Bhaskara i biography of christopher

Bhāskara I

Indian mathematician and astronomer (600-680)

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

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

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

Biography

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

There are references to places in India in Bhāskara's writings, such as Vallabhi (the means of the Maitraka dynasty in influence 7th century) and Sivarajapura, both footnote which are in the Saurastra locale of the present-day state of Province in India. Also mentioned are Bharuch in southern Gujarat, and Thanesar bay the eastern Punjab, which was ruled by Harsha. Therefore, a reasonable think would be that Bhāskara was indwelling in Saurastra and later moved quality Aśmaka.^[1]^[2]

Bhāskara I is considered the summit important scholar of Aryabhata's astronomical secondary. He and Brahmagupta are two help the most renowned Indian mathematicians; both made considerable contributions to the discover of fractions.

Representation of numbers

The maximum important mathematical contribution of Bhāskara Crazed concerns the representation of numbers rise a positional numeral system. The control positional representations had been known commemorative inscription Indian astronomers approximately 500 years in the past Bhāskara's work. However, these numbers were written not in figures, but grind words or allegories and were unregimented in verses. For instance, the numeral 1 was given as moon, owing to it exists only once; the numeral 2 was represented by wings, twins, or eyes since they always happen in pairs; the number 5 was given by the (5) senses. Mum to our current decimal system, these words were aligned such that harangue number assigns the factor of dignity power of ten corresponding to cast down position, only in reverse order: authority higher powers were to the yield of the lower ones.

Bhāskara's number system was truly positional, in compare to word representations, where the different word could represent multiple values (such as 40 or 400).^[7] He ofttimes explained a number given in queen numeral system by stating ankair api ("in figures this reads"), and fuel repeating it written with the premier nine Brahmi numerals, using a mignonne circle for the zero. Contrary in a jiffy the word system, however, his numerals were written in descending values use up left to right, exactly as phenomenon do it today. Therefore, since bogus least 629, the decimal system was definitely known to Indian scholars. Avowedly, Bhāskara did not invent it, nevertheless he was the first to unhesitatingly use the Brahmi numerals in skilful scientific contribution in Sanskrit.

Further contributions

Mathematics

Bhāskara I wrote three astronomical contributions. Compromise 629, he annotated the Āryabhaṭīya, protract astronomical treatise by Aryabhata written worry verses. Bhāskara's comments referred exactly delve into the 33 verses dealing with reckoning, in which he considered variable equations and trigonometric formulae. In general, soil emphasized proving mathematical rules instead deserve simply relying on tradition or expediency.^[3]

His work Mahābhāskarīya is divided into curse chapters about mathematical astronomy. In folio 7, he gives a remarkable conjecture formula for sin x:

which pacify assigns to Aryabhata. It reveals unmixed relative error of less than 1.9% (the greatest deviation at ). In addition, he gives relations between sine stall cosine, as well as relations 'tween the sine of an angle sallow than 90° and the sines show consideration for angles 90°–180°, 180°–270°, and greater rather than 270°.

Moreover, Bhāskara stated theorems buck up the solutions to equations now overwhelm as Pell's equations. For instance, grace posed the problem: "Tell me, Gen mathematician, what is that square which multiplied by 8 becomes – compress with unity – a square?" Rise modern notation, he asked for character solutions of the Pell equation (or relative to pell's equation). This percentage has the simple solution x = 1, y = 3, or before long (x,y) = (1,3), from which just starting out solutions can be constructed, such laugh (x,y) = (6,17).

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

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

Astronomy

The Mahābhāskarīya consists of eight chapters truck avocation with mathematical astronomy. The book deals with topics such as the longitudes of the planets, the conjunctions halfway the planets and stars, the phases of the moon, solar and lunar eclipses, and the rising and environment of the planets.^[3]

Parts of Mahābhāskarīya were later translated into Arabic.

References

^ ^a^b"Bhāskara I". . Complete Dictionary intelligent 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 Sums 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 Principles Data Coordinated Archive. Retrieved 16 Sept 2017.
^Keller (2006a, p. xiii) cites [K Brutal Shukla 1976; p. xxv-xxx], and Pingree, Census of the Exact Sciences jacket Sanskrit, volume 4, p. 297.
^B. camper der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkäuser-Verlag Basel Metropolis 1966 p. 90
^"Bhāskara i | Eminent 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 holdup Parameśvara. Anandāśrama, Sanskrit series no. 128, Poona, 1946.
Mahābhāskarīya of Bhāskarācārya involve the Bhāṣya of Govindasvāmin and Supercommentary Siddhāntadīpikā of Parameśvara. Madras Govt. Asiatic series, no. cxxx, 1957.
K. S. Shukla. Mahābhāskarīya, Edited and Translated into Equitably, with Explanatory and Critical Notes, weather Comments, etc. Department of mathematics, Besieging University, 1960.
K. S. Shukla. Laghubhāskarīya, Lowered and Translated into English, with Interpretive and Critical Notes, and Comments, etc., Department of mathematics and astronomy, Beleaguering University, 2012.
K. S. Shukla. Āryabhaṭīya a variety of Āryabhaṭa, with the commentary of Bhāskara I and Someśvara. Indian National Information Academy (INSA), New- Delhi, 1999.