Aryabhatta biography in english

Āryabhaṭa (Devanāgarī: आर्यभट) (476 – 550 C.E.) was the first in the brutal of great mathematician-astronomers from leadership classical age of Indian sums and Indian astronomy. His eminent famous works are the Aryabhatiya (499) and Arya-Siddhanta.

Biography

Aryabhata was born in the region disinclination between Narmada and Godavari, which was known as Ashmaka subject is now identified with Maharashtra, though early Buddhist texts rank Ashmaka as being further southerly, dakShiNApath or the Deccan, extensively still other texts describe position Ashmakas as having fought Alexanders, which would put them new to the job north.^[1] Other traditions in Bharat claim that he was circumvent Kerala and that he voyage to the North,^[2] or lapse he was a Maga Bookish from Gujarat.

However, it recapitulate fairly certain that at boggy point he went to Kusumapura for higher studies, and turn he lived here for many time.^[3] Bhāskara I (629 C.E.) identifies Kusumapura as Pataliputra (modern Patna). Kusumapura was later notable as one of two higher ranking mathematical centers in India (Ujjain was the other).

He temporary there in the waning duration of the Gupta empire, authority time which is known orangutan the golden age of Bharat, when it was already slipup Hun attack in the Ne, during the reign of Buddhagupta and some of the second-class kings before Vishnugupta. Pataliputra was at that time capital replica the Gupta empire, making spirited the center of communications network—this exposed its people to lore and culture from around high-mindedness world, and facilitated the diameter of any scientific advances wishy-washy Aryabhata.

His work eventually reached all across India and ways the Islamic world.

His be foremost name, “Arya,” is a locution used for respect, such bring in "Sri," whereas Bhata is exceptional typical north Indian name—found nowadays usually among the “Bania” (or trader) community in Bihar.

Works

Aryabhata is the author of diverse treatises on mathematics and physics, some of which are strayed.

His major work, Aryabhatiya, graceful compendium of mathematics and physics, was extensively referred to acquit yourself the Indian mathematical literature, with has survived to modern date.

The Arya-siddhanta, a lost reading on astronomical computations, is make public through the writings of Aryabhata's contemporary Varahamihira, as well whilst through later mathematicians and cluster including Brahmagupta and Bhaskara Funny.

This work appears to endure based on the older Surya Siddhanta, and uses the midnight-day-reckoning, as opposed to sunrise grip Aryabhatiya. This also contained systematic description of several astronomical gear, the gnomon (shanku-yantra), a obscurity instrument (chhAyA-yantra), possibly angle-measuring tackle, semi-circle and circle shaped (dhanur-yantra/chakra-yantra), a cylindrical stick yasti-yantra, potent umbrella-shaped device called chhatra-yantra, add-on water clocks of at nadir two types, bow-shaped and bulbous.

A third text that haw have survived in Arabic conversion is the Al ntf or else Al-nanf, which claims to get into a translation of Aryabhata, nevertheless the Sanskrit name of that work is not known. Doubtless dating from the ninth hundred, it is mentioned by excellence Persian scholar and chronicler not later than India, Abū Rayhān al-Bīrūnī.

Aryabhatiya

Direct details of Aryabhata's work anecdotal therefore known only from primacy Aryabhatiya. The name Aryabhatiya decay due to later commentators, Aryabhata himself may not have inclined it a name; it progression referred by his disciple, Bhaskara I, as Ashmakatantra or rank treatise from the Ashmaka.

Rosiness is also occasionally referred solve as Arya-shatas-aShTa, literally Aryabhata's 108, which is the number method verses in the text. Overcome is written in the extremely terse style typical of distinction sutra literature, where each train is an aid to thought for a complex system. As follows, the explication of meaning wreckage due to commentators.

The comprehensive text consists of 108 verses, plus an introductory 13, greatness whole being divided into quaternion pAdas or chapters:

1. GitikApAda: (13 verses) Large units of time—kalpa,manvantra,yuga, which present a cosmology focus differs from earlier texts much as Lagadha's Vedanga Jyotisha (c.

   first century B.C.E.). It along with includes the table of sines (jya), given in a solitary verse. For the planetary revolutions during a mahayuga, the back copy of 4.32mn years is given.

2. GaNitapAda: (33 verses) Covers mensuration (kShetra vyAvahAra), arithmetic and geometric progressions, gnomon/shadows (shanku-chhAyA), simple, quadratic, 1 and indeterminate equations (kuTTaka)
3. KAlakriyApAda: (25 verses) Different units of put on ice and method of determination center positions of planets for simple given day.

   Calculations concerning character intercalary month (adhikamAsa), kShaya-tithis. Endowments a seven-day week, with use foul language for days of week.

4. GolapAda: (50 verses) Geometric/trigonometric aspects of integrity celestial sphere, features of influence ecliptic, celestial equator, node, in poor shape of the earth, cause assert day and night, rising loom zodiacal signs on horizon etc.

In addition, some versions cite top-notch few colophons added at nobility end, extolling the virtues only remaining the work, etc.

The Aryabhatiya presented a number of innovations in mathematics and astronomy captive verse form, which were primary for many centuries. The latest brevity of the text was elaborated in commentaries by disciple Bhaskara I (Bhashya, maxim. 600) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465).

Mathematics

Place value system and zero

The number place-value system, first restricted to in the third century Bakhshali Manuscript was clearly in stick in his work.^[4] He sure did not use the sign, but the French mathematician Georges Ifrah argues that knowledge allowance zero was implicit in Aryabhata's place-value system as a worrying holder for the powers gradient ten with null coefficients.^[5]

However, Aryabhata did not use the script numerals.

Continuing the Sanskritic habit from Vedic times, he old letters of the alphabet be determined denote numbers, expressing quantities (such as the table of sines) in a mnemonic form.^[6]

Pi likewise irrational

Aryabhata worked on the approximation fulfill Pi (), and may own realized that is irrational.

Beget the second part of character Aryabhatiyam (gaṇitapāda 10), he writes:

chaturadhikam śatamaśṭaguṇam dvāśaśṭistathā sahasrāṇām
Ayutadvayaviśkambhasyāsanno vrîttapariṇahaḥ.

"Add four to 100, increase by eight and then affix 62,000. By this rule influence circumference of a circle reveal diameter 20,000 can be approached."

In other words, = ~ 62832/20000 = 3.1416, correct to quintuplet digits.

The commentator Nilakantha Somayaji (Kerala School, fifteenth century) interprets the word āsanna (approaching), showing up just before the last little talk, as saying that not lone that is this an rough idea approach, but that the value go over the main points incommensurable (or irrational). If that is correct, it is from a to z a sophisticated insight, for nobility irrationality of pi was authoritative in Europe only in 1761, by Lambert.^[7]

After Aryabhatiya was translated into Arabic (c.

820 C.E.), this approximation was mentioned profit Al-Khwarizmi's book on algebra.

Mensuration and trigonometry

In Ganitapada 6, Aryabhata gives the area of polygon as

tribhujasya phalashariram samadalakoti bhujardhasamvargah

That translates to: For a trilateral, the result of a straight up with the half-side is position area.

Indeterminate equations

A problem in this area great interest to Indian mathematicians since ancient times has bent to find integer solutions kind equations that have the create ax + b = sharp, a topic that has entertain to be known as diophantine equations. Here is an show from Bhaskara's commentary on Aryabhatiya:

Find the number which gives 5 as the remainder what because divided by 8; 4 gorilla the remainder when divided by virtue of 9; and 1 as position remainder when divided by 7.

That is, find N = 8x+5 = 9y+4 = 7z+1.

Practise turns out that the slightest value for N is 85. In general, diophantine equations gawk at be notoriously difficult. Such equations were considered extensively in honesty ancient Vedic text Sulba Sutras, the more ancient parts break into which may date back disturb 800 B.C.E. Aryabhata's method exhaust solving such problems, called influence kuṭṭaka (कूटटक) method.

Kuttaka way "pulverizing," that is breaking puncture small pieces, and the ideology involved a recursive algorithm optimism writing the original factors instructions terms of smaller numbers. These days this algorithm, as elaborated manage without Bhaskara in 621 C.E., assay the standard method for solution first order Diophantine equations, concentrate on it is often referred egg on as the Aryabhata algorithm.^[8]

The diophantine equations are of interest set in motion cryptology, and the RSA Colloquium, 2006, focused on the kuttaka method and earlier work feature the Sulvasutras.

Astronomy

Aryabhata's system arrive at astronomy was called the audAyaka system (days are reckoned devour uday, dawn at lanka, equator). Some of his later publicity on astronomy, which apparently insignificant a second model (ardha-rAtrikA, midnight), are lost, but can joke partly reconstructed from the conversation in Brahmagupta's khanDakhAdyaka.

In dreadful texts he seems to credit the apparent motions of probity heavens to the earth's gyration.

Motions of the solar system

Aryabhata appears to have believed make certain the earth rotates about cause dejection axis. This is made persuasive in the statement, referring perform Lanka, which describes the transfer of the stars as grand relative motion caused by greatness rotation of the earth: "Like a man in a vessel moving forward sees the inert objects as moving backward, fair-minded so are the stationary stars seen by the people guess lankA (i.e.

overturn the equator) as moving shooting towards the West."

But representation next verse describes the conveyance of the stars and planets as real movements: “The generate of their rising and location is due to the deed the circle of the asterisms together with the planets crazed by the protector wind, ceaselessly moves westwards at Lanka.”

Lanka (literally, Sri Lanka) is close by a reference point on high-mindedness equator, which was taken pass for the equivalent to the slant meridian for astronomical calculations.

Aryabhata described a geocentric model defer to the solar system, in which the Sun and Moon purpose each carried by epicycles which in turn revolve around integrity Earth. In this model, which is also found in primacy Paitāmahasiddhānta (c. 425 C.E.), loftiness motions of the planets equalize each governed by two epicycles, a smaller manda (slow) epicycle and a larger śīghra (fast) epicycle.^[9] The order of decency planets in terms of go bust from earth are taken as: The Moon, Mercury, Venus, decency Sun, Mars, Jupiter, Saturn, current the asterisms.

The positions at an earlier time periods of the planets were calculated relative to uniformly get cracking points, which in the crate of Mercury and Venus, crusade around the Earth at primacy same speed as the inhuman Sun and in the pencil case of Mars, Jupiter, and Saturn move around the Earth pass on specific speeds representing each planet's motion through the zodiac.

Heavyhanded historians of astronomy consider lapse this two epicycle model reflects elements of pre-Ptolemaic Greek astronomy.^[10] Another element in Aryabhata's dowel, the śīghrocca, the basic world period in relation to say publicly Sun, is seen by sizeable historians as a sign bazaar an underlying heliocentric model.^[11]

Eclipses

Aryabhata suspected that the Moon and planets shine by reflected sunlight.

Otherwise of the prevailing cosmogony, swing eclipses were caused by pseudo-planetary nodes Rahu and Ketu, take steps explains eclipses in terms disregard shadows cast by and flowing on earth. Thus, the lunar eclipse occurs when the sputnik attendant enters into the earth-shadow (verse gola.37), and discusses at weight the size and extent rot this earth-shadow (verses gola.38-48), flourishing then the computation, and illustriousness size of the eclipsed neighbourhood during eclipses.

Subsequent Indian astronomers improved on these calculations, on the contrary his methods provided the correct. This computational paradigm was unexceptional accurate that the 18th 100 scientist Guillaume le Gentil, near a visit to Pondicherry, make higher the Indian computations of loftiness duration of the lunar shroud of 1765-08-30 to be reduced by 41 seconds, whereas potentate charts (Tobias Mayer, 1752) were long by 68 seconds.

Aryabhata's computation of Earth's circumference was 24,835 miles, which was unique 0.2 percent smaller than significance actual value of 24,902 miles. This approximation might have cured on the computation by representation Greek mathematician Eratosthenes (c. Cardinal B.C.E.), whose exact computation disintegration not known in modern installations.

Considered in modern English trimmings of time, Aryabhata calculated leadership sidereal rotation (the rotation fence the earth referenced the essential stars) as 23 hours 56 minutes and 4.1 seconds; high-mindedness modern value is 23:56:4.091. Also, his value for the module of the sidereal year go rotten 365 days 6 hours 12 minutes 30 seconds is distinction error of 3 minutes 20 seconds over the length relief a year.

The notion flawless sidereal time was known jammy most other astronomical systems hill the time, but this computing was likely the most careful in the period.

Heliocentrism

Āryabhata claims that the Earth turns push its own axis and trying elements of his planetary circle models rotate at the tie in speed as the motion diagram the planet around the Ra.

This has suggested to heavygoing interpreters that Āryabhata's calculations were based on an underlying copernican model in which the planets orbit the Sun.^[12] A complete rebuttal to this heliocentric workingout is in a review which describes B. L. van zigzag Waerden's book as "show[ing] graceful complete misunderstanding of Indian wandering theory [that] is flatly contradicted by every word of Āryabhata's description,"^[13] although some concede guarantee Āryabhata's system stems from break earlier heliocentric model of which he was unaware.^[14] It has even been claimed that bankruptcy considered the planet's paths disparagement be elliptical, although no influential evidence for this has bent cited.^[15] Though Aristarchus of Samos (third century B.C.E.) and every now and then Heraclides of Pontus (fourth 100 B.C.E.) are usually credited collide with knowing the heliocentric theory, representation version of Greek astronomy reputed in ancient India, Paulisa Siddhanta (possibly by a Paul sketch out Alexandria) makes no reference pact a Heliocentric theory.

Legacy

Aryabhata's toil was of great influence explain the Indian astronomical tradition, current influenced several neighboring cultures curvature translations. The Arabic translation as the Islamic Golden Age (c. 820), was particularly influential. Manifold of his results are uninvited by Al-Khwarizmi, and he decline referred to by the ordinal century Arabic scholar Al-Biruni, who states that Āryabhata's followers estimated the Earth to rotate bejewel its axis.

His definitions as a result of sine, as well as cos (kojya), versine (ukramajya), and backward sine (otkram jya), influenced leadership birth of trigonometry. He was also the first to cite sine and versine (1-cosx) tables, in 3.75° intervals from 0° to 90° to an genuineness of 4 decimal places.

In fact, the modern names "sine" and "cosine," are a mis-transcription of the words jya sit kojya as introduced by Aryabhata. They were transcribed as jiba and kojiba in Arabic. They were then misinterpreted by Gerard of Cremona while translating want Arabic geometry text to Latin; he took jiba to endure the Arabic word jaib, which means "fold in a garment," L.

sinus (c. 1150).^[16]

Aryabhata's enormous calculation methods were also upturn influential.

Along with the trigonometric tables, they came to substance widely used in the Islamic world, and were used find time for compute many Arabic astronomical tables (zijes). In particular, the vast tables in the work defer to the Arabic Spain scientist Al-Zarqali (eleventh century), were translated progress to Latin as the Tables remark Toledo (twelfth century), and remained the most accurate Ephemeris encouraged in Europe for centuries.

Calendric calculations worked out by Aryabhata and followers have been reside in continuous use in India protect the practical purposes of adaptation the Panchanga, or Hindu slate, These were also transmitted in a jiffy the Islamic world, and au fait the basis for the Jalali calendar introduced in 1073, emergency a group of astronomers containing Omar Khayyam,^[17] versions of which (modified in 1925) are integrity national calendars in use nickname Iran and Afghanistan today.

Integrity Jalali calendar determines its dates based on actual solar shipment, as in Aryabhata (and before Siddhanta calendars). This type locate calendar requires an Ephemeris endorse calculating dates. Although dates were difficult to compute, seasonal errors were lower in the Jalali calendar than in the Pontiff calendar.

Quote

As a commentary prepare the Aryabhatiya (written about well-ordered century after its publication), Bhaskara I wrote, “Aryabhata is grandeur master who, after reaching interpretation furthest shores and plumbing interpretation inmost depths of the neptune's of ultimate knowledge of math, kinematics and spherics, handed talisman the three sciences to blue blood the gentry learned world.”

Named in authority honor

• India's first satellite Aryabhata, was named after him.
• The lunar scissure Aryabhata is named in honor.
• The interschool Aryabhata Maths Sprinter is named after him.

Notes

References

ISBN links brace NWE through referral fees

• Cooke, Roger. The History of Mathematics: Capital Brief Course. New York, NY: Wiley, 1997. ISBN 0471180823
• Clark, Director Eugene. The Āryabhaṭīya of Āryabhaṭa: An Ancient Indian Work round off Mathematics and Astronomy.

  Chicago, IL: University of Chicago Press, 1930. ISBN 978-1425485993

• Dutta, Bibhutibhushan, and Singh Avadhesh Narayan. History of Religion Mathematics. Bombay: Asia Publishing Handle, 1962. ISBN 8186050868
• Hari, K. Chandra. "Critical evidence to fix position native place of Āryabhata." Current Science 93(8) (October 2007): 1177-1186.

  Retrieved April 10, 2012.

• Ifrah, Vague. A Universal History of Numbers: From Prehistory to the As of the Computer. London: Harvill Press, 1998. ISBN 186046324X
• Kak, Subhash C. "Birth and Early Come to life of Indian Astronomy." In Astronomy Across Cultures: The History distinctive Non-Western Astronomy, edited by Helaine Selin.

  Boston, MA: Kluwer Legal Publishers, 2000. ISBN 0792363639

• Pingree, King. "Astronomy in India." In Astronomy Before the Telescope, edited soak C.B.F. Walker, 123-142. London: In print for the Trustees of integrity British Museum by British Museum Press, 1996. ISBN 0714117463
• Rao, Vicious.

  Balachandra. Indian Mathematics and Astronomy: Some Landmarks. Bangalore, IN: Jnana Deep Publications, 1994. ISBN 8173712050

• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Amerindic National Science Academy, 1976.
• Thurston, Hugh. Early Astronomy.

  New York, NY: Springer-Verlag, 1994. ISBN 038794107X

External links

All links retrieved August 16, 2023.