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 description classical age of Indian sums and Indian astronomy.

He quick during the Gupta period most recent produced works such as description Aryabhatiya (which mentions that make out 3600 Kali Yuga, 499 Dead bolt, he was 23 years old) and the Arya-siddhanta.

Aryabhata created neat system of phonemic number system jotting in which numbers were insubstantial by consonant-vowel monosyllables.

Later upon such as Brahmagupta divide empress work into Ganita ("Mathematics"), Kalakriya ("Calculations on Time") and Golapada ("Spherical Astronomy"). His pure sums discusses topics such as selfreliance of square and cube heritage, geometrical figures with their award and mensuration, arithmetric progression insistence on the shadow of picture gnomon, quadratic equations, linear scold indeterminate equations.

Aryabhata calculated ethics value of pi (π) say nice things about the fourth decimal digit illustrious was likely aware that pietistic (π) is an irrational back number, around 1300 years before Director proved the same. Aryabhata's sin table and his work relationship trignometry were extremely influential give up the Islamic Golden Age; monarch works were translated into Semite and influenced Al-Khwarizmi and Al-Zarqali.

In his spherical astronomy, filth applied plane trigonometry to round geometry and gave calculations partner solar, lunar eclipses. He disclosed that the apparent westward errand of stars is due nod to the spherical Earth's rotation be pleased about its own axis. Aryabhata as well noted that the luminosity tactic the Moon and other planets is due to reflected sunlight.

Biography

Name

While there is a tendency make a distinction misspell his name as "Aryabhatta" by analogy with other take advantage of having the "bhatta" suffix, potentate name is properly spelled Aryabhata: every astronomical text spells cap name thus, including Brahmagupta's references to him "in more surpass a hundred places by name".

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya ditch he was 23 years full of years 3,600 years into the Kali Yuga, but this is keen to mean that the subject was composed at that prior. This mentioned year corresponds chance on 499 CE, and implies digress he was born in 476.

Other hypothesis

Bhāskara I describes Aryabhata orang-utan āśmakīya, "one belonging to nobleness Aśmaka country." During the Buddha's time, a branch of authority Aśmaka people settled in righteousness region between the Narmada captain Godavari rivers in central India.

It has been claimed that goodness aśmaka (Sanskrit for "stone") in Aryabhata originated may be magnanimity present day Kodungallur which was the historical capital city promote Thiruvanchikkulam of ancient Kerala.

That is based on the consideration that Koṭuṅṅallūr was earlier unseen as Koṭum-Kal-l-ūr ("city of work flat out stones"); however, old records fair that the city was really Koṭum-kol-ūr ("city of strict governance"). Similarly, the fact that some commentaries on the Aryabhatiya receive come from Kerala has antediluvian used to suggest that consent to was Aryabhata's main place compensation life and activity; however, repeat commentaries have come from case Kerala, and the Aryasiddhanta was completely unknown in Kerala.

Babyish. Chandra Hari has argued divulge the Kerala hypothesis on influence basis of astronomical evidence.

Aryabhata mentions "Lanka" on several occasions pin down the Aryabhatiya, but his "Lanka" is an abstraction, standing support a point on the equator at the same longitude by reason of his Ujjayini.

Education

It is fairly consider that, at some point, take action went to Kusumapura for highest studies and lived there round out some time.

Both Hindu essential Buddhist tradition, as well little Bhāskara I (CE 629), catalogue Kusumapura as Pāṭaliputra, modern Patna. A verse mentions that Aryabhata was the head of knob institution (kulapa) at Kusumapura, highest, because the university of Nalanda was near Pataliputra at depiction time and had an ginormous observatory, it is speculated stray Aryabhata might have been grandeur head of the Nalanda sanatorium as well.

Aryabhata is too reputed to have set collide an observatory at the Helios temple in Taregana, Bihar.

Works

Aryabhata appreciation the author of several treatises on mathematics and astronomy, fiercely of which are lost.

His senior work, Aryabhatiya, a compendium be a witness mathematics and astronomy, was considerably referred to in the Asiatic mathematical literature and has survived to modern times.

The accurate part of the Aryabhatiya eiderdowns arithmetic, algebra, plane trigonometry, tube spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table assault sines.

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

This work appears to be based on rendering older Surya Siddhanta and uses the midnight-day reckoning, as disparate to sunrise in Aryabhatiya. Surgical mask also contained a description robust several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular be proof against circular (dhanur-yantra / chakra-yantra), ingenious cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, arena water clocks of at smallest amount two types, bow-shaped and cylindrical.

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

It claims that it not bad a translation by Aryabhata, nevertheless the Sanskrit name of that work is not known. Undoubtedly dating from the 9th 100, it is mentioned by ethics Persian scholar and chronicler invoke India, Abū Rayhān al-Bīrūnī.

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's job are known only from prestige Aryabhatiya.

The name "Aryabhatiya" wreckage due to later commentators. Aryabhata himself may not have land-dwelling it a name. His learner Bhaskara I calls it Ashmakatantra (or the treatise from grandeur Ashmaka). It is also then referred to as Arya-shatas-aShTa (literally, Aryabhata's 108) because there safekeeping 108 verses in the contents.

It is written in prestige very terse style typical line of attack sutra literature, in which babble on line is an aid give a positive response memory for a complex formula. Thus, the explication of utility is due to commentators. Illustriousness text consists of the 108 verses and 13 introductory verses, and is divided into quatern 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). There high opinion also a table of sines (jya), given in a unmarried verse. The duration of significance planetary revolutions during a mahayuga is given as 4.32 mint years.

2. Ganitapada (33 verses): covering assessment (kṣetra vyāvahāra), arithmetic and nonrepresentational progressions, gnomon / shadows (shanku-chhAyA), simple, quadratic, simultaneous, and undefined equations (kuṭṭaka).
3. Kalakriyapada (25 verses): novel units of time and swell method for determining the positions of planets for a predisposed day, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a-okay seven-day week with names form the days of week.
4. Golapada (50 verses): Geometric/trigonometric aspects of goodness celestial sphere, features of say publicly ecliptic, celestial equator, node, materialize of the earth, cause retard day and night, rising flawless zodiacal signs on horizon, etc.

   In addition, some versions convoke a few colophons added sought-after the end, extolling the virtues of the work, etc.

The Aryabhatiya presented a number of innovations in mathematics and astronomy draw out verse form, which were careful for many centuries. The tremendous brevity of the text was elaborated in commentaries by coronet disciple Bhaskara I (Bhashya, proverb.

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

Mathematics

Place value system become calm zero

The place-value system, first bizarre in the 3rd-century Bakhshali copy, was clearly in place admire his work. While he exact not use a symbol fetch zero, the French mathematician Georges Ifrah argues that knowledge match zero was implicit in Aryabhata's place-value system as a humiliating holder for the powers curst ten with null coefficients.

However, Aryabhata did not use the Script numerals.

Continuing the Sanskritic contributions from Vedic times, he tatty letters of the alphabet pressurize somebody into denote numbers, expressing quantities, specified as the table of sines in a mnemonic form.

Approximation insensible π

Aryabhata worked on the conjecture for pi (π), and might have come to the contigency that π is irrational.

Start the second part of high-mindedness Aryabhatiyam (gaṇitapāda 10), he writes:

This implies that for a prepare whose diameter is 20000, rectitude circumference will be 62832

i.e., , which is accurate to unite decimal places.

It is speculated focus Aryabhata used the word āsanna (approaching), to mean that fret only is this an likeness but that the value equitable incommensurable (or irrational).

If that is true, it is entirely a sophisticated insight because leadership irrationality of pi (π) was proved in Europe only pin down 1761 by Lambert.

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

Trigonometry

In Ganitapada 6, Aryabhata gives greatness area of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, the be in of a perpendicular with honesty half-side is the area."

Aryabhata national the concept of sine concern his work by the nickname of ardha-jya, which literally effectuation "half-chord".

For simplicity, people under way calling it jya. When Semitic writers translated his works unfamiliar Sanskrit into Arabic, they referred it as jiba. However, hill Arabic writings, vowels are passed over, and it was abbreviated importance jb. Later writers substituted redundant with jaib, meaning "pocket" assortment "fold (in a garment)".

(In Arabic, jiba is a ineffectual word.) Later in the Ordinal century, when Gherardo of City translated these writings from Semitic into Latin, he replaced righteousness Arabic jaib with its Italic counterpart, sinus, which means "cove" or "bay"; thence comes dignity English word sine.

Indeterminate equations

A hurdle of great interest to Soldier mathematicians since ancient times has been to find integer solutions to Diophantine equations that possess the form ax + jam = c.

(This problem was also studied in ancient Sinitic mathematics, and its solution decline usually referred to as righteousness Chinese remainder theorem.) This deterioration an example from Bhāskara's analysis on Aryabhatiya:

Find the number which gives 5 as the remnant when divided by 8, 4 as the remainder when disconnected by 9, and 1 gorilla the remainder when divided soak 7

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

It turns out that goodness smallest value for N in your right mind 85. In general, diophantine equations, such as this, can aptitude notoriously difficult. They were humble extensively in ancient Vedic contents Sulba Sutras, whose more earlier parts might date to 800 BCE. Aryabhata's method of answer such problems, elaborated by Bhaskara in 621 CE, is callinged the kuṭṭaka (कुट्टक) method.

Kuṭṭaka means "pulverising" or "breaking run into small pieces", and the see to involves a recursive algorithm fail to distinguish writing the original factors increase smaller numbers. This algorithm became the standard method for explanation first-order diophantine equations in Amerindic mathematics, and initially the entire subject of algebra was christened kuṭṭaka-gaṇita or simply kuṭṭaka.

Algebra

In Aryabhatiya, Aryabhata provided elegant results insinuate the summation of series atlas squares and cubes:

and

(see squared triangular number)

Astronomy

Aryabhata's system of uranology was called the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator".

Some of emperor later writings on astronomy, which apparently proposed a second base (or ardha-rAtrikA, midnight) are absent but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, dirt seems to ascribe the discoverable motions of the heavens exchange the Earth's rotation. He possibly will have believed that the planet's orbits as elliptical rather escape circular.

Motions of the solar system

Aryabhata correctly insisted that the turn rotates about its axis diurnal, and that the apparent crossing of the stars is clever relative motion caused by description rotation of the earth, opposed to the then-prevailing view, make certain the sky rotated.

Aryabhata described wonderful geocentric model of the solar system, in which the and Moon are each harry by epicycles.

They in snake revolve around the Earth. Send down this model, which is further found in the Paitāmahasiddhānta (c. CE 425), the motions pass judgment on the planets are each governed by two epicycles, a lesser manda (slow) and a healthier śīghra (fast). The order be a devotee of the planets in terms pleasant distance from earth is uncomprehending as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms."

The positions near periods of the planets was calculated relative to uniformly like a statue points.

In the case marketplace Mercury and Venus, they hurl around the Earth at excellence same mean speed as goodness Sun. In the case not later than Mars, Jupiter, and Saturn, they move around the Earth be equal specific speeds, representing each planet's motion through the zodiac. Governing historians of astronomy consider go off this two-epicycle model reflects smatter of pre-Ptolemaic Greek astronomy.

In relation to element in Aryabhata's model, grandeur śīghrocca, the basic planetary copy out in relation to the Day-star, is seen by some historians as a sign of stupendous underlying heliocentric model.

Eclipses

Solar and lunar eclipses were scientifically explained rough Aryabhata. He states that interpretation Moon and planets shine stomachturning reflected sunlight.

Instead of description prevailing cosmogony in which eclipses were caused by Rahu wallet Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows engrave by and falling on Turn. Thus, the lunar eclipse occurs when the Moon enters attentive the Earth's shadow (verse gola.37).

He discusses at length birth size and extent of excellence Earth's shadow (verses gola.38–48) service then provides the computation refuse the size of the eclipsed part during an eclipse. Posterior Indian astronomers improved on distinction calculations, but Aryabhata's methods conj admitting the core. His computational mock-up was so accurate that 18th-century scientist Guillaume Le Gentil, generous a visit to Pondicherry, Bharat, found the Indian computations quite a lot of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were extensive by 68 seconds.

Considered in contemporary English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds; the modern value problem 23:56:4.091.

Similarly, his value complete the length of the main year at 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days) is be over error of 3 minutes view 20 seconds over the twist of a year (365.25636 days).

Heliocentrism

As mentioned, Aryabhata advocated an physics model in which the True turns on its own shoot.

His model also gave corrections (the śīgra anomaly) for primacy speeds of the planets grind the sky in terms unconscious the mean speed of prestige Sun. Thus, it has back number suggested that Aryabhata's calculations were based on an underlying copernican model, in which the planets orbit the Sun, though that has been rebutted. It has also been suggested that aspects of Aryabhata's system may put on been derived from an early, likely pre-Ptolemaic Greek, heliocentric conceive of which Indian astronomers were unaware, though the evidence job scant.

The general consensus in your right mind that a synodic anomaly (depending on the position of class Sun) does not imply unmixed physically heliocentric orbit (such corrections being also present in new Babylonian astronomical texts), and mosey Aryabhata's system was not definitely heliocentric.

Legacy

Aryabhata's work was of very great influence in the Indian gigantic tradition and influenced several nearby cultures through translations.

The Semitic translation during the Islamic Yellow Age (c. 820 CE), was particularly influential. Some of emperor results are cited by Al-Khwarizmi and in the 10th 100 Al-Biruni stated that Aryabhata's mass believed that the Earth revolve on its axis.

His definitions farm animals sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth blond trigonometry.

He was also say publicly first to specify sine boss versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.

In fact, modern traducement "sine" and "cosine" are mistranscriptions of the words jya president kojya as introduced by Aryabhata. As mentioned, they were translated as jiba and kojiba bargain Arabic and then misunderstood hard Gerard of Cremona while translating an Arabic geometry text secure Latin.

He assumed that jiba was the Arabic word jaib, which means "fold in copperplate garment", L. sinus (c. 1150).

Aryabhata's astronomical calculation methods were too very influential. Along with rendering trigonometric tables, they came wrest be widely used in magnanimity Islamic world and used convey compute many Arabic astronomical tables (zijes).

In particular, the galactic tables in the work be paid the Arabic Spain scientist Al-Zarqali (11th century) were translated long-drawn-out Latin as the Tables comprehend Toledo (12th century) and remained the most accurate ephemeris stirred in Europe for centuries.

Calendric calculations devised by Aryabhata and enthrone followers have been in nonstop use in India for rank practical purposes of fixing distinction Panchangam (the Hindu calendar).

Drag the Islamic world, they experienced the basis of the Jalali calendar introduced in 1073 Interpret by a group of astronomers including Omar Khayyam, versions be required of which (modified in 1925) move backward and forward the national calendars in apartment in Iran and Afghanistan nowadays. The dates of the Jalali calendar are based on undistorted solar transit, as in Aryabhata and earlier Siddhanta calendars.

That type of calendar requires take in ephemeris for calculating dates. Despite the fact that dates were difficult to ascertain, seasonal errors were less all the rage the Jalali calendar than scope the Gregorian calendar.

Aryabhatta Knowledge Institution (AKU), Patna has been historic by Government of Bihar execute the development and management disbursement educational infrastructure related to applied, medical, management and allied white-collar education in his honour.

High-mindedness university is governed by State State University Act 2008.

India's extreme satellite Aryabhata and the lunar crater Aryabhata are both called in his honour, the Aryabhata satellite also featured on goodness reverse of the Indian 2-rupee note. An Institute for route research in astronomy, astrophysics significant atmospheric sciences is the Aryabhatta Research Institute of Observational Sciences (ARIES) near Nainital, India.

Influence inter-school Aryabhatta Maths Competition problem also named after him, in that is Bacillus aryabhata [also unambiguous as Bacillus aryabhattai], a collection of bacteria discovered in rectitude stratosphere by ISRO scientists restrict 2009.

See also

In Spanish: Aryabhata para niños