How Arjuna used Algebraic method to kill Karna

Bhāskarāchārya (1114 -1185 CE), has been called the greatest mathematician of medieval India. He was born in Bijapur in Karnataka, and is considered the progenitor of Differential Calculus - 500 years before Newton and Leibniz. Bhāskarāchārya wrote at least four mathematical treatises in Sanskrit. One of them, titled Leelavati, contains many algebra-related teasers in this book, which have become the subject of significant research by scholars. These teasers are in the form of shlokas which pose problems.The shlokas need to be interpreted correctly to decipher the meaning in order to find the solution. Take a look at the shloka displayed in the infographic below. The direct meaning of Basic algebra easily yields the answer to this question, if the equation is formulated correctly.

Let the total number of arrows be X. The statements above can be reduced to the algebraic form X = X/2 + 4√X + 6 + 3 + 1This is the greatness of our ancestors in Sanatana dharma - just one shloka includes so much of knowledge! Bhāskarāchārya (1114 -1185 CE), has been called the greatest mathematician of medieval India.? He is considered the progenitor of Differential Calculus - 500 years before Newton and Leibniz ! Bhāskarāchārya wrote at least four mathematical treatises in Sanskrit.?One of them, titled Leelavati, contains many algebra-related teasers, which have become the subject of significant research by scholars.?These teasers are in the form of shlokas which pose the problems.?The shlokas need to be interpreted correctly to decipher the meaning in order to find the solution. Take a look at the shloka displayed below.?

?????: ???????? ????????? ???????? ??? ????? ?????????? ??????? ???????? ?????????????????? |

????? ??????????????????????? ??????? ????? ????????????????????? ???? ???? ??? ?? ????????? ????????

The direct meaning of this shloka is a question formulated as follows:

During the battle between Arjuna and Karna in the Mahabharata, Arjuna released some arrows. Of the released arrows :

?? Half were consumed in stopping the arrows coming from Karna

?? 4 times the square root of the arrows were consumed to control the horses of Karna's chariot

?? 6 were for gaining control over Shalya, the charioteer of Karna. (Shalya was the maternal uncle of Nakula and Sahadeva)

?? 3 were used to take on the umbrella and flag of the chariot and the bow of Karna.

?? Finally Karna was killed by a single arrow.

So how many arrows were released by Arjuna in the battle ?

Basic algebra easily yields the answer to this question, if the equation is formulated correctly. Let the total number of arrows be X. The statements above can be reduced to the algebraic form

X = X/2 + 4√X + 6 + 3 + 1

Solving the above, we get the value of X=100 for the total number of arrows shot by Arjuna.

However, the fun is not just in getting the algebra right. There is so much hidden information in this shloka. If we pause to think a little deeper about the hidden meanings :

?? Even for an atirathi like Arjuna, it took as many as 50 arrows to stop the arrows of Karna - it tells us about the skills of Karna.

?? That the horses needed 40 arrows to immobilize the chariot tells us about the kind of training given to the horses in the battle field.

?? When even the horses needed 40 arrows, that Shalya the charioteer surrendered with just 6 tells us that he is favouring Arjuna.

?? 3 arrows to take the chariot and the bow shows the helplessness of Karna.

?? Once everything is in control the enemy should vanquished in just a single arrow.

So the rules and skills required to win such a battle operationally?are :?

?? Firstly, stop the enemy fire-power ;?

?? Second, immobilize the enemy by taking on his mobility- the horses and the driver ;?

?? Thirdly signal to him his helplessness by destroying the carriage,?

?? And finally eliminate the enemy himself.

If we analyze the same shloka on the spiritual side :

?? To attain ultimate liberation, firstly one needs to control over his / her personal desires, this being a very difficult task, thus takes 50 arrows.

?? Then take control over 5 senses and sensual pleasures indicated by the horses. The 40 arrows needed to do this indicate the difficulty of the task.

?? Gaining control over 5 senses will lead one to the control over the consciousness (manas, thought, ego) indicated by the driver.

?? If all the foregoing are done, achieving the ultimate liberation (moksha) should be relatively easy.

?? This is the greatness of our ancestors in Sanatana dharma - Vidya integrated with Values.

?? Just a single shloka includes so much of knowledge ! ??

It is because Karna was more efficient than Arjuna is using celestial weapons. This is also evident when Arjuna himself expresses his inability to counter the Bhargavastra of Karna and when Arjuna’s Agneyastra made his own body to light up. The son of Indra then sped at Karna a fiery weapon capable of slaying all foes. Covering the earth and the welkin and the ten points of the compass and the very course of the sun with its effulgence, it caused his own body also to blaze up with light. The robes of all the warriors took fire, at which they fled away. Loud sounds also arose there, like what is heard when a forest of bamboos in a wilderness is on fire. Beholding that fiery weapon acting on all sides, the suta's son Karna of great valour shot in that encounter the varunastra for quenching it. That conflagration then, in consequence of Karna's weapon, became quenched.

The weapon’s power also depends on who uses it, everyone who uses the Pasupatha can’t destroy the universe, if that was the case, then Indrajit’s Pasupatha would have destroyed Rama, Lakshmana and the whole universe but that did not happen, the weapon’s destructive capabilities will be highest only in the hands of the deity, in this case lord Shiva. Vaishnavastra will be more powerful in hands of lord Vishnu, Brahmastra and other Brahma weapons will be more powerful in the hands of Brahma.

“Let me have your permission, that of the gods, Brahma, Bhava and all the ones who are knowledgeable about the brahman.’ Having said this, he invoked the invincible Brahmastra in his mind, in accordance with the prescribed rites. All the directions and sub-directions were covered by extremely energetic arrows. O bull among the Bharat lineage! Many hundreds of swift arrows were released from it. In the midst of this, Vaikartana also created many thousands of arrows.These descended on Pandava with a large roar, like showers of rain released from a cloud. He performed a superhuman deed and pierced Bhimasena, Janardana and Kiriti with three arrows each. Terrible in his strength, he then emitted a loud and fierce roar. Kiriti saw that Bhima and Janardana had also been struck by Karna’s arrows.”

It says Arjuna invoked Brahmastra in his mind and all the directions and sub-directions were covered by extremely energetic arrows. Many hundreds of swift arrows were released from it. Now from Karna side it's written that Vaikartana also created many thousands of arrows. Now we don't have a full description that how karn created these thousands of arrows. Now important point is that simple arrows can never baffle Brahmastra which is so destructive. Secondly it could be the lower Brahmastra too. But I don't think karn baffled Brahmastra from simple arrows. Finally Arjuna used the Algebraic method finally to kill Karna.