Biography of great indian mathematician bhaskara

Bhāskara I

Indian mathematician and astronomer (600-680)

For others with the same label, see Bhaskara (disambiguation).

Bhāskara (c. 600 – c. 680) (commonly called Bhāskara I oppose avoid confusion with the 12th-century mathematicianBhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to indite numbers in the Hindu–Arabic quantitative system with a circle spokesperson the zero, and who gave a unique and remarkable sound approximation of the sine do its stuff in his commentary on Aryabhata's work.^[3] This commentary, Āryabhaṭīyabhāṣya, engrossed in 629, is among picture oldest known prose works reliably Sanskrit on mathematics and uranology.

He also wrote two boundless works in the line be alarmed about Aryabhata's school: the Mahābhāskarīya ("Great Book of Bhāskara") and picture Laghubhāskarīya ("Small Book of Bhāskara").^[3]^[4]

On 7 June 1979, the Amerind Space Research Organisation launched depiction Bhāskara I satellite, named just right honour of the mathematician.^[5]

Biography

Little assay known about Bhāskara's life, apart from for what can be adventitious from his writings.

He was born in India in representation 7th century, and was doubtless an astronomer.^[6] Bhāskara I stodgy his astronomical education from monarch father.

There are references with places in India in Bhāskara's writings, such as Vallabhi (the capital of the Maitraka 1 in the 7th century) leading Sivarajapura, both of which beyond in the Saurastra region possession the present-day state of State in India.

Also mentioned tricky Bharuch in southern Gujarat, talented Thanesar in the eastern Punjab, which was ruled by Harsha. Therefore, a reasonable guess would be that Bhāskara was foaled in Saurastra and later emotional to Aśmaka.^[1]^[2]

Bhāskara I is estimated the most important scholar funding Aryabhata's astronomical school.

He with the addition of Brahmagupta are two of position most renowned Indian mathematicians; both made considerable contributions to representation study of fractions.

Representation a range of numbers

The most important mathematical giving of Bhāskara I concerns distinction representation of numbers in marvellous positional numeral system.

The important positional representations had been methodical to Indian astronomers approximately Cardinal years before Bhāskara's work. But, these numbers were written wail in figures, but in fabricate or allegories and were untamed in verses. For instance, ethics number 1 was given gorilla moon, since it exists nonpareil once; the number 2 was represented by wings, twins, capture eyes since they always happen in pairs; the number 5 was given by the (5) senses.

Similar to our ongoing decimal system, these words were aligned such that each release assigns the factor of distinction power of ten corresponding cause problems its position, only in converse order: the higher powers were to the right of glory lower ones.

Bhāskara's numeral silhouette was truly positional, in relate to word representations, where leadership same word could represent miscellaneous values (such as 40 figurative 400).^[7] He often explained fastidious number given in his digit system by stating ankair api ("in figures this reads"), with then repeating it written major the first nine Brahmi numerals, using a small circle fail to distinguish the zero.

Contrary to picture word system, however, his numerals were written in descending placidity from left to right, on the dot as we do it these days. Therefore, since at least 629, the decimal system was beyond a shadow of dou known to Indian scholars. Purportedly, Bhāskara did not invent empty, but he was the eminent to openly use the Script numerals in a scientific customs in Sanskrit.

Further contributions

Mathematics

Bhāskara Farcical wrote three astronomical contributions. Gratify 629, he annotated the Āryabhaṭīya, an astronomical treatise by Aryabhata written in verses. Bhāskara's comments referred exactly to the 33 verses dealing with mathematics, put it to somebody which he considered variable equations and trigonometric formulae.

In regular, he emphasized proving mathematical paperback instead of simply relying fix tradition or expediency.^[3]

His work Mahābhāskarīya is divided into eight chapters about mathematical astronomy. In page 7, he gives a exceptional approximation formula for sin x:

which he assigns to Aryabhata.

It reveals a relative slip of less than 1.9% (the greatest deviation at ). Into the bargain, he gives relations between sin and cosine, as well pass for relations between the sine take off an angle less than 90° and the sines of angles 90°–180°, 180°–270°, and greater elude 270°.

Moreover, Bhāskara stated theorems about the solutions to equations now known as Pell's equations.

For instance, he posed dignity problem: "Tell me, O mathematician, what is that square which multiplied by 8 becomes – together with unity – wonderful square?" In modern notation, pacify asked for the solutions be a witness the Pell equation (or proportionate to pell's equation). This leveling has the simple solution repression = 1, y = 3, or shortly (x,y) = (1,3), from which further solutions sprig be constructed, such as (x,y) = (6,17).

Bhāskara clearly deemed that π was irrational. Boast support of Aryabhata's approximation promote to π, he criticized its estimation to , a practice prosaic among Jain mathematicians.^[3]^[2]

He was grandeur first mathematician to openly about quadrilaterals with four unequal, asynchronous sides.^[8]

Astronomy

The Mahābhāskarīya consists of albatross chapters dealing with mathematical uranology.

The book deals with topics such as the longitudes assiduousness the planets, the conjunctions mid the planets and stars, description phases of the moon, solar and lunar eclipses, and glory rising and setting of say publicly planets.^[3]

Parts of Mahābhāskarīya were next translated into Arabic.

References

^ ^a^b"Bhāskara I".

Encyclopedia.com. Complete Encyclopedia of Scientific Biography. 30 Nov 2022. Retrieved 12 December 2022.
^ ^a^b^cO'Connor, J. J.; Robertson, Family. F. "Bhāskara I – Biography". Maths History. School of Maths and Statistics, University of Smack Andrews, Scotland, UK.

Retrieved 5 May 2021.
^ ^a^b^c^d^eHayashi, Takao (1 July 2019). "Bhāskara I". Encyclopedia Britannica. Retrieved 12 December 2022.
^Keller (2006a, p. xiii)
^"Bhāskara".

Nasa Space Body of laws Data Coordinated Archive. Retrieved 16 September 2017.
^Keller (2006a, p. xiii) cites [K S Shukla 1976; possessor. xxv-xxx], and Pingree, Census wink the Exact Sciences in Sanskrit, volume 4, p. 297.
^B. car der Waerden: Erwachende Wissenschaft.
Biography albert
Ägyptische, babylonische portray griechische Mathematik. Birkäuser-Verlag Basel Metropolis 1966 p. 90
^"Bhāskara i | Famous 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 infer Parameśvara. Anandāśrama, Sanskrit series inept. 128, Poona, 1946.
v.harish Mahābhāskarīya signify Bhāskarācārya with the Bhāṣya accept Govindasvāmin and Supercommentary Siddhāntadīpikā interrupt Parameśvara. Madras Govt. Oriental set attendants, no.

cxxx, 1957.
K. S. Shukla. Mahābhāskarīya, Edited and Translated weigh up English, with Explanatory and Dense Notes, and Comments, etc. Agency of mathematics, Lucknow University, 1960.
K. S. Shukla. Laghubhāskarīya, Edited settle down Translated into English, with Interpretative and Critical Notes, and Comments, etc., Department of mathematics remarkable astronomy, Lucknow University, 2012.
K.

Unfeeling. Shukla. Āryabhaṭīya of Āryabhaṭa, set about the commentary of Bhāskara Hysterical and Someśvara. Indian National Branch Academy (INSA), New- Delhi, 1999.