Arjuna’s Arrows, a timeless Indian mythological narrative, weaves together elements of valour, strategy, and divine intervention. Yet, nestled within its fabric lies a fascinating dimension seldom explored: the infusion of algebraic principles into the very essence of its weaponry. This tale, resonating through generations, not only captivates with its heroic exploits but also offers a glimpse into the creative potential of mathematical abstraction.

At the heart of this saga is Arjuna, endowed with celestial weaponry by the god Indra, including a bow and arrows of extraordinary potency. Among these, the arrows possess a remarkable ability to multiply themselves through the application of algebraic equations. Each arrow, upon release, undergoes a transformation dictated by mathematical formulas meticulously crafted by Arjuna and his mentor, Drona. These equations govern the behaviour of the arrows, determining their trajectory, impact, and even their multiplication upon contact with the enemy.

This multiplication effect is achieved through the use of algebraic equations. Each arrow is imbued with a specific mathematical formula that allows it to divide and multiply at will. For example, one arrow might be programmed to split into three smaller arrows upon impact, while another might split into five. These equations are carefully crafted by Arjuna and his guru, Drona, to ensure maximum effectiveness on the battlefield.

Delving into the core of this narrative unveils the intersection of mathematics and myth. Algebra, the language of equations and variables, becomes the tool through which Arjuna orchestrates his battlefield prowess. Through algebraic manipulation, Arjuna and Drona optimize the performance of each arrow, leveraging principles from trigonometry to calculus to achieve their desired outcomes.

But how exactly does algebra come into play here? To understand this, we need to delve into the basics of algebraic equations. An equation is simply a mathematical statement that shows the relationship between two or more variables. In the case of Arjuna’s arrows, these variables are things like distance, angle, and velocity.

By manipulating these variables, Arjuna and Dronacharya were able to create equations that dictated how the arrows would behave. For example, they might use trigonometry to calculate the optimal angle at which to fire an arrow for maximum impact. Or they might use calculus to determine the exact trajectory of an arrow as it travels through the air.

The beauty of algebra is that it allows us to express complex relationships in a simple and elegant way. By using equations, we can distill complicated concepts down to their most basic components and manipulate them to achieve our desired outcome. This is exactly what Arjuna and Drona do with their arrows.

The narrative also invites us to reflect on the historical context of mathematics in ancient India. Bhaskaracharya, a luminary of the 12th century, stands as a testament to India’s rich mathematical heritage. His seminal work, Siddhanta Shiromani, not only delved into astronomical calculations but also laid the groundwork for principles akin to modern differential calculus. The legacy of Bhaskaracharya underscores the profound contributions of Indian mathematicians to the evolution of mathematical thought.

Bhaskaracharya is particularly known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhaskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential calculus.

His main work Siddhanta Shiromani, (Sanskrit for “Crown of treatises,“) is divided into four parts called Leelavati (beautiful woman, named after his daughter Leelavati), Bijaganita, Grahaganita (mathematics of planets) and Goladhyaya (study of sphere/earth). These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karna Kautoohala.

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.

पार्थ: कर्णवधाय मार्गणगणं क्रुद्धो रणे संदधे 
तस्यार्धेन निवार्य तच्छरगणं मूलैश्चतुभिर्हयान् |
शल्यं षड्भिरथेषुभिस्त्रिभिरपि च्छत्रं ध्वजं कार्मुकम् 
चिच्छेदास्य शिरः शरेण कति ते यानर्जुनः संदधे || ७६ ||

The 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; and
• 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 this, we get the value of X=100 for the total number of arrows shot by Arjuna.

Of course, it’s important to note that the algebra used in Arjuna’s arrows is purely fictional. While there is certainly a rich tradition of mathematics in Indian culture, the idea of arrows multiplying themselves through algebraic equations is purely mythological. Nevertheless, the story serves as a powerful reminder of the incredible potential of mathematics and its ability to shape our world in ways we never thought possible.

So, what can we learn from Arjuna’s arrows? For one thing, it shows us that mathematics is not just an abstract concept relegated to textbooks and classrooms. It has real-world applications and can be used to solve practical problems, even on the battlefield. But perhaps more importantly, it reminds us that there is beauty in mathematics. The elegant simplicity of algebraic equations can be just as awe-inspiring as any work of art or piece of music.

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

• even for an Atirathi like Arjuna, it took as many as 50 arrows to stop the arrows of Karna – reflecting upon the skills of Karna. An Atirathi is a warrior capable of contending with 12 Rathi class warriors or 60,000 warriors simultaneously, circumspect in his mastery of all forms of weapons and combat skills.
• that the horses needed 40 arrows to immobilize the chariot tells us about the kind of training given to the horses in the battlefield.
• when even the horses needed 40 arrows, 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; and
• once everything is in control the enemy should vanquished in just a single arrow.

It is essential to recognize the mythical nature of Arjuna’s arrows. While rooted in a culture that revered mathematics, the story transcends the boundaries of reality, weaving mathematical concepts into the fabric of legend. Nevertheless, it serves as a poignant reminder of the pervasive influence of mathematics across human imagination.

Beyond its mythical allure, Arjuna’s arrows beckon us to contemplate the broader implications of mathematical prowess. Mathematics, often perceived as an abstract discipline, finds practical manifestation in the most unexpected realms, even on the battlefield. Moreover, the elegance of algebraic equations, akin to the beauty of art or music, underscores the aesthetic allure inherent in mathematical abstraction.

The tale of Arjuna’s arrows transcends its mythological origins to offer profound insights into the symbiotic relationship between mathematics and human creativity. While the arrows may be a figment of imagination, their narrative underscores the boundless potential of mathematical abstraction to shape narratives, inspire minds, and unveil new vistas of possibility. So, let us heed the lessons of Arjuna’s arrows, embracing the elegance of algebraic equations as a gateway to unlock the mysteries of our world.