Bhaskara is also known as Bhaskara II or as Bhaskaracharya, this latter name meaning "Bhaskara the Teacher". Since he is known in India as Bhaskaracharya we will refer to him throughout this article by that name. Bhaskaracharya's father was a Brahman named Mahesvara. Mahesvara himself was famed as an astrologer. This happened frequently in Indian society with generations of a family being excellent mathematicians and often acting as teachers to other family members.
Bhaskaracharya became head of the astronomical observatory at Ujjain, the leading mathematical centre in India at that time. Outstanding mathematicians such as Varahamihira and Brahmagupta had worked there and built up a 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 equations which was not to be achieved in Europe for several centuries.
Six works by Bhaskaracharya are known but a seventh work, which is claimed to be by him, is thought by many historians to be a late forgery. The six works are: Lilavati(The Beautiful) which is on mathematics; Bijaganita(Seed Counting or Root Extraction) which is on algebra; the Siddhantasiromani which is in two parts, the first on mathematical astronomy with the second part on the sphere; the Vasanabhasya of Mitaksara which is Bhaskaracharya's own commentary on the Siddhantasiromani ; the Karanakutuhala(Calculation of Astronomical Wonders) or Brahmatulya which is a simplified version of the Siddhantasiromani ; and the 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, and we will concentrate on the contents of these.
Given that he was building on the knowledge and understanding of Brahmagupta it is not surprising that Bhaskaracharya u
Bhaskara I, also known as Bhaskara Acharya or Bhaskara the First, was a 7th-century Indian mathematician and astronomer. He was born in 600 CE in the town of Vijjadavida, near present-day Bijapur in Karnataka, India. Bhaskara I is often considered one of the earliest mathematicians and astronomers in Indian history. Celebrated for his significant contributions to mathematics, he is particularly known for pioneering the Hindu decimal system. As a devoted follower of Aryabhata, Bhaskara wrote a critique titled 'Aryabhatiyabhasya' in 629 CE, considered the oldest Sanskrit work in the fields of mathematics and astronomy.
The works of Bhaskara I are not as well-documented or preserved as those of later Indian mathematicians, and much of his contributions are inferred from references in later texts. One of the main works attributed to Bhaskara I is the "Mahabhaskariya," a commentary on the Brahmasphutasiddhanta, which was originally written by Brahmagupta. Comprising 8 chapters, 'Mahabhaskariya' delves into mathematical astronomy, exploring the correlation between cosine and sine and presenting an approximation formula for sin x. The book also addresses planetary longitudes, planetary conjunctions, solar and lunar eclipses, celestial bodies, lunar crescents, risings, and settings. Additionally, it elucidates the relationship between the sine of angles greater than 90°, 180°, or 270° and those less than 90°. Bhaskara I is credited with providing the Pell Equation (8x² + 1 = y²).
Bhaskara I's legacy is, to some extent, overshadowed by the works of later Indian mathematicians, such as Brahmagupta and Bhaskara II. Bhaskara I's influence is often acknowledged through references and commentaries made by later scholars who valued and built upon his contributions to the field of mathematics and astronomy.
Bhāskara I
Indian mathematician and astronomer (600-680)
For others with the same name, see Bhaskara (disambiguation).
Bhāskara (c. 600 – c. 680) (commonly called Bhāskara I to avoid confusion with the 12th-century mathematicianBhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work. This commentary, Āryabhaṭīyabhāṣya, written in 629, is among the oldest known prose works in Sanskrit on mathematics and astronomy. He also wrote two astronomical works in the line of Aryabhata's school: the Mahābhāskarīya ("Great Book of Bhāskara") and the Laghubhāskarīya ("Small Book of Bhāskara").
On 7 June 1979, the Indian Space Research Organisation launched the Bhāskara I satellite, named in honour of the mathematician.
Biography
Little is known about Bhāskara's life, except for what can be deduced from his writings. He was born in India in the 7th century, and was probably an astronomer. Bhāskara I received his astronomical education from his father.
There are references to places in India in Bhāskara's writings, such as Vallabhi (the capital of the Maitraka dynasty in the 7th century) and Sivarajapura, both of which are in the Saurastra region of the present-day state of Gujarat in India. Also mentioned are Bharuch in southern Gujarat, and Thanesar in the eastern Punjab, which was ruled by Harsha. Therefore, a reasonable guess would be that Bhāskara was born in Saurastra and later moved to Aśmaka.
Bhāskara I is considered the most important scholar of Aryabhata's astronomical school. He and Brahmagupta are two of the most renowned Indian mathematicians; both made considerable contributions to the study of fractions.
Repr
Bhāskara II
Indian mathematician and astronomer (1114–1185)
Not to be confused with Bhāskara I.
Bhāskara II
Statue of Bhaskara II at Patnadevi
Born
c. 1114
Vijjadavida, Maharashtra (probably Patan in Khandesh or Beed in Marathwada)
Died
c. 1185(1185-00-00) (aged 70–71)
Ujjain, Madhya Pradesh
Other names
Bhāskarācārya
Occupation(s)
Astronomer, mathematician
Era
Shaka era
Discipline
Mathematician, astronomer, geometer
Main interests
Algebra, arithmetic, trigonometry
Notable works
Bhāskara II ([bʰɑːskərə]; c.1114–1185), also known as Bhāskarāchārya (lit. 'Bhāskara the teacher'), was an Indian polymath, mathematician, astronomer and engineer. From verses in his main work, Siddhānta Śiromaṇi, it can be inferred that he was born in 1114 in Vijjadavida (Vijjalavida) and living in the Satpura mountain ranges of Western Ghats, believed to be the town of Patana in Chalisgaon, located in present-day Khandesh region of Maharashtra by scholars. In a temple in Maharashtra, an inscription supposedly created by his grandson Changadeva, lists Bhaskaracharya's ancestral lineage for several generations before him as well as two generations after him.Henry Colebrooke who was the first European to translate (1817) Bhaskaracharya II's mathematical classics refers to the family as Maharashtrian Brahmins residing on the banks of the Godavari.
Born in a Hindu Deshastha Brahmin family of scholars, mathematicians and astronomers, Bhaskara II was the leader of a cosmic observatory at Ujjain, the main mathematical centre of ancient India. Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India. His main work, Siddhānta-Śiromaṇi (Sa