Aryabhatawas the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the Āryabhaṭīya (499 CE, when he was 23 years old)[6] and the Arya-siddhanta.
The place-value system, first seen in the 3rd-century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients. However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form. |
Aryabhata worked on the approximation for pi (π), and may have come to the conclusion that π is irrational.
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Varahamihira
Varāhamihira pronunciation (help·info) (505–587 CE), also called Varaha or Mihir, was an Indian astronomer, mathematician, and astrologer who lived in Ujjain. He was born in Avanti (India) region, roughly corresponding to modern-day Malwa, to Adityadasa, who was himself an astronomer. According to one of his own works, he was educated at Kapitthaka. He is considered to be one of the "Nine Jewels" (Navaratnas) of the court of legendary ruler Yashodharman Vikramaditya of Malwa.
Varahamihira's mathematical work included the discovery of the trigonometric formulas and
improved the accuracy of the sine tables of Aryabhata. He defined the algebraic properties of zero as well as of negative numbers. He was among the first mathematicians to discover a version of what is now known as the Pascal's triangle. He used it to calculate the binomial coefficients.
Varahamihira's mathematical work included the discovery of the trigonometric formulas and
improved the accuracy of the sine tables of Aryabhata. He defined the algebraic properties of zero as well as of negative numbers. He was among the first mathematicians to discover a version of what is now known as the Pascal's triangle. He used it to calculate the binomial coefficients.
Brahmagupta
"Brahmagupta was born in 598 CE according to his own statement. He lived in Bhillamala (modern Bhinmal) during the reign of the Chapa dynasty ruler Vyagrahamukha. He was the son of Jishnugupta. He was a Shaivite by religion.[3] Even though most scholars assume that Brahmagupta was born in Bhillamala, there is no conclusive evidence for it. However, he lived and worked there for a good part of his life. Prithudaka Svamin, a later commentator, called him Bhillamalacharya, the teacher from Bhillamala.[4] Sociologist G. S. Ghurye believed that he might have been from the Multan region or the Abu region."-Wikipedia
Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals. Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and an exact formula for the figure's area. |
Bhaskara Ⅱ
"Bhāskara(ಭಾಸ್ಕರ ೨) (also known as Bhāskarāchārya ("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 Karnataka.
Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India. His main work Siddhānta Shiromani, (Sanskrit for "Crown of Treatises") is divided into four parts called Lilāvatī, Bījagaṇita, Grahagaṇita and Golādhyāya,[5] which are also sometimes considered four independent works. These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karaṇa Kautūhala."-Wikipedia |