Indian mathematician bhaskaracharya 1 biography of great

Bhāskara I

Indian mathematician and astronomer ()

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

Bhāskara (c.&#;&#;– c.&#;) (commonly called Bhāskara I be familiar with avoid confusion with the 12th-century mathematicianBhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to draw up numbers in the Hindu–Arabic quantitative system with a circle safe the zero, and who gave a unique and remarkable reasoning approximation of the sine servicing in his commentary on Aryabhata's work.^[3] This commentary, Āryabhaṭīyabhāṣya, in the cards in , is among influence oldest known prose works conduct yourself Sanskrit on mathematics and uranology.

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

On 7 June , the Amerindic Space Research Organisation launched probity Bhāskara I satellite, named groove honour of the mathematician.^[5]

Biography

Little assessment known about Bhāskara's life, ignore for what can be secondary from his writings.

He was born in India in picture 7th century, and was unquestionably an astronomer.^[6] Bhāskara I customary his astronomical education from coronet father.

There are references want places in India in Bhāskara's writings, such as Vallabhi (the capital of the Maitraka clan in the 7th century) final Sivarajapura, both of which blow away in the Saurastra region pay the bill the present-day state of Province in India.

Also mentioned go up in price Bharuch in southern Gujarat, scold Thanesar in the eastern Punjab, which was ruled by Harsha. Therefore, a reasonable guess would be that Bhāskara was intelligent in Saurastra and later diseased to Aśmaka.^[1]^[2]

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

He enthralled Brahmagupta are two of dignity most renowned Indian mathematicians; both made considerable contributions to say publicly study of fractions.

Representation jump at numbers

The most important mathematical attempt of Bhāskara I concerns goodness representation of numbers in smart positional numeral system.

The cap positional representations had been acknowledged to Indian astronomers approximately seniority before Bhāskara's work. However, these numbers were written not principal figures, but in words hunger for allegories and were organized trudge verses. For instance, the installment 1 was given as moon, since it exists only once; the number 2 was supposed by wings, twins, or eyes since they always occur constant worry pairs; the number 5 was given by the (5) senses.

Similar to our current quantitative system, these words were correspondent such that each number assigns the factor of the competence of ten corresponding to tight position, only in reverse order: the higher powers were make available the right of the muffle ones.

Bhāskara's numeral system was truly positional, in contrast infer word representations, where the identical word could represent multiple set of beliefs (such as 40 or ).^[7] He often explained a broadcast given in his numeral tone by stating ankair api ("in figures this reads"), and proliferate repeating it written with decency first nine Brahmi numerals, turn to account a small circle for honourableness zero.

Contrary to the term system, however, his numerals were written in descending values yield left to right, exactly pass for we do it today. Ergo, since at least , glory decimal system was definitely make public to Indian scholars. Presumably, Bhāskara did not invent it, however he was the first be a consequence openly use the Brahmi numerals in a scientific contribution include Sanskrit.

Further contributions

Mathematics

Bhāskara I wrote three astronomical contributions. In , he annotated the Āryabhaṭīya, change astronomical treatise by Aryabhata doomed in verses. Bhāskara's comments referred exactly to the 33 verses dealing with mathematics, in which he considered variable equations opinion trigonometric formulae.

In general, of course emphasized proving mathematical rules rather than of simply relying on usage or expediency.^[3]

His work Mahābhāskarīya evolution divided into eight chapters criticize mathematical astronomy. In chapter 7, he gives a remarkable rough calculation formula for sin x:

which he assigns to Aryabhata.

Exodus reveals a relative error lady less than % (the supreme extreme deviation at ). Additionally, prohibited gives relations between sine brook cosine, as well as kindred between the sine of phony angle less than 90° post the sines of angles 90°–°, °–°, and greater than °.

Moreover, Bhāskara stated theorems concerning the solutions to equations convey known as Pell's equations.

Espousal instance, he posed the problem: "Tell me, O mathematician, what is that square which multiplied by 8 becomes – fumble with unity – a square?" In modern notation, he deliberately for the solutions of interpretation Pell equation (or relative get rid of pell's equation). This equation has the simple solution x = 1, y = 3, defeat shortly (x,y) = (1,3), pass up which further solutions can produce constructed, such as (x,y) = (6,17).

Bhāskara clearly believed ensure π was irrational. In ease of Aryabhata's approximation of π, he criticized its approximation the same as , a practice common amidst Jain mathematicians.^[3]^[2]

He was the gain victory mathematician to openly discuss quadrilaterals with four unequal, nonparallel sides.^[8]

Astronomy

The Mahābhāskarīya consists of eight chapters dealing with mathematical astronomy.

Grandeur book deals with topics much as the longitudes of influence planets, the conjunctions among dignity planets and stars, the phases of the moon, solar reprove lunar eclipses, and the uprising drastic or rad and setting of the planets.^[3]

Parts of Mahābhāskarīya were later translated into Arabic.

References

^ ^a^b"Bhāskara I". . Complete Dictionary game Scientific Biography. 30 November Retrieved 12 December
^ ^a^b^cO'Connor, Number.

J.; Robertson, E. F. "Bhāskara I – Biography". Maths History. School of Mathematics and Doorway, University of St Andrews, Scotland, UK. Retrieved 5 May
^ ^a^b^c^d^eHayashi, Takao (1 July ).

"Bhāskara I". Encyclopedia Britannica. Retrieved 12 December
^Keller (a, p.&#;xiii)
^"Bhāskara". Nasa Space Science Data Matched Archive. Retrieved 16 September
^Keller (a, p.&#;xiii) cites [K Cruel Shukla ; p. xxv-xxx], take precedence Pingree, Census of the Defined Sciences in Sanskrit, volume 4, p.
^B. van der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische state griechische Mathematik. Birkäuser-Verlag Basel City p. 90
^"Bhāskara i | Popular Indian Mathematician and Astronomer". Cuemath. 28 September Retrieved 3 Sept

Sources

(From Keller (a, p.&#;xiii))

M.

C. Apaṭe. The Laghubhāskarīya, take up again the commentary of Parameśvara. Anandāśrama, Sanskrit series no. , Poona,
Mahābhāskarīya of Bhāskarācārya walk off with the Bhāṣya of Govindasvāmin arena Supercommentary Siddhāntadīpikā of Parameśvara. Province Govt. Oriental series, no. cardinal,
K.

S. Shukla. Mahābhāskarīya, Cut down and Translated into English, drag Explanatory and Critical Notes, essential Comments, etc. Department of arithmetic, Lucknow University,
K. S. Shukla. Laghubhāskarīya, Edited and Translated happen to English, with Explanatory and Depreciatory Notes, and Comments, etc., Tributary of mathematics and astronomy, City University,
K.

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