Physics

# Write the biography of Bhaskaracharya ? and describe their main scientific works in detail?

##### SOLUTION
Bhaskara was born in 1114, near Vijjadavida (believed to Bijjaragi of Vijayapur in modern Karnataka).
Bhaskara II, also known as Bhaskara or as Bhaskaracharya, was a 12th-century Indian mathematician. He was also a renowned astronomer, who accurately defined many astronomical quantities, including the length of the sidereal year. A brilliant mathematician, he made the significant discovery of the principles of differential calculus and its application to astronomical problems and computations centuries before European mathematicians, like Newton and Leibniz made similar discoveries.
It is believed that Bhaskara II was the first to conceive the differential coefficient and differential calculus. Bhaskara II wrote the first work with full and systematic use of the decimal number system and also wrote extensively on other mathematical techniques and on his astronomical observations of planetary positions, conjunctions, eclipses, cosmography, and geography. In addition, he also filled many of the gaps, in his predecessor, Brahmagupta’s work. In recognition of his invaluable contributions, to mathematics and astronomy, he has been called the greatest mathematician of medieval India.
Scientific work and achievements:
1. He made many significant contributions to mathematics, throughout his career. He is credited to have given a proof of the Pythagorean theorem, by calculating the same area in two different ways, and then cancelling out terms, to get $a_2 + b_2 = c_2.$
2. His work on calculus was groundbreaking and much ahead of his times. He not only discovered the principles of differential calculus and its application to astronomical problems and computations but also determined solutions of linear and quadratic indeterminate equations (Kuttaka). The works in calculus performed by the European mathematicians of the 17th century is comparable to the rules he had discovered, way back in the 12th century.
3. His major work ‘Siddhanta Siromani’(“Crown of treatises”) was completed in 1150 when he was 36 years old. Composed in the Sanskrit Language, the treatise consists of 1450 verses. The work is divided into four parts called “Lilavati, “Bijaganita’, and ‘Goladhyaya’, which are also sometimes considered four independent works. The different sections deal with different mathematical and astronomical fields.
4. The first part “Lilavati’ consists of 13 chapters, mainly definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry and solid geometry and many others aspects of mathematics. It also has a number of methods for computing numbers, such as multiplication, squares, and progression.
5. His work “Bijaganita’(“Algebra”) was a work in 12 chapters. This book covered topics like positive and negative numbers, zero, surds, determining unknown quantities, and elaborated the method of ‘Kuttaka’for solving indeterminate equations and Diophantine equations. He also filled many of the gaps in his predecessor, Brahmagupta’s work.
6. The sections ‘Ganitadhyaya’ and ‘Goladhyaya’ of ‘Siddhanta Shiromani ’ are devoted to astronomy. He used an astronomical model developed by Brahmagupta, to accurately define many astronomical quantities, including the length of the sidereal year. These sections covered topics such as mean longitudes of the planets, true longitudes of the planets, solar and lunar eclipses, cosmography, geography etc.
7. Bhaskara II was especially known for his in-depth knowledge of trigonometry Discoveries first found in his works, including computation of sine of angles of 18 and 36 degrees. He is credited to have discovered spherical trigonometry, a branch of spherical geometry, which is of great importance for calculations, in astronomy, geodesy and navigation.
8. Bhaskara-II major work was the treatise-‘Siddhanta Siromani’, which was further divided into four parts, each of them dealing with diverse topics on arithmetic, algebra, calculus, trigonometry, and astronomy. He is considered to be a pioneer in the field of calculus, as it is probable that he was the first to conceive the differential coefficient and differential calculus.

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Subjective Hard Published on 18th 08, 2020
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