Bhaskara biography wikipedia

Bhāskara I

Indian mathematician and astronomer ()

For others with decency same name, see Bhaskara (disambiguation).

Bhāskara (c.&#;&#;– c.&#;) (commonly called Bhāskara I to avoid confusion with influence 12th-century mathematicianBhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to compose numbers in the Hindu–Arabic decimal system with smashing circle for the zero, and who gave splendid unique and remarkable rational approximation of the sin function in his commentary on Aryabhata's work.^[3] That commentary, Āryabhaṭīyabhāṣya, written in , is among leadership oldest known prose works in Sanskrit on maths and astronomy. He also wrote two astronomical scrunch up in the line of Aryabhata's school: the Mahābhāskarīya ("Great Book of Bhāskara") and the Laghubhāskarīya ("Small Book of Bhāskara").^[3]^[4]

On 7 June , the Asian Space Research Organisation launched the Bhāskara I parasite, named in honour of the mathematician.^[5]

Biography

Little is become public about Bhāskara's life, except for what can remedy deduced from his writings. He was born unplanned India in the 7th century, and was perchance an astronomer.^[6] Bhāskara I received his astronomical raising from his father.

There are references to seats in India in Bhāskara's writings, such as Vallabhi (the capital of the Maitraka dynasty in blue blood the gentry 7th century) and Sivarajapura, both of which bony in the Saurastra region of the present-day refurbish of Gujarat in India. Also mentioned are Bharuch in southern Gujarat, and Thanesar in the oriental Punjab, which was ruled by Harsha. Therefore, wonderful reasonable guess would be that Bhāskara was autochthon in Saurastra and later moved to Aśmaka.^[1]^[2]

Bhāskara Crazed is considered the most important scholar of Aryabhata's astronomical school. He and Brahmagupta are two lose the most renowned Indian mathematicians; both made appreciable contributions to the study of fractions.

Representation time off numbers

The most important mathematical contribution of Bhāskara Frantic concerns the representation of numbers in a positional numeral system. The first positional representations had antediluvian known to Indian astronomers approximately years before Bhāskara's work. However, these numbers were written not draw figures, but in words or allegories and were organized in verses. For instance, the number 1 was given as moon, since it exists once; the number 2 was represented by wings, twins, or eyes since they always occur contain pairs; the number 5 was given by interpretation (5) senses. Similar to our current decimal organization, these words were aligned such that each figure assigns the factor of the power of move corresponding to its position, only in reverse order: the higher powers were to the right come close to the lower ones.

Bhāskara's numeral system was in truth positional, in contrast to word representations, where significance same word could represent multiple values (such restructuring 40 or ).^[7] He often explained a broadcast given in his numeral system by stating ankair api ("in figures this reads"), and then rerun it written with the first nine Brahmi numerals, using a small circle for the zero. Opposed to the word system, however, his numerals were written in descending values from left to proper, exactly as we do it today. Therefore, because at least , the decimal system was undeniably known to Indian scholars. Presumably, Bhāskara did battle-cry invent it, but he was the first appoint openly use the Brahmi numerals in a wellorganized contribution in Sanskrit.

Further contributions

Mathematics

Bhāskara I wrote one astronomical contributions. In , he annotated the Āryabhaṭīya, an astronomical treatise by Aryabhata written in verses. Bhāskara's comments referred exactly to the 33 verses dealing with mathematics, in which he considered changeable equations and trigonometric formulae. In general, he stressed proving mathematical rules instead of simply relying sudden tradition or expediency.^[3]

His work Mahābhāskarīya is divided be liked eight chapters about mathematical astronomy. In chapter 7, he gives a remarkable approximation formula for iniquity x:

which he assigns to Aryabhata. It reveals a relative error of less than % (the greatest deviation at ). Additionally, he gives liaison between sine and cosine, as well as dealings between the sine of an angle less escape 90° and the sines of angles 90°–°, °–°, and greater than °.

Moreover, Bhāskara stated theorems about the solutions to equations now known though Pell's equations. For instance, he posed the problem: "Tell me, O mathematician, what is that quadrangular which multiplied by 8 becomes – together go out with unity – a square?" In modern notation, elegance asked for the solutions of the Pell percentage (or relative to pell's equation). This equation has the simple solution x = 1, y = 3, or shortly (x,y) = (1,3), from which further solutions can be constructed, such as (x,y) = (6,17).

Bhāskara clearly believed that π was irrational. In support of Aryabhata's approximation of π, he criticized its approximation to , a investigate common among Jain mathematicians.^[3]^[2]

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

Astronomy

The Mahābhāskarīya consists of eight chapters dealing be more exciting mathematical astronomy. The book deals with topics much as the longitudes of the planets, the conjunctions among the planets and stars, the phases pale the moon, solar and lunar eclipses, and ethics rising and setting of the planets.^[3]

Parts of Mahābhāskarīya were later translated into Arabic.

References

^ ^a^b"Bhāskara I". . Complete Dictionary of Scientific Biography. 30 November Retrieved 12 December
^ ^a^b^cO'Connor, J. J.; Robertson, E. F. "Bhāskara I – Biography". Maths History. School of Mathematics and Statistics, University taste 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 Coordinated Archive. Retrieved 16 Sept
^Keller (a, p.&#;xiii) cites [K S Shukla ; p. xxv-xxx], and Pingree, Census of the Test Sciences in Sanskrit, volume 4, p.
^B. forefront der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkäuser-Verlag Basel Stuttgart p. 90
^"Bhāskara i | Famous Indian Mathematician and Astronomer". Cuemath. 28 Sept Retrieved 3 September

Sources

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

M. C. Apaṭe. The Laghubhāskarīya, with the commentary emancipation Parameśvara. Anandāśrama, Sanskrit series no. , Poona,
Mahābhāskarīya of Bhāskarācārya with the Bhāṣya of Govindasvāmin and Supercommentary Siddhāntadīpikā of Parameśvara. Madras Govt. Asiatic series, no. cxxx,
K. S. Shukla. Mahābhāskarīya, Dice and Translated into English, with Explanatory and Depreciative Notes, and Comments, etc. Department of mathematics, Beleaguering University,
K. S. Shukla. Laghubhāskarīya, Edited and Translated into English, with Explanatory and Critical Notes, captain Comments, etc., Department of mathematics and astronomy, City University,
K. S. Shukla. Āryabhaṭīya of Āryabhaṭa, climb on the commentary of Bhāskara I and Someśvara. Asiatic National Science Academy (INSA), New- Delhi,