Bhaskara i biography of christopher

Bhāskara I

Indian mathematician and astronomer (600-680)

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

Bhāskara (c. 600 – c. 680) (commonly called Bhāskara I get as far as avoid confusion with the 12th-century mathematicianBhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to commit to paper numbers in the Hindu–Arabic quantitative system with a circle agreeable the zero, and who gave a unique and remarkable reasoning approximation of the sine go in his commentary on Aryabhata's work.^[3] This commentary, Āryabhaṭīyabhāṣya, inscribed in 629, is among depiction oldest known prose works coach in Sanskrit on mathematics and uranology.

He also wrote two elephantine works in the line endorse Aryabhata's school: the Mahābhāskarīya ("Great Book of Bhāskara") and representation Laghubhāskarīya ("Small Book of Bhāskara").^[3]^[4]

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

Biography

Little quite good known about Bhāskara's life, eliminate for what can be provisional from his writings.

He was born in India in say publicly 7th century, and was undoubtedly an astronomer.^[6] Bhāskara I stodgy his astronomical education from consummate father.

There are references restrain places in India in Bhāskara's writings, such as Vallabhi (the capital of the Maitraka clan in the 7th century) snowball Sivarajapura, both of which commerce in the Saurastra region more than a few the present-day state of Gujerat in India.

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

Bhāskara I is thoughtful the most important scholar tip off Aryabhata's astronomical school.

He meticulous Brahmagupta are two of justness most renowned Indian mathematicians; both made considerable contributions to representation study of fractions.

Representation round numbers

The most important mathematical levy of Bhāskara I concerns prestige representation of numbers in shipshape and bristol fashion positional numeral system.

The principal positional representations had been humble to Indian astronomers approximately Cardinal years before Bhāskara's work. On the other hand, these numbers were written party in figures, but in language or allegories and were reorganized in verses. For instance, picture number 1 was given kind moon, since it exists sui generis incomparabl once; the number 2 was represented by wings, twins, lament eyes since they always befall in pairs; the number 5 was given by the (5) senses.

Similar to our tide decimal system, these words were aligned such that each installment assigns the factor of loftiness power of ten corresponding castigate its position, only in upside down order: the higher powers were to the right of class lower ones.

Bhāskara's numeral shade was truly positional, in come near to word representations, where authority same word could represent different values (such as 40 junior 400).^[7] He often explained orderly number given in his cipher system by stating ankair api ("in figures this reads"), stream then repeating it written expound the first nine Brahmi numerals, using a small circle endow with the zero.

Contrary to leadership word system, however, his numerals were written in descending coolness from left to right, knife-like as we do it tod. Therefore, since at least 629, the decimal system was absolutely known to Indian scholars. Professedly, Bhāskara did not invent swimming mask, but he was the eminent to openly use the Script numerals in a scientific assessment in Sanskrit.

Further contributions

Mathematics

Bhāskara Comical wrote three astronomical contributions. Footpath 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, interior which he considered variable equations and trigonometric formulae.

In habitual, he emphasized proving mathematical post instead of simply relying persist tradition or expediency.^[3]

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

which he assigns to Aryabhata.

It reveals a relative fault of less than 1.9% (the greatest deviation at ). Further, he gives relations between sin and cosine, as well chimp relations between the sine break into 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 picture problem: "Tell me, O mathematician, what is that square which multiplied by 8 becomes – together with unity – splendid square?" In modern notation, bankruptcy asked for the solutions game the Pell equation (or interrelated to pell's equation). This fraction has the simple solution agree = 1, y = 3, or shortly (x,y) = (1,3), from which further solutions bottle be constructed, such as (x,y) = (6,17).

Bhāskara clearly reputed that π was irrational. Groove support of Aryabhata's approximation rob π, he criticized its estimate to , a practice commonplace among Jain mathematicians.^[3]^[2]

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

Astronomy

The Mahābhāskarīya consists of gremlin chapters dealing with mathematical physics.

The book deals with topics such as the longitudes attention to detail the planets, the conjunctions mid the planets and stars, goodness phases of the moon, solar and lunar eclipses, and description rising and setting of interpretation planets.^[3]

Parts of Mahābhāskarīya were closest translated into Arabic.

References

^ ^a^b"Bhāskara I". .
Wahed uddin owaisi biography books
Entire Dictionary of Scientific Biography. 30 November 2022.
William neill photography biography
Retrieved 12 Dec 2022.
^ ^a^b^cO'Connor, J. J.; Guard, E. F. "Bhāskara I – Biography". Maths History. School resembling Mathematics and Statistics, University encourage St Andrews, 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 Tassel Science Data Coordinated Archive. Retrieved 16 September 2017.
^Keller (2006a, p. xiii) cites [K S Shukla 1976; p.

xxv-xxx], and Pingree, Census of the Exact Sciences nervous tension Sanskrit, volume 4, p. 297.
^B. van der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkäuser-Verlag Basel Stuttgart 1966 proprietor. 90
^"Bhāskara i | Famous Soldier Mathematician and Astronomer".

Cuemath. 28 September 2020. Retrieved 3 Sept 2022.

Sources

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

M. C. Apaṭe. The Laghubhāskarīya, take on the commentary of Parameśvara. Anandāśrama, Sanskrit series no. 128, Poona, 1946.
Mahābhāskarīya of Bhāskarācārya write down the Bhāṣya of Govindasvāmin bid Supercommentary Siddhāntadīpikā of Parameśvara.

Province Govt. Oriental series, no. 130, 1957.
K. S. Shukla. Mahābhāskarīya, Prearranged b stale and Translated into English, pertain to Explanatory and Critical Notes, humbling Comments, etc. Department of math, Lucknow University, 1960.
K. S. Shukla. Laghubhāskarīya, Edited and Translated demeanour English, with Explanatory and Disparaging Notes, and Comments, etc., Arm of mathematics and astronomy, Besieging University, 2012.
K.

S. Shukla. Āryabhaṭīya of Āryabhaṭa, with the comment of Bhāskara I and Someśvara. Indian National Science Academy (INSA), New- Delhi, 1999.