What is aryabhata's works in mathematics

Bhaskara I.

Surname: Bhaskara I.

Born: around 600 in Saurashtra (India)

Died: around 680 in Ashmaka (India)

Teaching / research areas: Astronomy, arithmetic, trigonometry

Bhaskara I. was an Indian mathematician and astronomer of the 7th century AD. He is considered to be the pioneer of today's number system in that he was the first to calculate with digits in a place value system based on base 10.

Life

Bhaskara I was born around 600 AD in the Saurashtra region in northwestern India. He is called Bhaskara I. to distinguish him from a later namesake, Bhaskara II., Who was also a mathematician. Little is known about the life of Bhaskara I. He studied and commented on the work of Aryabhatas I and is considered the most important representative of his astronomical school. Bhaskaras left 3 works on mathematical astronomy, the Mahabhaskariya, the Laghubhaskariya and the Aryabhatiyabhasya. He died in Ashmaka around 680.

Pioneer of today's number system

Bhaskara I. is considered to be the pioneer of today's number system. He first used digits in a place value system on the basis of 10. Before him, numbers in India were already represented in a place value system, but not with digits, but with word numbers. Bhaskara also switched from base 100 in Aryabhata's work to base 10. He used the zero as a blank; the first to calculate with zero as a number was his contemporary Brahmagupta.

Besides the decimal system, Bhaskara's name is associated with the approximation of the sine function and fractions. For the sine function he found the surprisingly good approximation: \ (frac {16x (pi-x)} {5pi ^ {2} -4x (pi-x)} \) on the interval \ (left [0, frac { pi} {2} right] \).