Bhaskara II is a famous mathematician of ancient India. He was born in 1114 A.D. in the city of Bijapur, Karnataka state, India. Peoples also know him as Bhaskaracharya, which means “Bhaskara the Teacher”. His father name was Mahesvara. By profession he was an astrologer, who taught him mathematics, which he later passed on to his son Loksamudra. In many ways, Bhaskaracharya represents the peak of mathematical knowledge in the 12th century. He reached an understanding of the number systems and solving equations, which was not to be achieved in Europe for several centuries.
Bhaskara II became head of the astronomical observatory at Ujjain, which was the leading mathematical centre in India at that time. It also goes to the credit of Varahamihira and Brahmagupta, the top mathematicians who worked there and built up this school of mathematical astronomy. He wrote six books and but a seventh work, which is claimed to be by him, is thought by many historian to be a late forgery. The topics of his six books are geometry, trigonometry, calculus, algebra arithmetic and astronomy. The six works are Lilavati (The Beautiful) on mathematics; Bijaganita (Root Extraction) on algebra; the siddhanta shiromani which is divided into two parts: mathematical astronomy and sphere; the Vasanabhasya of Mitaksara which is Bhaskaracharya’s views on the Siddhantashiromani; the Karanakutuhala (Calculation of Astronomical Wonders) or Brahmatulya in which he simplified the concepts of Siddhantashiromani; and the Vivarana which comments on the Shishyadhividdhidatantra of Lalla. From the mathematical point of view, the first three of these works are the most interesting.
Bhaskara II also wrote Siddhanta Shiromani at the age of 36 in 1150 A.D. This colossal work has divided into four categories Goladhyaya, Ganitadhyaya, Lilavati and Bijaganita and consists of about 1450 verses. Each and every categories of the book consigns of huge number of verses. Each of them can be considered as a separate book, Lilavati has 278 verses, Bijaganita has 213 verses, Ganitadhyaya has 451 verses, and Goladhyaya has 501 verses. He formulated simple ways of calculations from Arithmetic to Astronomy in this book. He wrote Lilavatis an excellent lucid and poetic language. It has been translated in various languages throughout the world. In English, the multiples of 1000 are termed as thousand, million, billion, trillion, quadrillion etc. These terms were named recently in English, but Bhaskaracharya gave the terms for Numbers in multiples of ten, which are as follows:
Eka (1), dasha (10), shata (100), sahastra (1000), ayuta (10000), laksha (100000), prayuta (1,000,000 = million), koti (107), arbuda (108), abja (109=billion), kharva (1010), nikharva (1011), mahapadma (1012=trillion), Shankh (1012), Jaladhi (1014), antya (1015=quadrillion), Madhya (1016) and parardha (1017).
The Siddhanta siromani too enjoyed great popularity. Bhaskara II calculated the equinoctial shadow at any place and the new corrections to be applied to the calculation of the time of sunrise. Bhaskara too accepted the precession of the equinoxes, through later astronomers allowed Bhaskara’s correct theory to be perverted. All this shows beyond doubt that Bhaskara was blessed with a remarkably active brain. Bhaskara’s works have served as reference books in every nook and corner of India. He died in 1185 in Ujjain, India.
BY BRAJ KISHOR SINGH