भास्कर
Bhaskara I (c. 600-c. 680) was a 7th century Indian mathematician, who was apparently the first to write numbers in the Hindu-Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work. This commentary, Aryabhatiyabhasya, written in 629 CE, is the oldest known prose work in Sanskrit on mathematics and astronomy. He also wrote two astronomical works in the line of Aryabhata's school, the Mahabhaskariya and the Laghubhaskariya. Little is known about Bhāskara's life. He was "probably a Marathi astronomer". He was born at Bori, in Parbhani district of Maharashtra state in India in 7th century. His astronomical education was given by his father. Bhaskara is considered the most important scholar of Aryabhata's astronomical school. He and Brahmagupta are one of the most renowned Indian mathematicians who made considerable contributions to the study of fractions.
Contributions of Bhaskara:
Contributions of Bhaskara:
- The most important mathematical contribution concerns the representation of numbers in a positional system. The first positional representations were known to Indian astronomers about 500 years ago. However, the numbers were not written in figures, but in words or symbols.
- He often explains a number given in this system, using the formula ankair api, by repeating it written with the first nine Brahmi numerals, using a small circle for the zero. At least since 629 the decimal system is definitely known to the Indian scientists.
- His work Mahabhaskariya divides into eight chapters about mathematical astronomy. He gives a remarkable approximation formula for sin x. Moreover, relations between sine and cosine, as well as between the sine of an angle >90° >180° or >270° to the sine of an angle <90° are given. Parts of Mahabhaskariya were later translated into Arabic.
- Bhaskara already dealt with the assertion that if p is a prime number, then 1 + (p - 1)! is divisible by p. And is now known as Wilson's theorem.
- Moreover, Bhaskara stated theorems about the solutions of today so called Pell equations.