Question

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

Answer 1

Hint: Bhaskara's other names include Bhaskara II and Bhaskaracharya, the latter of which means "Bhaskara the Teacher." We'll call him Bhaskaracharya in this article because that's how he's known in India.

Complete answer:
Biography of Bhaskaracharya -
Mahesvara, Bhaskaracharya's father, was a Brahman. Mahesvara was a well-known astrologer in his own right. This was common in Indian culture, with generations of a family becoming exceptional mathematicians and often serving as teachers to other members of the family. In the year 1114, Bhaskara was born near Vijjadavida (believed to be Bijjaragi of Vijayapur in modern Karnataka).

Bhaskara II, also known as Bhaskara or Bhaskaracharya, was an Indian mathematician who lived in the 12th century. He was also a well-known astronomer who correctly described many astronomical quantities, including the sidereal year's period. He was a genius mathematician who discovered the concepts of differential calculus and how to apply them to astronomical problems and computations centuries before European mathematicians such as Newton and Leibniz.

Bhaskara II is thought to be the first to invent the differential coefficient and differential calculus.
 Bhaskara II was the first to use the decimal number system in its entirety, and he also wrote extensively on other mathematical methods, as well as his astronomical observations of celestial locations, conjunctions, eclipses, cosmography, and geography. He also filled in many of the holes in his predecessor's work, Brahmagupta's. He has been dubbed the greatest mathematician of mediaeval India in honour of his invaluable contributions to mathematics and astronomy.

Research and accomplishments in science:
- During his career, he made several important contributions to mathematics. He is credited with proving the Pythagorean theorem by multiplying the same region twice and then cancelling out terms to get $a^2 +b^2 = c^2$.
- His calculus research was revolutionary and well ahead of its time. He not only discovered the concepts of differential calculus and how to apply them to astronomical problems and computations, but he also found solutions to indeterminate linear and quadratic equations (Kuttaka). The calculus works of European mathematicians in the seventeenth century are equivalent to the rules he discovered in the 12th century.
- Bhaskara II was noted for his extensive knowledge of trigonometry, which he demonstrated in his works, such as the calculation of the sine of angles of 18 and 36 degrees. He is credited with inventing spherical trigonometry, a branch of spherical geometry that is critical in astronomy, geodesy, and navigation calculations.
- Bhaskara-most II's famous work was the treatise titled "Siddhanta Siromani," which was divided into four sections, each of which dealt with different aspects of arithmetic, algebra, calculus, trigonometry, and astronomy. He is regarded as a pioneer in the field of calculus since he is thought to be the first to think of the differential coefficient and differential calculus.
- When he was 36 years old, he completed his main work, Siddhanta Siromani (the "Crown of Treatises"). The treatise contains 1450 verses and was written in Sanskrit. The work is divided into four parts, known as "Lilavati," "Bijaganita," and "Goladhyaya," which are often considered four separate works. The various sections cover various mathematical and astronomical topics.
- The first section, titled "Lilavati," contains 13 chapters that cover concepts, arithmetical terminology, interest computation, arithmetical and geometrical progressions, plane geometry and solid geometry, and a variety of other topics in mathematics. It also includes a variety of number-computing methods, including multiplication, squares, and progression.

Note: By more than half a century, Bhaskara's thesis on calculus predates Newton and Leibniz. He is best known for discovering differential calculus concepts and applying them to astronomical problems and computations. Although differential and integral calculus are attributed to Newton and Leibniz, there is clear evidence that Bhaskara was a pioneer in some of the concepts of differential calculus. He may have been the first to think about differential calculus and the differential coefficient.