Bhaskaracharya’s astronomical findings on planetary position, occurrence of eclipses and cosmography, written in his treatise titled “Siddhanta Shiromani”, stuns everyone, write MEERA S. SASHITAL.
We are told the period between 500 and 1200 A.D. was the Golden Age of Indian Astronomy. During this golden period an Indian wizard was born who contributed greatly to the conception of Astronomy and Mathematics. He was none other than Bhaskaracharya. He was bestowed an apt title by Ganesh Daivadnya for his genius work in Astronomy and Mathematics calling Bhaskaracharya “Ganakachakra chudamani” which means “a Gem among all the calculators of astronomical phenomena.”
Bhaskaracharya’s ‘Siddhanta Shiromani’ is considered as the pinnacle of all the astronomical works of those 700 years. It can be aptly called the “essence of ancient Indian Astronomy and Mathematics. In the 9th century Brahmagupta’s Brahmasputa Siddhanta was translated in Arabic. These translations proved to be an important event in the history of numbers. The Arabs quickly grasped the importance of Indian Decimal system of numbers. They played a key role in transmitting this system of numbers to Europeans. For a long time Europeans were using Roman numerals but after accepting the Decimal System of numbers, European Mathematicians made remarkable progress in Mathematics, but that was about 500 years A.D. after Bhaskaracharya.
Bhaskaracharya himself, it seems, has written about his birth, his place of residence, his teacher and his education in his Siddhanta Shiromani. Bhaskaracharya’s father named Mahesvara was a Brahmin of Shandilya Gotra, well versed in Shroud (originated from “shut” or “Vedas”) and “Smart (originated from “smut”) Dharma, respected by all and who was an authority in all the branches of knowledge. Bhaskaracharya acquired knowledge at his feet. We also come to know that Bhaskaracharya was a resident of Vijjadveed and that his father taught him Mathematics and Astronomy. Vijjadveed surrounded by the hills of Sahyadri was the centre of learning at the time of Bhaskaracharya.
Bhaskaracharya was born in Shaka 1036 (1114 A.D.) and wrote “Siddhanta Shiromani: when he was 36 years old a feat next to impossible for any other person to achieve. He studied eigh books of Grammar,six texts of Medicine, six books on Yoga, five books of Mathematics, four Vedas, five books on Bharat Shastras and two Mimansas. Bhaskaracharya calls himself a poet and most probably he was a Vedanti, since he has mentoned “Parambrahman” in his verse.
Bhaskaracharya’s name was actually Bhaskara only but the title ‘Acharya’ was added and conferred to mean “Bhaskara the Teacher”. He is also known as Bhaskaracharya II. Bhaskaracharya became the head of the Astronomical Observatory at Ujjain, the leading Mathematical centre in India at that time. Outstanding mathematicians such as Varadamihira and Brahmagupta had worked there and built up strong school of Mathematical astronomy.
In many ways Bhaskaracharya represents the peak of Mathematical knowledge in the 12th century. He reached an understanding of the number systems and solving equation which was not to be achieved in Europe for several centuries. Six works by Bhaskaracharya are known and they are: 1) Lilavati (The Beautiful) which is on Mathematics; 2)Bijaganita (Which is on Algebra); 3) The Siddhanta Shiromani which is in two parts, the first on mathematical astronomy with the second part on the sphere; 4)The Vasanabhasya of Mitaksha which is Bhaskaracharya’s own commentary on the Siddhanta Shiromani; 5) Karana-kutuhala (Calculations of Astronomical Wonders or Brahmatulya which is a simplified version of the Siddhanta Shiromani, and; 6) Vivarana which is a commentary on the Shishyadhividdhidatantra of Lalla.
It is the first three of these works which are the most interesting certainly from the point of view of Mathematics. Given that he was building on the knowledge and understanding of Brahmagupta, it is not surprising that Bhaskaracharya understood about Zero and Negative numbers. However, his understanding went further even that of Brahmagupta. He discovered many new formulae’s, and studied difficult equations and problems.
As we saw, Bhaskaracharya was a born genius and an authority in Mathematics, especially in Algebra and Geometry. His famous works Lilavati and Bijaganita remain unparalleled works by substantiating his profound intelligence. His Astronomical findings on planetary position, occurrence of eclipses and cosmography, written in his treatise titled “Siddhanta Shiromani”, stuns everyone. Lilavati is divided into 13 chapters. It covers branches of Mathematics, Arithmetic, Algebra, Geometry and a part of Trigonometry.
In his book “Surya Siddhant” he wrote on the gravitational force, that helps to keep the planets, the sun and the moon in their respective orbits much before the world could even wake and realize these findings. “KUTTAKA” the Quadratic Indeterminate equations was given by him in 12th century well before the European Mathematicians got it in the 17th century. Brahmagupta in the 7th century developed an “Astronomical Model” using which Bhaskaracharya was able to define “Astronomical Quantities”.
He accurately calculated the time that earth took to revolve around the Sun as 365.2588 days that is a difference of 3 minutes of modern acceptance of 365.2563 days. This was much before Leibniz or Newton could come up with Differential or Integral Calculus and to explain the forces of gravity. He was the first to conceive the Differential Coefficient and Differential Calculus.
There is an interesting story regarding naming his treatise “Lilavati”. It seems Lilavati was the name of Bhaskaracharya’s daughter. While casting her horoscope he discovered that the auspicious time for her wedding would be a particular hour on a certain day. He placed a cup with a small hole at the bottom of the vessel filled with water, arranged so that the cup would sink at the beginning of the propitious hour. When everything was ready and the cup was placed over the vessel, Lilavati suddenly out of curiosity bent over the vessel and a pearl from her dress fell into the cup and blocked the hole in it. The auspicious hour passed without the cup sinking and Bhaskaracharya believed that the way to console his dejected daughter, who now would never get married, was to write a manual of Mathematics in her name.
Bhaskaracharya was a teacher, mathematician and an astronomer. He also headed the Astronomical Observatory in Ujjain that was the learning centre of India. His contribution to Astronomy and Mathematics in the 12th century was unparalleled and significant.
