BHASKARA II

VERONICA PAIS - 38

S.Y.B.Ed (Semester III)

CONTENTS:

> INTRODUCTION

> CONTRIBUTION TO MATHEMATICS

> CONTRIBUTION TO OTHER FIELDS

> CONCLUSION 

INTRODUCTION

1. Bhaskara a.k.a Bhaskaracharya a.k.a Bhaskara II was an Indian Mathematician and an Astronomer.

2. According to the verses of his main book - Siddhant Shiromani, he was born in 1114 AD in Vijjalvid (Vijjadavida) in the Sahyadri Mountain range near the town of Patan in the Western Ghat region (present-day Khandesh) in Maharashtra.

3. Bhaskara II's father Mahesvara - a scholarly person and a mathematician himself is the one who taught him Mathematics. 

4. 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.

5. Bhaskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century

6.  He has been called the greatest mathematician of medieval India.

CONTRIBUTION TO MATHEMATICS

1. Bhaskara II wrote his book Siddhant Shiromani which is divided in 4 parts - Lilavati, Bijaganita, Grahaganita and Goladhyaya. 

2. Each of these parts can be considered as independent works.

3. Lilavati (named after his daughter) talks about Arithmetic. Bijaganita talks about Algebra. Grahaganita talks about the mathematics of planets and Goladhyaya talks about spheres.

4. Bhaskara II is particularly known in the discovery of the principles of differential calculus and its application to astronomical problems and computations.

5. Bhaskara's work on calculus predates Newton and Leibniz's work by over half a millennium

6. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhaskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential calculus

7. Bhaskara II first discovered that any number divided by zero is "infinity" and sum of any number and infinity is "infinity".

8. The first section of his book Siddhant Shiromani named "Lilavati" has 277 verses. It covers calculations, progressions, measurements, permutation among many other topics.

9. The second section Bijaganita has 12 chapters and 213 verses which covers zero, infinity, positive and negative numbers and indeterminate equations (now called Pell's equation).

CONTRIBUTION TO OTHER FIELDS

(ASTRONOMY)

1. Bhaskara was also a renowned astronomer. 

2. Using an astronomical model developed by Brahmagupta in the 7th century, Bhaskara accurately defined many astronomical quantities, including, the length of the sidereal year. 

3. The time that is required for the Earth to orbit the Sun, as approximately 365.2588 days which is the same as in Suryasiddhanta. The modern accepted measurement is 365.25636 days, a difference of just 3.5 minutes.

4. His mathematical astronomy text Siddhanta Shiromani is written in two parts: the first part on mathematical astronomy - Grahaganita and the second part on the sphere - Goladhyaya.

5. Grahaganita consists of 12 chapters and Goladhaya consists of 13 chapters.