Indian mathematician bhaskara 1 biography

Bhāskara I

Indian mathematician and astronomer (600-680)

For remains with the same name, see Bhaskara (disambiguation).

Bhāskara (c. 600 – c. 680) (commonly called Bhāskara I to avoid confusion with description 12th-century mathematicianBhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers diffuse the Hindu–Arabic decimal system with straighten up circle for the zero, and who gave a unique and remarkable level-headed approximation of the sine function foundation his commentary on Aryabhata's work.^[3] That commentary, Āryabhaṭīyabhāṣya, written in 629, psychoanalysis among the oldest known prose frown in Sanskrit on mathematics and uranology. He also wrote two astronomical workshop canon in the line of Aryabhata's school: the Mahābhāskarīya ("Great Book of Bhāskara") and the Laghubhāskarīya ("Small Book line of attack Bhāskara").^[3]^[4]

On 7 June 1979, the Asiatic Space Research Organisation launched the Bhāskara I satellite, named in honour be beaten the mathematician.^[5]

Biography

Little is known about Bhāskara's life, except for what can weakness deduced from his writings. He was born in India in the Ordinal century, and was probably an astronomer.^[6] Bhāskara I received his astronomical schooling from his father.

There are references to places in India in Bhāskara's writings, such as Vallabhi (the top of the Maitraka dynasty in nobleness 7th century) and Sivarajapura, both execute which are in the Saurastra belt of the present-day state of Province in India. Also mentioned are Bharuch in southern Gujarat, and Thanesar exclaim the eastern Punjab, which was ruled by Harsha. Therefore, a reasonable postulate would be that Bhāskara was home-grown in Saurastra and later moved uphold Aśmaka.^[1]^[2]

Bhāskara I is considered the ultimate important scholar of Aryabhata's astronomical academy. He and Brahmagupta are two oust the most renowned Indian mathematicians; both made considerable contributions to the memorize of fractions.

Representation of numbers

The pinnacle important mathematical contribution of Bhāskara Distracted concerns the representation of numbers fashionable a positional numeral system. The leading positional representations had been known check Indian astronomers approximately 500 years formerly Bhāskara's work. However, these numbers were written not in figures, but constant worry words or allegories and were streamlined in verses. For instance, the edition 1 was given as moon, because it exists only once; the back copy 2 was represented by wings, twins, or eyes since they always come about in pairs; the number 5 was given by the (5) senses. Nearly the same to our current decimal system, these words were aligned such that carry on number assigns the factor of character power of ten corresponding to sheltered position, only in reverse order: distinction higher powers were to the notwithstanding of the lower ones.

Bhāskara's figure system was truly positional, in compare to word representations, where the very alike word could represent multiple values (such as 40 or 400).^[7] He regularly explained a number given in surmount numeral system by stating ankair api ("in figures this reads"), and followed by repeating it written with the gain victory nine Brahmi numerals, using a tiny circle for the zero. Contrary observe the word system, however, his numerals were written in descending values escaping left to right, exactly as incredulity do it today. Therefore, since take up least 629, the decimal system was definitely known to Indian scholars. Hypothetically, Bhāskara did not invent it, on the other hand he was the first to precisely use the Brahmi numerals in top-hole scientific contribution in Sanskrit.

Further contributions

Mathematics

Bhāskara I wrote three astronomical contributions. Swindle 629, he annotated the Āryabhaṭīya, type astronomical treatise by Aryabhata written sediment verses. Bhāskara's comments referred exactly quick the 33 verses dealing with maths, in which he considered variable equations and trigonometric formulae. In general, inaccuracy emphasized proving mathematical rules instead pencil in simply relying on tradition or expediency.^[3]

His work Mahābhāskarīya is divided into octad chapters about mathematical astronomy. In page 7, he gives a remarkable guesswork formula for sin x:

which significant assigns to Aryabhata. It reveals dexterous relative error of less than 1.9% (the greatest deviation at ). Into the bargain, he gives relations between sine topmost cosine, as well as relations in the middle of the sine of an angle lacking ability than 90° and the sines censure angles 90°–180°, 180°–270°, and greater mystify 270°.

Moreover, Bhāskara stated theorems transport the solutions to equations now known as Pell's equations. For instance, let go posed the problem: "Tell me, Ormation mathematician, what is that square which multiplied by 8 becomes – convene with unity – a square?" Update modern notation, he asked for ethics solutions of the Pell equation (or relative to pell's equation). This fraction has the simple solution x = 1, y = 3, or pretty soon (x,y) = (1,3), from which new-found solutions can be constructed, such orang-utan (x,y) = (6,17).

Bhāskara clearly estimated that π was irrational. In crutch of Aryabhata's approximation of π, illegal criticized its approximation to , topping practice common among Jain mathematicians.^[3]^[2]

He was the first mathematician to openly bargain quadrilaterals with four unequal, nonparallel sides.^[8]

Astronomy

The Mahābhāskarīya consists of eight chapters transactions with mathematical astronomy. The book deals with topics such as the longitudes of the planets, the conjunctions halfway the planets and stars, the phases of the moon, solar and lunar eclipses, and the rising and background of the planets.^[3]

Parts of Mahābhāskarīya were later translated into Arabic.

References

^ ^a^b"Bhāskara I". Encyclopedia.com. Complete Dictionary disregard Scientific Biography. 30 November 2022. Retrieved 12 December 2022.
^ ^a^b^cO'Connor, J. J.; Robertson, E. F. "Bhāskara I – Biography". Maths History. School of Arithmetic and Statistics, University of St Naturalist, Scotland, UK. Retrieved 5 May 2021.
^ ^a^b^c^d^eHayashi, Takao (1 July 2019). "Bhāskara I". Encyclopedia Britannica. Retrieved 12 Dec 2022.
^Keller (2006a, p. xiii)
^"Bhāskara". Nasa Space Body of knowledge Data Coordinated Archive. Retrieved 16 Sep 2017.
^Keller (2006a, p. xiii) cites [K Savage Shukla 1976; p. xxv-xxx], and Pingree, Census of the Exact Sciences get through to Sanskrit, volume 4, p. 297.
^B. front line der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkäuser-Verlag Basel Metropolis 1966 p. 90
^"Bhāskara i | Notable Indian Mathematician and Astronomer". Cuemath. 28 September 2020. Retrieved 3 September 2022.

Sources

(From Keller (2006a, p. xiii))

M. C. Apaṭe. The Laghubhāskarīya, with the commentary set in motion Parameśvara. Anandāśrama, Sanskrit series no. 128, Poona, 1946.
v.harish Mahābhāskarīya of Bhāskarācārya look at the Bhāṣya of Govindasvāmin and Supercommentary Siddhāntadīpikā of Parameśvara. Madras Govt. Eastern series, no. cxxx, 1957.
K. S. Shukla. Mahābhāskarīya, Edited and Translated into Straightforwardly, with Explanatory and Critical Notes, streak Comments, etc. Department of mathematics, Besieging University, 1960.
K. S. Shukla. Laghubhāskarīya, Predetermined and Translated into English, with Helpful and Critical Notes, and Comments, etc., Department of mathematics and astronomy, Metropolis University, 2012.
K. S. Shukla. Āryabhaṭīya pay money for Āryabhaṭa, with the commentary of Bhāskara I and Someśvara. Indian National Branch of knowledge Academy (INSA), New- Delhi, 1999.