I'm currently engrossed in solving a captivating mathematical problem presented in the context of the Bangladesh Math Olympiad ($2017$). This particular problem delves into the fascinating world of parallelograms and presents an intriguing construction challenge.
Problem Description:
$AEJF$ is a parallelogram, whose base $FJ$ has length $1$. $B, I$ is taken such that the area of $ABF, BFIE, IJE$ are equal. Again, $C, G$ are taken from parallelogram $BFIE$ in a similar way. If, we continue like this, what is the summation of the sides which are on the base of each parallelogram?
As I draw this mathematical journey to a close, the enigma of constructing parallelograms with equi-area triangles still looms large. Despite diligent efforts, I find myself at a mathematical crossroads, unable to discern a clear pattern or solution to this captivating problem. If you can offer any fresh perspectives, additional insights, or a comprehensive solution to decipher the mysteries of this intriguing problem, I would be immensely grateful.
Your expertise and support are invaluable in my quest to unravel the intricacies of this mathematical puzzle. I look forward to your contributions and extend my heartfelt thanks in advance for your assistance in solving this captivating parallelogram construction mystery.