The city of Bijapur
If Narayana of Bijapur, better known as Kumar Valmiki, wrote Torvi Ramayana and Naga Chandra, a devout Jain penned the Jain version of the Ramayana, there was another writer who became a famous mathematician and astronomer. He is Bhaskaracharya.
Bhaskaracharya or Bhaskara is believed to be born near Bijapur.
Though there are no precise records to tell us where or when he was born, it is believed that he was born in 1114 A D in a Deshastha Brahmin family somewhere near Bijjada Bida, which was the earlier name of Bijapur.
His father, Mahadeva, was an astrologer. It was his father who taught the young Bhaskara the rudiments of mathematics( Bhaskara passed on this knowledge to his son Lokasamudra). In one of his books, Bhaskara himself speaks about how and where he studied. He said he had studied grammer, vedas, Bharata shastras, Mimasa, mathematics, medicine and logic by the time he reached 36 years of age.
He calls himself a poet. He is the author of Siddhanta Shiromani (Crown of Treatises), a book of 1450 verses written in 1150 AD. The book can be broadly classified into four parts - Lilawathi, Beejaganita, Ganitadhyaya and Goladhyaya. There are 278 verses in Lilawathi, 213 in Beejaganita, 451 verses in Ganitadhyaya and 501 verses in Goladhyaya.
This is a book on calculations in arthematic and astronomy. Even today, it is regarded by experts as being one of the nest books in ancient Indian astronomy.
Lilawathi mainly deals with mathematics. Pleas read it to know how mathematics can be written in poetic form. The language is simple and lucid. It was only after the British set up the universities in Bombay , Calcutta
The Lilawathi and Beejaganita is a mathematician’s delight. It gives us easy methods to find the squares, square roots, cube, and cube roots of numbers. Bhaskara was such a genius that he has proved the Pythagoras theorem in two lines.
Pascal’s Triangle was Bhaskara’s Khandameru. Bhaskara has worked out this number triangle 500 years before Pascal.
Lilawathi has also details on permutations and combinations in a unique method called Ankapaash. Bhaskara has given us the approximate value of PI as 22/7 and its more accurate value as 3.1416. He knew infinity and called it khahar rashi.
The two sections has problems on spherical trignometry, interest computation, plane and solid geometry.
Lilawathi is sub-divided into 13 chapters and each covers different branches of arithematic, algebra, geometry and mathematics..
Beejaganita deals with Algebra in twelve chapters. It was the first book to recognize that a positive number has two square roots (a positive and negative square root).
It deals with positive and negative numbers, Zero, simple equations, Diophantine and indeterminate quadratic equations.
Chakravala was a cyclic format devised by Bhaskara to solve indeterminate quadratic equations of the form ax² + bx + c = y.
His method also helps us solve other similar problems such as quartic equations, cubic equations, indeterminate cubic equations, indeterminate quartic equations and higher-order polynomial equations.
Check out his poetic forms on Trignomotry and the Sine functions and calculus (integral and differential calculus). His work on calculus predates Newton
He has also accurately measures the distance between the planets and their farthest and nearest positions with earth as the base.
The two sections has problems on spherical trignometry, interest computation, plane and solid geometry.
Lilawathi is sub-divided into 13 chapters and each covers different branches of arithematic, algebra, geometry and mathematics..
Beejaganita deals with Algebra in twelve chapters. It was the first book to recognize that a positive number has two square roots (a positive and negative square root).
It deals with positive and negative numbers, Zero, simple equations, Diophantine and indeterminate quadratic equations.
Chakravala was a cyclic format devised by Bhaskara to solve indeterminate quadratic equations of the form ax² + bx + c = y.
His method also helps us solve other similar problems such as quartic equations, cubic equations, indeterminate cubic equations, indeterminate quartic equations and higher-order polynomial equations.
Bhaskara’s contribution to astronomy is too immense to be written in this part of the article. He calcluated the orbital periods of several planets. He also wrote about several astronomical instruments that he used for his calculations.
He died in 1185. His son Lopamudra built school in 1206 to teach his father's works.
A persian translation of Siddanta Shiromani says Bhaskara wrote it for his daughter Lilawathi. It also has an interesting anecdote on his daughter's marriage. I will write about this in another article.
He died in 1185. His son Lopamudra built school in 1206 to teach his father's works.
A persian translation of Siddanta Shiromani says Bhaskara wrote it for his daughter Lilawathi. It also has an interesting anecdote on his daughter's marriage. I will write about this in another article.
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