Bhaskara ii mathematician images and biography
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Bhāskara II, born in 1114 in Biddur, India, and likely passing away around 1185, emerged as the preeminent mathematician of the 12th century. He notably authored the initial comprehensive work that systematically employed the decimal number system. As the successor to the renowned Indian mathematician Brahmagupta at the Ujjain astronomical observatory, a prominent mathematical hub in ancient India, Bhāskara II adopted the numeral "II" to differentiate himself from a namesake astronomer of the 7th century.
One of his most well-known works is the "Lilavati," a comprehensive treatise on arithmetic, algebra, geometry, and mensuration. The Lilavati covers a wide range of mathematical topics, including rules for solving indeterminate equations, methods for computing square and cube roots, and techniques for determining areas and volumes of geometric shapes.
Bhaskara II also wrote the "Bijaganita" (Algebra), where he dealt with algebraic concepts and equations. All his mathematical treatises, such as "Līlāvatī" and "Bījagaṇita," are composed in verses, a common style among Indian mathematical classics. Bhāskara II not only embraced the decimal system but also gathered problems from previous scholars like Brahmagupta. He bridged gaps in Brahmagupta's work, notably offering a general solution to the Pell equation and presenting various specific solutions. Noteworthy among these is the solution to the equation x² = 1 + 61y², famously posed by French mathematician Pierre de Fermat centuries later.
Delving into astronomy and astrology, his works like "Siddhāntaśiromaṇi" and "Karaṇakutūhala" documented his observations of planetary positions, eclipses, and cosmography. A legend suggests that Bhāskara II named his work "Līlāvatī" after his daughter, and his attempt to determine her optimal marriage time using a water clock became part of this tale. Despite the
Bhaskara II is a famous Indian mathematician. He also goes by the name of Bhaskara or Bhaskaracharya, which means Bhaskara the Teacher. Bhaskara is famous for a number of innovations in mathematics.
His knowledge of solving equations and number systems were at such a high level that it would take European mathematicians hundreds of years to attain this level.
Bhaskara is viewed as one of the greatest mathematicians of medieval India and his work has influenced both Indian and Islamic mathematicians as well as European ones.
Early Life
Not a lot is known about Bhaskara’s life. It is known that he was born in 1114 A.D. near Bijjada Bida (present day Bijapur). His father was a famous astrologer and mathematician by the name of Mahesvara. It was Bhaskara’s father who taught his son all about mathematics and astrology. This was a common practice at the time as sons followed in their father’s footsteps. In fact, Bhaskara also taught mathematics to his son Loksamudra. In 1207, his son helped establish a school focused on the study of Bhaskara’s writings.
Bhaskara worked at the astronomical observatory at Ujjain and soon became the head of the facility.
This observatory was the top mathematical center in India and excellent mathematicians, such as Varahamihira and Brahmagupta, had also worked at the observatory.
Bhaskara, as did other Indian mathematicians, wrote in verse. He looked at various branches of mathematics, such as algebra, trigonometry, and calculus. He also studied and wrote about astronomy. In fact, half of his most famous work dealt with mathematical astronomy.
Bhaskara died in 1185 at Ujjain. His work was built on and developed after his death by another Indian mathematician, Madhava of Sangamagrama, as well as by mathematicians at the Kerala School. This work not only helped to expand Bhaskara’s work but it also expanded the development of calculus in India.
His Writings
Bhaskara wrote a number of books but the work that has had the most influe Indian mathematician and astronomer (1114–1185) Not to be confused with Bhāskara I. Bhāskara II Statue of Bhaskara II at Patnadevi Vijjadavida, Maharashtra (probably Patan in Khandesh or Beed in Marathwada) Ujjain, Madhya Pradesh 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 Bhaskara
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 Bhāskara II
Born c. 1114 Died c. 1185(1185-00-00) (aged 70–71) Other names Bhāskarācārya Occupation(s) Astronomer, mathematician Era Shaka era Discipline Mathematician, astronomer, geometer Main interests Algebra, arithmetic, trigonometry Notable works