## History, Mathematics

# The Interesting Tale of Bhaskara II

## Learn about the history and contributions of this 12th-century Indian mathematician

India has had a long legacy of mathematicians and mathematical discoveries, but mostly only three mathematicians are known by name — Aryabhatta, Bhaskara II and Brahmagupta. In this article, we will focus on the contributions of Bhaskara II.

He was born in Bijapur, in present-day Karnataka in the 12th century. II is added to his name to not confuse him with a seventh-century astronomer of the same name. His magnum opus was the Siddhanta Siromani (Crown of Treatises), which he published in parts or sections.

One of the most famous sections of the Siddhanta Siromani is called ‘Lilavati’, which contains concepts related to algebra, permutations, and trigonometry, in the form of word problems and sums addressed to his daughter. Most of these word problems were unrealistic and unserious at first glance, some referring to the whereabouts of flocks of geese, but were in fact, framed quadratic algebra equations aimed to confuse students and promote lateral thinking. The book also touched upon the topic of negative and positive numbers and the rules of their operations (i.e. A negative number multiplied by another negative number equals a positive number and so on).

In the book, he also explored the basic principles of division by zero, stating that the resulting number would be infinite. However, he was incorrect in his notion that a/0 * 0 = a.

In another section of the Siddhanta Siromani called the Bijaganita (also spelt as Vijaganita), he propounded that the Rule of Three was the founding principle of both algebra and arithmetic. The Rule of Three is a method of calculating the missing value in a proportion — a:b::c:x — x=b*c/a. He discussed this almost 500 years before European mathematicians did.

Speaking at a World Maths Day event, retired Professor Sudhakar C. Agarkar, said,

“Bhaskaracharya’s works in the field of mathematics aimed at providing solutions to our day-to-day life. His simple way of calculating basic multiplication and square roots help people connect with the subject in an easy format.”

Other contributions by him include the introduction of nomenclature of large multiples of ten. For example, he introduced the word for million (10⁶) as prayuta, long before modern terminology.

He also gave one of the earliest definitions of algebra:* ‘algebra is the analysis of unknown quantities represented by designated signs.’ *He also calculated the volume of the sphere by considering it to be composed of small pyramids and finally calculating it through the method of integration.

Bhaskara II is also famous for being one of the first mathematicians to figure out the second proof of the Pythagoras Theorem and laying the foundations of what is known today as calculus. Unfortunately, much of his works went uncredited, and his name is little-known outside India. However, on the 20th of November in 1981, the ISRO (Indian Space Research Organization) launched a satellite named Bhaskara II in honour of the mathematician.

Note: This is article was earlier submitted as a Mathematics project for the Grade 9 ICSE Board Examinations. It has been abridged, merged, and edited to make it suitable for publication. Also, thanks to Abhimanyu Kapoor for pointing out two mistakes in the article. They have been subsequently changed. The link to the first part of the project is: