Bhaskaracharya – The Crown Jewel of Mathematics and Astronomy
Some of Bhaskara&#;s contributions to mathematics include the following:
-Bhaskara is the first to give the general solution to the quadratic equation ax2 + bx + c = 0, the answer being x = (-b ± (b2 &#; 4ac)1/2)/2a.
-He also gives the (now) well known results for sin (a + b) and sin (a &#; b).
-Stated Rolle&#;s Theorem, a special case of one of the most important theorems in analysis, the mean value theorem. Traces of the general mean value theorem are also found in his works.
-Solutions of indeterminate quadratic equations (of the type ax² + b = y²).
-Bhaskara also goes deeper into the &#;differential calculus&#; and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of &#;infinitesimals&#;
Bhaskaracharya wrote Siddhanta Shiromani in AD when he was 36 years old. This is a mammoth work containing about verses. It is divided into four parts and each part can be considered as separate book. The numbers of verses in each part are as follows, 1. Lilawati has 2. Beejaganit has 3. Ganitadhyaya has 4. Goladhyaya has verses.
One of the most impor
Bhaskara II - The Great Indian Mathematician
Works of Bhaskara ii
Bhaskara developed an understanding of calculus, the number systems, and solving equations, which were not to be achieved anywhere else in the world for several centuries.
Bhaskara is mainly remembered for his A. D. masterpiece, the Siddhanta Siromani (Crown of Treatises) which he wrote at the age of The treatise comprises verses which have four segments. Each segment of the book focuses on a separate field of astronomy and mathematics.
They were:
- Lilavati: A treatise on arithmetic, geometry and the solution of indeterminate equations
- Bijaganita: ( A treatise on Algebra),
- Goladhyaya: (Mathematics of Spheres),
- Grahaganita: (Mathematics of the Planets).
He also wrote another treatise named Karaṇā Kautūhala.
Lilavati
Lilavati is composed in verse form so that pupils could memorise the rules without the need to refer to written text. Some of the problems in Leelavati are addressed to a young maiden of that same name. There are several stories around Lilavati being his daughter Lilavati has thirteen chapters which include several methods of computing numbers
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;
Early Life and Education
Bhaskara II, whose full name was Bhaskaracharya, was born around AD in Vijjadavida, India. He was from a lineage of scholars, with his father, Mahesvara, being a well-known mathematician and astrologer. His father opened his intellectual journey, educating him in mathematics, astronomy, and science. His father’s teachings in these fields were instrumental in Bhaskara’s development as a scholar in these fields.
Significant Works
The most significant works of Bhaskara include the Lilavati and the Bijaganita. The Lilavati is a detailed exposition of several mathematical topics, such as arithmetic, algebra, geometry, and mensuration. The subjects are arranged into 13 chapters, each focusing on specific mathematical problems and their solutions. The treatise was written to spread mathematical knowledge, and Bhaskara’s genius in breaking down complex concepts and presenting them in simplified forms that could be easily understood revolutionized the field.
The Bijaganita focuses mainly on algebraic concepts and techniques. He developed methods for solving equations, and quadratic equations, and even gave methods for indeterminate equations, which laid th
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