Bhaskara-II

• Bhaskara-II was another influential mathematician from Medieval times. He was a twelfth-century Indian maths wizard known as Bhaskaracharya.
• One of his important pieces of work was the Siddhanta Siromani consisting of four parts:
  • Leelavati- Dealing with arithmetic and geometry.
  • Bijaganita- A treatise on algebra
  • Graha Ganita-deals with astronomy.
  • Goladhyaya-deals with astronomy.
• Bhaskara-II had been a well-known astronomer who specifically defined many astronomical quantities, such as the sidereal year’s length.
• Bhaskara-II, a mathematical genius, made the significant discovery of differential calculus principles and their application to astronomical problems. Furthermore, calculations hundreds of years before European mathematicians like Newton and Leibniz.
• Bhaskara II is credited with inventing the differential coefficient and differential calculus.
• The son of a mathematician and astronomer, Bhaskara-II was trained by his father in the subjects. He rose to prominence as a mathematician and astronomer and was regarded as the lineal successor to the eminent Indian mathematician Brahmagupta as director of an astronomical observatory in Ujjain.
• Bhaskara composed the absolute first work, which utilised the decimal number system completely and systematically. It is just as extensive as chips away at other numerical procedures and his galactic view of planetary positions, conjunctions, obscurations, cosmography, and geology.
• Moreover, Bhaskara-II filled many holes in his archetype Brahmagupta’s work. He has been named the best mathematician of archaic India, acknowledging his priceless commitments to arithmetic and space science.

His Childhood & Early Life:

• Bhaskara himself revealed the details of his birth in an Arya metre verse, stating that Bhaskara-II was born in 1114 near Vijjadavida (believed to be Bijjaragi of Vijayapur in modern Karnataka).
• His father Maheswara  was a mathematician, astronomer, and astrologer who educated his son on everything he knew.

His Later Years:

• Bhaskara-II trained as a mathematician, astronomer, and astrologer. He became the director of an astronomical observatory in Ujjain, ancient India’s leading mathematical centre. The centre was a well-known mathematical astronomy school.
• Bhaskara-II is credited with giving proof of the Pythagorean theorem by calculating the same area in two different ways and then cancelling out terms.
• His calculus research was groundbreaking and far ahead of its time. He also unearthed the fundamentals 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 Renaissance European mathematicians of the 17th century are comparable to the rules he discovered in the 12th century.
• When he was 36 years old, he completed his major work, ‘Siddhanta Siromani’ (“Crown of Treatises”). The treatise is written in Sanskrit and contains 1450 verses.
• The first section, titled ‘Lilavati,’ comprises 13 chapters covering definitions, arithmetic terms, interest computation, arithmetic, and geometric progressions, plane geometry, and solid geometry, among others. It also has several number-crunching methods, such as multiplications, squares, and progressions.
• ‘Bijaganita’ (“Algebra”) was a 12-chapter work by him. This book discussed positive and negative numbers, zero, surds, and determining unknown quantities, as well as the ‘Kuttaka’ method for solving indeterminate and Diophantine equations. He also filled in a few holes in his archetype Brahmagupta’s work. 
• Cosmology is canvassed in the segments ‘Ganitadhyaya’ and ‘Goladhyaya’ of ‘Siddhanta Shiromani.’ 
• Numerous cosmic amounts, including the length of the sidereal year, were precisely calculated by Bhaskara-II utilising a galactic model created by Brahmagupta.
• These sections covered topics such as mean and true longitudes of the planets, solar and lunar eclipses, cosmography and geography, etc.
• Bhaskara II was well-known for his extensive knowledge of trigonometry. Among the first discoveries made in his works was the computation of sines of angles of 18 and 36 degrees.
• Bhaskara-II is credited with discovering spherical trigonometry, a branch of spherical geometry used in astronomy, geodesy, and navigation calculations.

His Major Works: 

• The treatise ‘Siddhanta Siromani,’ written by Bhaskara II, was divided into four parts, each dealing with a different topic in arithmetic, algebra, calculus, trigonometry, and astronomy.
• Bhaskara-II is regarded as a calculus pioneer because he is thought to have been the first to devise differential calculus.

Personal Life & Legacy: 

• Bhaskara was a married man with kids. Bhaskara-II gave his numerical information to his child Loksamudra, and a long time later, Loksamudra’s child aided the foundation of a school for the investigation of Bhaskara’s works in 1207. It is believed that Bhaskara named his book ‘Lilavati’ after his little girl.

An inscription in an Indian temple from the Middle Ages reads:

• The illustrious Bhaskaracharya triumphs and his exploits are admired by both the wise and the learned. He is like the crest of a peacock, a poet endowed with fame and religious merit.

The Indian Space Research Organisation (ISRO) launched the Bhaskara II satellite in honour of the great mathematician and astronomer on November 20, 1981.

Conclusion

Bhaskara was a great mathematician of the mediaeval time. In this article we studied about his early life and his childhood along with some of his major contributions in Indian mathematics. We also threw some light on his personal life and some of his latter works.