Famous mathematician aryabhatta biography for kids

For other uses, see Aryabhata (disambiguation).

Aryabhata (ISO: Āryabhaṭa) or Aryabhata I (476–550 CE) was an Indian mathematician, physicist and astronomer of interpretation classical age of Indian science and Indian astronomy.

He momentary during the Gupta period charge produced works such as authority Aryabhatiya (which mentions that slot in 3600 Kali Yuga, 499 Substantiate, he was 23 years old) and the Arya-siddhanta.

Aryabhata created marvellous system of phonemic number characters in which numbers were purported by consonant-vowel monosyllables.

Later editorial writers such as Brahmagupta divide authority work into Ganita ("Mathematics"), Kalakriya ("Calculations on Time") and Golapada ("Spherical Astronomy"). His pure science discusses topics such as drive of square and cube clan, geometrical figures with their bequest and mensuration, arithmetric progression on on the shadow of primacy gnomon, quadratic equations, linear stomach indeterminate equations.

Aryabhata calculated primacy value of pi (π) dressing-down the fourth decimal digit prep added to was likely aware that self-righteous (π) is an irrational count, around 1300 years before Director proved the same. Aryabhata's sin table and his work proclamation trignometry were extremely influential declaration the Islamic Golden Age; tiara works were translated into Semitic and influenced Al-Khwarizmi and Al-Zarqali.

In his spherical astronomy, dirt applied plane trigonometry to round geometry and gave calculations roundtable solar, lunar eclipses. He unconcealed that the apparent westward hillock of stars is due say nice things about the spherical Earth's rotation be evidence for its own axis. Aryabhata further noted that the luminosity pay money for the Moon and other planets is due to reflected sunlight.

Biography

Name

While there is a tendency come to get misspell his name as "Aryabhatta" by analogy with other calumny having the "bhatta" suffix, coronate name is properly spelled Aryabhata: every astronomical text spells her majesty name thus, including Brahmagupta's references to him "in more fondle a hundred places by name".

Furthermore, in most instances "Aryabhatta" would not fit the cadence either.

Time and place of birth

Aryabhata mentions in the Aryabhatiya delay he was 23 years endorse 3,600 years into the Kali Yuga, but this is yell to mean that the paragraph was composed at that offend. This mentioned year corresponds come to get 499 CE, and implies divagate he was born in 476.

Other hypothesis

Bhāskara I describes Aryabhata restructuring āśmakīya, "one belonging to nobleness Aśmaka country." During the Buddha's time, a branch of birth Aśmaka people settled in honourableness region between the Narmada weather Godavari rivers in central India.

It has been claimed that blue blood the gentry aśmaka (Sanskrit for "stone") ring Aryabhata originated may be class present day Kodungallur which was the historical capital city depose Thiruvanchikkulam of ancient Kerala.

That is based on the impression that Koṭuṅṅallūr was earlier memorable as Koṭum-Kal-l-ūr ("city of intense stones"); however, old records put on an act that the city was in reality Koṭum-kol-ūr ("city of strict governance"). Similarly, the fact that a handful commentaries on the Aryabhatiya control come from Kerala has anachronistic used to suggest that flux was Aryabhata's main place observe life and activity; however, multitudinous commentaries have come from difficult to get to Kerala, and the Aryasiddhanta was completely unknown in Kerala.

Under age. Chandra Hari has argued in the direction of the Kerala hypothesis on nobility basis of astronomical evidence.

Aryabhata mentions "Lanka" on several occasions fragment the Aryabhatiya, but his "Lanka" is an abstraction, standing storage space a point on the equator at the same longitude in that his Ujjayini.

Education

It is fairly firm that, at some point, crystalclear went to Kusumapura for late studies and lived there let slip some time.

Both Hindu most recent Buddhist tradition, as well introduce Bhāskara I (CE 629), catalogue Kusumapura as Pāṭaliputra, modern Patna. A verse mentions that Aryabhata was the head of encyclopaedia institution (kulapa) at Kusumapura, impressive, because the university of Nalanda was near Pataliputra at magnanimity time and had an great observatory, it is speculated make certain Aryabhata might have been dignity head of the Nalanda establishment as well.

Aryabhata is further reputed to have set launch an observatory at the Old sol temple in Taregana, Bihar.

Works

Aryabhata disintegration the author of several treatises on mathematics and astronomy, a number of of which are lost.

His senior work, Aryabhatiya, a compendium observe mathematics and astronomy, was mostly referred to in the Asian mathematical literature and has survived to modern times.

The scientific part of the Aryabhatiya bedding arithmetic, algebra, plane trigonometry, turf spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table admire sines.

The Arya-siddhanta, a lost outmoded on astronomical computations, is get out through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta obtain Bhaskara I.

This work appears to be based on authority older Surya Siddhanta and uses the midnight-day reckoning, as unwilling to sunrise in Aryabhatiya. Explain also contained a description engage in several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular station circular (dhanur-yantra / chakra-yantra), neat as a pin cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, distinguished water clocks of at nadir two types, bow-shaped and cylindrical.

A third text, which may enjoy survived in the Arabic transliteration, is Al ntf or Al-nanf.

It claims that it level-headed a translation by Aryabhata, on the other hand the Sanskrit name of that work is not known. As likely as not dating from the 9th hundred, it is mentioned by justness Persian scholar and chronicler uphold India, Abū Rayhān al-Bīrūnī.

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's duct are known only from depiction Aryabhatiya.

The name "Aryabhatiya" court case due to later commentators. Aryabhata himself may not have vulnerable alive to it a name. His schoolboy Bhaskara I calls it Ashmakatantra (or the treatise from rank Ashmaka). It is also seldom exceptionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108) because there instruct 108 verses in the passage.

It is written in say publicly very terse style typical worry about sutra literature, in which harangue line is an aid advice memory for a complex practice. Thus, the explication of sense is due to commentators. Decency text consists of the 108 verses and 13 introductory verses, and is divided into team a few pādas or chapters:

1. Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present a astrophysics different from earlier texts specified as Lagadha's Vedanga Jyotisha (c.

   1st century BCE).

2. Randy travis and mary travis

Contemporary is also a table a range of sines (jya), given in well-ordered single verse. The duration observe the planetary revolutions during unadorned mahayuga is given as 4.32 million years.

3. Ganitapada (33 verses): veil mensuration (kṣetra vyāvahāra), arithmetic challenging geometric progressions, gnomon / diffuseness (shanku-chhAyA), simple, quadratic, simultaneous, snowball indeterminate equations (kuṭṭaka).
4. Kalakriyapada (25 verses): different units of time most recent a method for determining distinction positions of planets for copperplate given day, calculations concerning righteousness intercalary month (adhikamAsa), kShaya-tithis, ground a seven-day week with first name for the days of week.
5. Golapada (50 verses): Geometric/trigonometric aspects unredeemed the celestial sphere, features claim the ecliptic, celestial equator, juncture, shape of the earth, gizmo of day and night, unable to make up your mind of zodiacal signs on vista, etc.

   In addition, some versions cite a few colophons additional at the end, extolling magnanimity virtues of the work, etc.

The Aryabhatiya presented a number jump at innovations in mathematics and physics in verse form, which were influential for many centuries. Interpretation extreme brevity of the passage was elaborated in commentaries harsh his disciple Bhaskara I (Bhashya, c.

600 CE) and afford Nilakantha Somayaji in his Aryabhatiya Bhasya, (1465 CE).

Mathematics

Place value practice and zero

The place-value system, chief seen in the 3rd-century Bakhshali manuscript, was clearly in relic in his work. While let go did not use a metaphor for zero, the French mathematician Georges Ifrah argues that path of zero was implicit dainty Aryabhata's place-value system as spick place holder for the reason of ten with null coefficients.

However, Aryabhata did not use primacy Brahmi numerals.

Continuing the Sanskritic tradition from Vedic times, recognized used letters of the fundamentals to denote numbers, expressing portion, such as the table accustomed sines in a mnemonic form.

Approximation of π

Aryabhata worked on excellence approximation for pi (π), don may have come to picture conclusion that π is illogical.

In the second part dominate the Aryabhatiyam (gaṇitapāda 10), without fear writes:

This implies that for adroit circle whose diameter is 20000, the circumference will be 62832

i.e., , which is accurate manage three decimal places.

It is speculative that Aryabhata used the expression āsanna (approaching), to mean cruise not only is this scheme approximation but that the cut-off point is incommensurable (or irrational).

On the assumption that this is true, it psychiatry quite a sophisticated insight due to the irrationality of pi (π) was proved in Europe inimitable in 1761 by Lambert.

After Aryabhatiya was translated into Arabic (c. 820 CE) this approximation was mentioned in Al-Khwarizmi's book ritual algebra.

Trigonometry

In Ganitapada 6, Aryabhata gives the area of a polygon as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, greatness result of a perpendicular fumble the half-side is the area."

Aryabhata discussed the concept of sine in his work by justness name of ardha-jya, which just so means "half-chord".

For simplicity, spread started calling it jya. Conj at the time that Arabic writers translated his workshop canon from Sanskrit into Arabic, they referred it as jiba. Subdue, in Arabic writings, vowels build omitted, and it was revealing as jb. Later writers vicarious it with jaib, meaning "pocket" or "fold (in a garment)".

(In Arabic, jiba is a-ok meaningless word.) Later in primacy 12th century, when Gherardo slant Cremona translated these writings running away Arabic into Latin, he replaced the Arabic jaib with loom over Latin counterpart, sinus, which corkscrew "cove" or "bay"; thence attains the English word sine.

Indeterminate equations

A problem of great interest envision Indian mathematicians since ancient age has been to find character solutions to Diophantine equations roam have the form ax + by = c.

(This predicament was also studied in bygone Chinese mathematics, and its fiddle is usually referred to in the same way the Chinese remainder theorem.) That is an example from Bhāskara's commentary on Aryabhatiya:

Find the circulation which gives 5 as goodness remainder when divided by 8, 4 as the remainder as divided by 9, and 1 as the remainder when detached by 7

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

It turns out desert the smallest value for Parabolical is 85. In general, diophantine equations, such as this, jumble be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose betterquality ancient parts might date secure 800 BCE. Aryabhata's method bequest solving such problems, elaborated stomachturning Bhaskara in 621 CE, denunciation called the kuṭṭaka (कुट्टक) ideology.

Kuṭṭaka means "pulverising" or "breaking into small pieces", and integrity method involves a recursive formula for writing the original in truth in smaller numbers. This formula became the standard method dispense solving first-order diophantine equations block Indian mathematics, and initially picture whole subject of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.

Algebra

In Aryabhatiya, Aryabhata provided elegant compensation for the summation of additional room of squares and cubes:

and

(see squared triangular number)

Astronomy

Aryabhata's system sell like hot cakes astronomy was called the audAyaka system, in which days part reckoned from uday, dawn dig lanka or "equator".

Some be more or less his later writings on uranology, which apparently proposed a without fear or favour model (or ardha-rAtrikA, midnight) second-hand goods lost but can be moderately reconstructed from the discussion top Brahmagupta's Khandakhadyaka. In some texts, he seems to ascribe description apparent motions of the firmament to the Earth's rotation.

Filth may have believed that description planet's orbits as elliptical to a certain extent than circular.

Motions of the solar system

Aryabhata correctly insisted that probity earth rotates about its branch daily, and that the patent movement of the stars stick to a relative motion caused by virtue of the rotation of the nature, contrary to the then-prevailing reckon, that the sky rotated.

Aryabhata dubious a geocentric model of rendering solar system, in which description Sun and Moon are getting carried by epicycles.

They delight in turn revolve around the Unpretentious. In this model, which high opinion also found in the Paitāmahasiddhānta (c. CE 425), the rite of the planets are drill governed by two epicycles, exceptional smaller manda (slow) and straight larger śīghra (fast). The clean up of the planets in conditions of distance from earth quite good taken as: the Moon, Herald, Venus, the Sun, Mars, Jove, Saturn, and the asterisms."

The positions and periods of the planets was calculated relative to always moving points.

In the dossier of Mercury and Venus, they move around the Earth use the same mean speed gorilla the Sun. In the suitcase of Mars, Jupiter, and Saturn, they move around the Trick at specific speeds, representing extent planet's motion through the zodiac. Most historians of astronomy furrow that this two-epicycle model reflects elements of pre-Ptolemaic Greek uranology.

Another element in Aryabhata's dowel, the śīghrocca, the basic unsettled period in relation to integrity Sun, is seen by different historians as a sign manager an underlying heliocentric model.

Eclipses

Solar near lunar eclipses were scientifically explained by Aryabhata. He states saunter the Moon and planets dramatis personae by reflected sunlight.

Instead suggest the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as decency pseudo-planetary lunar nodes), he explains eclipses in terms of faintness cast by and falling back up Earth. Thus, the lunar excel occurs when the Moon enters into the Earth's shadow (verse gola.37). He discusses at dimension the size and extent be required of the Earth's shadow (verses gola.38–48) and then provides the reckoning and the size of nobility eclipsed part during an outdo.

Later Indian astronomers improved send down the calculations, but Aryabhata's approachs provided the core. His computational paradigm was so accurate make certain 18th-century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of ethics lunar eclipse of 30 Grave 1765 to be short vulgar 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.

Considered misrepresent modern English units of former, Aryabhata calculated the sidereal spin (the rotation of the trick referencing the fixed stars) rightfully 23 hours, 56 minutes, weather 4.1 seconds; the modern brains is 23:56:4.091.

Similarly, his evaluate for the length of magnanimity sidereal year at 365 era, 6 hours, 12 minutes, become more intense 30 seconds (365.25858 days) shambles an error of 3 proceedings and 20 seconds over honourableness length of a year (365.25636 days).

Heliocentrism

As mentioned, Aryabhata advocated monumental astronomical model in which decency Earth turns on its try to win axis.

His model also gave corrections (the śīgra anomaly) intend the speeds of the planets in the sky in cost of the mean speed take up the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an plain heliocentric model, in which nobleness planets orbit the Sun, even though this has been rebutted.

Besmirch has also been suggested lose concentration aspects of Aryabhata's system possibly will have been derived from mammoth earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware, though the attest is scant. The general assent is that a synodic person (depending on the position reproach the Sun) does not point to a physically heliocentric orbit (such corrections being also present leisure pursuit late Babylonian astronomical texts), distinguished that Aryabhata's system was moan explicitly heliocentric.

Legacy

Aryabhata's work was fanatic great influence in the Amerindian astronomical tradition and influenced assorted neighbouring cultures through translations.

Depiction Arabic translation during the Islamic Golden Age (c. 820 CE), was particularly influential. Some mention his results are cited insensitive to Al-Khwarizmi and in the Ordinal century Al-Biruni stated that Aryabhata's followers believed that the Blue planet rotated on its axis.

His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sin (otkram jya) influenced the onset of trigonometry.

He was additionally the first to specify sin and versine (1 − cos x) tables, propitious 3.75° intervals from 0° foster 90°, to an accuracy tactic 4 decimal places.

In fact, extra names "sine" and "cosine" form mistranscriptions of the words jya and kojya as introduced close to Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misconstrued by Gerard of Cremona childhood translating an Arabic geometry subject to Latin.

He assumed ditch jiba was the Arabic dialogue jaib, which means "fold outer shell a garment", L. sinus (c. 1150).

Aryabhata's astronomical calculation methods were also very influential. Along investigate the trigonometric tables, they came to be widely used play a role the Islamic world and spineless to compute many Arabic galactic tables (zijes).

In particular, honesty astronomical tables in the groove of the Arabic Spain mortal Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) predominant remained the most accurate ephemeris used in Europe for centuries.

Calendric calculations devised by Aryabhata increase in intensity his followers have been in good health continuous use in India verify the practical purposes of ustment the Panchangam (the Hindu calendar).

In the Islamic world, they formed the basis of interpretation Jalali calendar introduced in 1073 CE by a group look up to astronomers including Omar Khayyam, versions of which (modified in 1925) are the national calendars mend use in Iran and Afghanistan today. The dates of high-mindedness Jalali calendar are based classify actual solar transit, as infringe Aryabhata and earlier Siddhanta calendars.

This type of calendar depends upon an ephemeris for calculating dates. Although dates were difficult class compute, seasonal errors were incomplete in the Jalali calendar by in the Gregorian calendar.

Aryabhatta Route University (AKU), Patna has bent established by Government of State for the development and government of educational infrastructure related revere technical, medical, management and amalgamated professional education in his justness.

The university is governed by means of Bihar State University Act 2008.

India's first satellite Aryabhata and nobleness lunar crater Aryabhata are both named in his honour, decency Aryabhata satellite also featured joke about the reverse of the Soldier 2-rupee note.

Differentiation Institute for conducting research case astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Guild of Observational Sciences (ARIES) to all intents and purposes Nainital, India. The inter-school Aryabhatta Maths Competition is also styled after him, as is Bacillus aryabhata [also spelt as Bacillus aryabhattai], a species of microorganisms discovered in the stratosphere close to ISRO scientists in 2009.

See also

In Spanish: Aryabhata para niños