The great Mahabharata epic and the stories it contains have always fascinated me since my childhood. However, my rooting interest lies on the concept of Chakravyuh, the multi-tiered war formation, known for its tactics and invincibility. And I was surprised to see the applications of mathematics, which we often tend to limit to the numbers and alphabets we scribble on our notebooks.

Joining the dots between a few mathematical concepts and research online, I came to a conclusion that breaching the Chakravyuh involves deep understanding of the logical approaches and specific calculations of speed, distance and time.

The formation of the Chakravyuh was designed as a spinning wheel (hence the “chakra” in the name) and a puzzle (hence the “vyuh”), with the formation in a constant state of rotation; the rotation may be seen as the motion of the helix of a screw. Warriors in unison keep rotating in the same direction, same speed and same distance per unit time (the exact numerical value cannot be determined due to lack of authentic information), distracting the attacker(s) from concentrating on the fixed target.

Secondly, even if the attacker successfully manages to kill the man in front of him, his position would be instantly taken over by another man to his right, thereby making a breach into the Chakravyuh impossible. The trick that Abhimanyu, the son of Arjuna, probably used was that he killed the warriors on left and right of the warrior in front of him, creating a movement of soldiers to cover up the gaps, but for a brief period.

In that precise moment, Abhimanyu then entered the Chakravyuh, eventually leading reaching the centre. Now the question arises why couldn’t Abhimanyu exit the Chakravyuh the way he entered it? Keeping an eye on the sun to navigate the direction, while entering, Abhimanyu could estimate the mensuration and direction of the spiral.

By the time he reached the centre, the Chakravyuh sort of lost its shape and accuracy and the whole formation broke, leaving Abhimanyu alone against the onslaught of warriors from the opponent’s side. Abhimanyu was killed by the Kauravas.

I wonder what if Subhadra had not fallen asleep so that the little Abhimanyu in his mother’s womb could have understood this little concept of correlating time and direction.