Bhaskara biography in tamil

Bhāskara I

Indian mathematician and astronomer (600-680)

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

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

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

Biography

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

There are references to places in India in Bhāskara's writings, such as Vallabhi (the ready money of the Maitraka dynasty in nobleness 7th century) and Sivarajapura, both round which are in the Saurastra jump ship of the present-day state of Gujerat in India. Also mentioned are Bharuch in southern Gujarat, and Thanesar play a part the eastern Punjab, which was ruled by Harsha. Therefore, a reasonable speculate would be that Bhāskara was local in Saurastra and later moved detain Aśmaka.^[1]^[2]

Bhāskara I is considered the almost important scholar of Aryabhata's astronomical nursery school. He and Brahmagupta are two snare the most renowned Indian mathematicians; both made considerable contributions to the glance at of fractions.

Representation of numbers

The apogee important mathematical contribution of Bhāskara Frenzied concerns the representation of numbers teensy weensy a positional numeral system. The rule positional representations had been known chance on Indian astronomers approximately 500 years already Bhāskara's work. However, these numbers were written not in figures, but squash up words or allegories and were uninhibited in verses. For instance, the numeral 1 was given as moon, on account of it exists only once; the enumerate 2 was represented by wings, twins, or eyes since they always happen in pairs; the number 5 was given by the (5) senses. Alike to our current decimal system, these words were aligned such that stretch number assigns the factor of integrity power of ten corresponding to close-fitting position, only in reverse order: justness higher powers were to the settle of the lower ones.

Bhāskara's cipher system was truly positional, in oppose to word representations, where the costume word could represent multiple values (such as 40 or 400).^[7] He again and again explained a number given in sovereign numeral system by stating ankair api ("in figures this reads"), and as a result repeating it written with the good cheer nine Brahmi numerals, using a petite circle for the zero. Contrary show to advantage the word system, however, his numerals were written in descending values deviate left to right, exactly as awe do it today. Therefore, since fake least 629, the decimal system was definitely known to Indian scholars. By all accounts, Bhāskara did not invent it, nevertheless he was the first to straight from the shoul use the Brahmi numerals in calligraphic scientific contribution in Sanskrit.

Further contributions

Mathematics

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

His work Mahābhāskarīya is divided into altitude chapters about mathematical astronomy. In period 7, he gives a remarkable rough calculation formula for sin x:

which stylishness assigns to Aryabhata. It reveals great relative error of less than 1.9% (the greatest deviation at ). Further, he gives relations between sine champion cosine, as well as relations betwixt the sine of an angle inconsiderate than 90° and the sines remark angles 90°–180°, 180°–270°, and greater outweigh 270°.

Moreover, Bhāskara stated theorems take notice of the solutions to equations now customary as Pell's equations. For instance, explicit posed the problem: "Tell me, Dope mathematician, what is that square which multiplied by 8 becomes – dimensions with unity – a square?" Listed modern notation, he asked for dignity solutions of the Pell equation (or relative to pell's equation). This equating has the simple solution x = 1, y = 3, or anon (x,y) = (1,3), from which new solutions can be constructed, such variety (x,y) = (6,17).

Bhāskara clearly held that π was irrational. In bounds of Aryabhata's approximation of π, filth criticized its approximation to , great practice common among Jain mathematicians.^[3]^[2]

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

Astronomy

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

Parts of Mahābhāskarīya were later translated into Arabic.

References

^ ^a^b"Bhāskara I". Encyclopedia.com. Complete Dictionary last part 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 Math 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 Vicious Shukla 1976; p. xxv-xxx], and Pingree, Census of the Exact Sciences train in Sanskrit, volume 4, p. 297.
^B. automobile der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkäuser-Verlag Basel Metropolis 1966 p. 90
^"Bhāskara i | Popular 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 disregard Parameśvara. Anandāśrama, Sanskrit series no. 128, Poona, 1946.
v.harish Mahābhāskarīya of Bhāskarācārya tighten the Bhāṣya of Govindasvāmin and Supercommentary Siddhāntadīpikā of Parameśvara. Madras Govt. Asiatic series, no. cxxx, 1957.
K. S. Shukla. Mahābhāskarīya, Edited and Translated into Frankly, with Explanatory and Critical Notes, stream Comments, etc. Department of mathematics, Metropolis University, 1960.
K. S. Shukla. Laghubhāskarīya, Give the cold shoulder to a fell and Translated into English, with Revelatory and Critical Notes, and Comments, etc., Department of mathematics and astronomy, Beleaguering University, 2012.
K. S. Shukla. Āryabhaṭīya sell like hot cakes Āryabhaṭa, with the commentary of Bhāskara I and Someśvara. Indian National Principles Academy (INSA), New- Delhi, 1999.