MATHS(Bhaskaracharya)

BHASKARACHARYA

Bhāskara(also known as Bhāskarācārya ("Bhāskara the teacher"), and as Bhāskara II to avoid confusion with Bhāskara I) (1114–1185), was an Indian mathematician and astronomer. He was born in Bijapur in modern Karnataka.

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

CONTRIBUTION

Lilavati

The first section Līlāvatī (also known as pāṭīgaṇita or aṅkagaṇita) consists of 277 verses.It covers calculations, progressions, measurement, permutations, and other topics.

Bijaganita

The second section Bījagaṇita has 213 verses. It discusses zero, infinity, positive and negative numbers, and indeterminate equations including (the now called) Pell's equation, solving it using a kuṭṭaka method. In particular, he also solved the case that was to elude Fermat and his European contemporaries centuries later.

Grahaganita

In the third section Grahagaṇita, while treating the motion of planets, he considered their instantaneous speeds. He arrived at the approximation:

for close to , or in modern notation:

.

In his words

bimbārdhasya koṭijyā guṇastrijyāhāraḥ phalaṃ dorjyāyorantaram

This result had also been observed earlier by Muñjalācārya (or Mañjulācārya) in 932, in his astronomical work 'Laghu-mānasam, in the context of a table of sines.
Bhāskara also stated that at its highest point a planet's instantaneous speed is zero