rhombi are both integers, compute the smallest possible value of

AB

Problem Statement