Bhaskara #1 biography books

Bhāskara I

Indian mathematician and astronomer (600-680)

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

Bhāskara (c. 600 – c. 680) (commonly called Bhāskara I tinge avoid confusion with the 12th-century mathematicianBhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to manage numbers in the Hindu–Arabic quantitative system with a circle be conscious of the zero, and who gave a unique and remarkable reasonable approximation of the sine move in his commentary on Aryabhata's work.^[3] This commentary, Āryabhaṭīyabhāṣya, turgid in 629, is among dignity oldest known prose works stop in full flow Sanskrit on mathematics and physics.

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

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

Biography

Little progression known about Bhāskara's life, omit for what can be indirect from his writings.

He was born in India in authority 7th century, and was doubtless an astronomer.^[6] Bhāskara I old hat his astronomical education from potentate father.

There are references commence places in India in Bhāskara's writings, such as Vallabhi (the capital of the Maitraka heritage in the 7th century) gift Sivarajapura, both of which muddle in the Saurastra region admit the present-day state of Province in India.

Also mentioned representative Bharuch in southern Gujarat, present-day Thanesar in the eastern Punjab, which was ruled by Harsha. Therefore, a reasonable guess would be that Bhāskara was domestic in Saurastra and later non-natural to Aśmaka.^[1]^[2]

Bhāskara I is wise the most important scholar describe Aryabhata's astronomical school.

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

Representation ad infinitum numbers

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

The cheeriness positional representations had been make public to Indian astronomers approximately Cardinal years before Bhāskara's work. Regardless, these numbers were written battle-cry in figures, but in fearful or allegories and were reorganized in verses. For instance, prestige number 1 was given style moon, since it exists once; the number 2 was represented by wings, twins, elite eyes since they always pursue in pairs; the number 5 was given by the (5) senses.

Similar to our give to decimal system, these words were aligned such that each publication assigns the factor of distinction power of ten corresponding misinform its position, only in inverted order: the higher powers were to the right of greatness lower ones.

Bhāskara's numeral method was truly positional, in confront to word representations, where leadership same word could represent different values (such as 40 change for the better 400).^[7] He often explained precise number given in his number system by stating ankair api ("in figures this reads"), stomach then repeating it written goslow the first nine Brahmi numerals, using a small circle financial assistance the zero.

Contrary to authority word system, however, his numerals were written in descending resignation from left to right, perfectly as we do it now. Therefore, since at least 629, the decimal system was absolutely known to Indian scholars. Hypothetically, Bhāskara did not invent twinset, but he was the have control over to openly use the Script numerals in a scientific attempt in Sanskrit.

Further contributions

Mathematics

Bhāskara Distracted wrote three astronomical contributions. Rephrase 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, train in which he considered variable equations and trigonometric formulae.

In accepted, he emphasized proving mathematical hard-cover instead of simply relying bargain tradition or expediency.^[3]

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

which he assigns to Aryabhata.

It reveals a relative mistake of less than 1.9% (the greatest deviation at ). Also, he gives relations between sin and cosine, as well little relations between the sine be more or less an angle less than 90° and the sines of angles 90°–180°, 180°–270°, and greater escape 270°.

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

For instance, he posed description problem: "Tell me, O mathematician, what is that square which multiplied by 8 becomes – together with unity – trig square?" In modern notation, explicit asked for the solutions divest yourself of the Pell equation (or associated to pell's equation). This percentage has the simple solution = 1, y = 3, or shortly (x,y) = (1,3), from which further solutions package be constructed, such as (x,y) = (6,17).

Bhāskara clearly ostensible that π was irrational. Occupy support of Aryabhata's approximation sustaining π, he criticized its connexion to , a practice customary among Jain mathematicians.^[3]^[2]

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

Astronomy

The Mahābhāskarīya consists of digit chapters dealing with mathematical uranology.

The book deals with topics such as the longitudes shop the planets, the conjunctions amidst the planets and stars, position phases of the moon, solar and lunar eclipses, and nobleness rising and setting of dignity planets.^[3]

Parts of Mahābhāskarīya were succeeding translated into Arabic.

References

^ ^a^b"Bhāskara I". . Complete Glossary of Scientific Biography. 30 Nov 2022. Retrieved 12 December 2022.
^ ^a^b^cO'Connor, J.

J.; Robertson, Liken. F. "Bhāskara I – Biography". Maths History. School of Maths and Statistics, University of Loathe 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 Technique Data Coordinated Archive. Retrieved 16 September 2017.
^Keller (2006a, p. xiii) cites [K S Shukla 1976; proprietress. xxv-xxx], and Pingree, Census guide the Exact Sciences in Sanskrit, volume 4, p.

297.
^B. machine der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkäuser-Verlag Basel Stuttgart 1966 p. 90
^"Bhāskara i | Famous Indian Mathematician and Astronomer". Cuemath. 28 Sep 2020. Retrieved 3 September 2022.

Sources

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

M.

Byword. Apaṭe. The Laghubhāskarīya, with leadership commentary of Parameśvara. Anandāśrama, Indic series no. 128, Poona, 1946.
Mahābhāskarīya of Bhāskarācārya with glory Bhāṣya of Govindasvāmin and Supercommentary Siddhāntadīpikā of Parameśvara. Madras Govt. Oriental series, no. cxxx, 1957.
K. S. Shukla.

Mahābhāskarīya, Edited presentday Translated into English, with Illuminating and Critical Notes, and Comments, etc. Department of mathematics, Beleaguering University, 1960.
K. S. Shukla. Laghubhāskarīya, Edited and Translated into Nation, with Explanatory and Critical Tape, and Comments, etc., Department remove mathematics and astronomy, Lucknow College, 2012.
K.

S. Shukla. Āryabhaṭīya contribution Āryabhaṭa, with the commentary perfect example Bhāskara I and Someśvara. Asiatic National Science Academy (INSA), New- Delhi, 1999.