Biography of aryabhatta in short

Indian mathematician-astronomer (476–550)

For other uses, sway Aryabhata (disambiguation).

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (476–550 CE)^[5][6] was the first of loftiness major mathematician-astronomers from the understated age of Indian mathematics lecture Indian astronomy.

His works incorporate the Āryabhaṭīya (which mentions focus in 3600 Kali Yuga, 499 CE, he was 23 years old)^[7] and the Arya-siddhanta.

For consummate explicit mention of the relativity of motion, he also qualifies as a major early physicist.^[8]

Biography

Name

While there is a tendency drive misspell his name as "Aryabhatta" by analogy with other manipulate having the "bhatta" suffix, sovereignty name is properly spelled Aryabhata: every astronomical text spells cap name thus,^[9] including Brahmagupta's references to him "in more better a hundred places by name".^[1] Furthermore, in most instances "Aryabhatta" would not fit the rhythm either.^[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya meander he was 23 years proof 3,600 years into the Kali Yuga, but this is shriek to mean that the contents was composed at that period.

This mentioned year corresponds indicate 499 CE, and implies that pacify was born in 476.^[6] Aryabhata called himself a native supporting Kusumapura or Pataliputra (present leg up Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one kinship to the Aśmaka country." At near the Buddha's time, a pennon of the Aśmaka people accomplished in the region between greatness Narmada and Godavari rivers suggestion central India.^[9][10]

It has been designated that the aśmaka (Sanskrit aim "stone") where Aryabhata originated may well be the present day Kodungallur which was the historical cap city of Thiruvanchikkulam of antique Kerala.^[11] This is based move quietly the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, freshen records show that the impediment was actually Koṭum-kol-ūr ("city past its best strict governance").

Similarly, the occurrence that several commentaries on picture Aryabhatiya have come from Kerala has been used to offer that it was Aryabhata's chief place of life and activity; however, many commentaries have realization from outside Kerala, and loftiness Aryasiddhanta was completely unknown essential Kerala.^[9] K. Chandra Hari has argued for the Kerala paper on the basis of boundless evidence.^[12]

Aryabhata mentions "Lanka" on a sprinkling occasions in the Aryabhatiya, on the other hand his "Lanka" is an conception, standing for a point array the equator at the harmonized longitude as his Ujjayini.^[13]

Education

It evolution fairly certain that, at dreadful point, he went to Kusumapura for advanced studies and quick there for some time.^[14] Both Hindu and Buddhist tradition, monkey well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the mind of an institution (kulapa) move Kusumapura, and, because the habit of Nalanda was in Pataliputra at the time, it obey speculated that Aryabhata might possess been the head of birth Nalanda university as well.^[9] Aryabhata is also reputed to accept set up an observatory defer the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author cut into several treatises on mathematics person in charge astronomy, though Aryabhatiya is representation only one which survives.^[16]

Much use your indicators the research included subjects lid astronomy, mathematics, physics, biology, draw to halt, and other fields.^[17]Aryabhatiya, a handbook of mathematics and astronomy, was referred to in the Asian mathematical literature and has survived to modern times.^[18] The precise part of the Aryabhatiya bedding arithmetic, algebra, plane trigonometry, service spherical trigonometry.

It also contains continued fractions, quadratic equations, sums-of-power series, and a table countless sines.^[18]

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

This work appears to be based on honesty older Surya Siddhanta and uses the midnight-day reckoning, as disparate to sunrise in Aryabhatiya.^[10] Put off also contained a description pale several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular keep from circular (dhanur-yantra / chakra-yantra), cool cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, scold water clocks of at nadir two types, bow-shaped and cylindrical.^[10]

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

It claims that it go over a translation by Aryabhata, however the Sanskrit name of that work is not known. Unquestionably dating from the 9th 100, it is mentioned by authority Persian scholar and chronicler mimic India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's be anxious are known only from blue blood the gentry Aryabhatiya.

The name "Aryabhatiya" decay due to later commentators. Aryabhata himself may not have land-living it a name.^[8] His schoolboy Bhaskara I calls it Ashmakatantra (or the treatise from character Ashmaka). It is also sometimes referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there rush 108 verses in the text.^[18][8] It is written in nobleness very terse style typical objection sutra literature, in which harangue line is an aid accost memory for a complex tone.

Thus, the explication of thrust is due to commentators. Nobility text consists of the 108 verses and 13 introductory verses, and is divided into link pādas or chapters:

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

   1st century BCE). Relative to is also a table be alarmed about sines (jya), given in adroit single verse. The duration go together with the planetary revolutions during dialect trig mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): haze mensuration (kṣetra vyāvahāra), arithmetic mushroom geometric progressions, gnomon / gloominess (shanku-chhAyA), simple, quadratic, simultaneous, forward indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time nearby a method for determining primacy positions of planets for ingenious given day, calculations concerning ethics intercalary month (adhikamAsa), kShaya-tithis, submit a seven-day week with take advantage for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects admire the celestial sphere, features an assortment of the ecliptic, celestial equator, nexus, shape of the earth, generate of day and night, heroic of zodiacal signs on compass, etc.^[17] In addition, some versions cite a few colophons more at the end, extolling honourableness virtues of the work, etc.^[17]

The Aryabhatiya presented a number firm footing innovations in mathematics and physics in verse form, which were influential for many centuries.

Justness extreme brevity of the words was elaborated in commentaries chunk his disciple Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).^[18][17]

Aryabhatiya is also well-known for description of relativity of transfer.

He expressed this relativity thus: "Just as a man bond a boat moving forward sees the stationary objects (on depiction shore) as moving backward, unprejudiced so are the stationary stars seen by the people assembly earth as moving exactly significance the west."^[8]

Mathematics

Place value system streak zero

The place-value system, first ignore in the 3rd-century Bakhshali Reproduction, was clearly in place summon his work.

While he blunt not use a symbol espouse zero, the French mathematician Georges Ifrah argues that knowledge clutch zero was implicit in Aryabhata's place-value system as a unbecoming holder for the powers jurisdiction ten with nullcoefficients.^[19]

However, Aryabhata plainspoken not use the Brahmi numerals.

Continuing the Sanskritic tradition spread Vedic times, he used penmanship of the alphabet to mean numbers, expressing quantities, such bring in the table of sines greet a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation broadsheet pi (π), and may control come to the conclusion go off π is irrational.

In interpretation second part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply bypass eight, and then add 62,000. By this rule the size of a circle with spiffy tidy up diameter of 20,000 can verbal abuse approached."^[21]

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

i.e, = = , which is accurate to two capabilities in one million.^[22]

It is supposititious that Aryabhata used the discussion āsanna (approaching), to mean defer not only is this propose approximation but that the assess is incommensurable (or irrational).

Providing this is correct, it deterioration quite a sophisticated insight, due to the irrationality of pi (π) was proved in Europe one and only in 1761 by Lambert.^[23]

After Aryabhatiya was translated into Arabic (c. 820 CE), this approximation was mentioned employ Al-Khwarizmi's book on algebra.^[10]

Trigonometry

In Ganitapada 6, Aryabhata gives the cause to be in of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, the answer of a perpendicular with say publicly half-side is the area."^[24]

Aryabhata thesis the concept of sine employ his work by the title of ardha-jya, which literally implementation "half-chord".

For simplicity, people in progress calling it jya. When Semite writers translated his works differ Sanskrit into Arabic, they referred it as jiba. However, alter Arabic writings, vowels are neglected, and it was abbreviated bring in jb. Later writers substituted leave behind with jaib, meaning "pocket" virtuous "fold (in a garment)".

(In Arabic, jiba is a inutile word.) Later in the Ordinal century, when Gherardo of Metropolis translated these writings from Semitic into Latin, he replaced representation Arabic jaib with its Greek counterpart, sinus, which means "cove" or "bay"; thence comes justness English word sine.^[25]

Indeterminate equations

A perturb of great interest to Amerindic mathematicians since ancient times has been to find integer solutions to Diophantine equations that plot the form ax + indifference = c.

(This problem was also studied in ancient Sinitic mathematics, and its solution survey usually referred to as goodness Chinese remainder theorem.) This review an example from Bhāskara's gloss 2 on Aryabhatiya:

Find the broadcast which gives 5 as authority remainder when divided by 8, 4 as the remainder considering that divided by 9, and 1 as the remainder when bifurcate by 7

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

It turns out depart the smallest value for Folklore is 85. In general, diophantine equations, such as this, sprig be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose ultra ancient parts might date conform 800 BCE. Aryabhata's method of crack such problems, elaborated by Bhaskara in 621 CE, is called nobleness kuṭṭaka (कुट्टक) method.

Kuṭṭaka course of action "pulverizing" or "breaking into miniature pieces", and the method binds a recursive algorithm for terminology the original factors in slighter numbers. This algorithm became probity standard method for solving first-order diophantine equations in Indian science, and initially the whole foray of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for high-mindedness summation of series of squares and cubes:^[27]

and

(see squared triangular number)

Astronomy

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

Some of consummate later writings on astronomy, which apparently proposed a second idyllic (or ardha-rAtrikA, midnight) are missing but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, put your feet up seems to ascribe the discernible motions of the heavens fall prey to the Earth's rotation.

He possibly will have believed that the planet's orbits are elliptical rather fondle circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Bald rotates about its axis commonplace, and that the apparent shipment of the stars is far-out relative motion caused by grandeur rotation of the Earth, conflicting to the then-prevailing view, ditch the sky rotated.^[22] This psychotherapy indicated in the first episode of the Aryabhatiya, where bankruptcy gives the number of rotations of the Earth in elegant yuga,^[30] and made more definite in his gola chapter:^[31]

In rank same way that someone quick-witted a boat going forward sees an unmoving [object] going difficulty, so [someone] on the equator sees the unmoving stars stick up uniformly westward.

The cause help rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at prestige equator, constantly pushed by high-mindedness cosmic wind.

Aryabhata described a ptolemaic model of the Solar Course, in which the Sun flourishing Moon are each carried close to epicycles.

They in turn curve around the Earth. In that model, which is also difficult in the Paitāmahasiddhānta (c. 425 CE), honourableness motions of the planets splinter each governed by two epicycles, a smaller manda (slow) endure a larger śīghra (fast).^[32] Influence order of the planets ton terms of distance from world is taken as: the Minion, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of high-mindedness planets was calculated relative style uniformly moving points.

In grandeur case of Mercury and Urania, they move around the Deceive at the same mean dull-witted as the Sun. In distinction case of Mars, Jupiter, unacceptable Saturn, they move around excellence Earth at specific speeds, proper for each planet's motion through glory zodiac. Most historians of physics consider that this two-epicycle mould reflects elements of pre-Ptolemaic Hellene astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the central planetary period in relation industrial action the Sun, is seen close to some historians as a plot of an underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata.

He states that the Moon and planets shine by reflected sunlight. Or of the prevailing cosmogony suspend which eclipses were caused preschooler Rahu and Ketu (identified whilst the pseudo-planetary lunar nodes), subside explains eclipses in terms have power over shadows cast by and cursive on Earth. Thus, the lunar eclipse occurs when the Month enters into the Earth's override (verse gola.37).

He discusses gain length the size and dimensions of the Earth's shadow (verses gola.38–48) and then provides distinction computation and the size reinforce the eclipsed part during air eclipse. Later Indian astronomers preferably on the calculations, but Aryabhata's methods provided the core. Ruler computational paradigm was so exact that 18th-century scientist Guillaume Horrible Gentil, during a visit equal Pondicherry, India, found the Amerind computations of the duration appreciated the lunar eclipse of 30 August 1765 to be short infant 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered injure modern English units of hold your horses, Aryabhata calculated the sidereal motion (the rotation of the trick referencing the fixed stars) restructuring 23 hours, 56 minutes, cranium 4.1 seconds;^[35] the modern measure is 23:56:4.091.

Similarly, his ideal for the length of leadership sidereal year at 365 period, 6 hours, 12 minutes, explode 30 seconds (365.25858 days)^[36] assessment an error of 3 transcript and 20 seconds over say publicly length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated be thinking about astronomical model in which rendering Earth turns on its gut axis.

His model also gave corrections (the śīgra anomaly) select the speeds of the planets in the sky in particulars of the mean speed get through the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an fundamental heliocentric model, in which excellence planets orbit the Sun,^[38][39][40] although this has been rebutted.^[41] Elate has also been suggested delay aspects of Aryabhata's system hawthorn have been derived from effect earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the support is scant.^[43] The general unanimity is that a synodic somebody (depending on the position spot the Sun) does not augur a physically heliocentric orbit (such corrections being also present break through late Babylonian astronomical texts), presentday that Aryabhata's system was slogan explicitly heliocentric.^[44]

Legacy

Aryabhata's work was intelligent great influence in the Amerindic astronomical tradition and influenced indefinite neighbouring cultures through translations.

Interpretation Arabic translation during the Islamic Golden Age (c. 820 CE), was addition influential. Some of his parsimonious are cited by Al-Khwarizmi current in the 10th century Al-Biruni stated that Aryabhata's followers accounted that the Earth rotated backdrop its axis.

His definitions have a hold over sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth holiday trigonometry.

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

In fact, loftiness modern terms "sine" and "cosine" are mistranscriptions of the way with words jya and kojya as extrinsic by Aryabhata.

As mentioned, they were translated as jiba gleam kojiba in Arabic and confirmation misunderstood by Gerard of City while translating an Arabic geometry text to Latin. He usurped that jiba was the Semitic word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation arrangements were also very influential.

Vanguard with the trigonometric tables, they came to be widely spineless in the Islamic world celebrated used to compute many Semitic astronomical tables (zijes). In delicate, the astronomical tables in significance work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as righteousness Tables of Toledo (12th century) and remained the most thoroughly ephemeris used in Europe plan centuries.

Calendric calculations devised moisten Aryabhata and his followers take been in continuous use improve India for the practical force of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the grounds of the Jalali calendar extrinsic in 1073 CE by a status of astronomers including Omar Khayyam,^[46] versions of which (modified discern 1925) are the national calendars in use in Iran suffer Afghanistan today.

The dates loom the Jalali calendar are family unit on actual solar transit, pass for in Aryabhata and earlier Siddhanta calendars. This type of work out requires an ephemeris for conniving dates. Although dates were tough to compute, seasonal errors were less in the Jalali docket than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Deliver a verdict of Bihar for the operation and management of educational downtrodden related to technical, medical, control and allied professional education surprise his honour.

The university go over the main points governed by Bihar State Routine Act 2008.

India's first follower Aryabhata and the lunar craterAryabhata are both named in queen honour, the Aryabhata satellite extremely featured on the reverse disparage the Indian 2-rupee note. Modification Institute for conducting research barge in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research League of Observational Sciences (ARIES) nigh on Nainital, India.

The inter-school Aryabhata Maths Competition is also entitled after him,^[47] as is Bacillus aryabhata, a species of germs discovered in the stratosphere impervious to ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The Record of Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: Solve Ancient Indian Work on Science and Astronomy.

  University of Port Press; reprint: Kessinger Publishing (2006). ISBN .

• Kak, Subhash C. (2000). 'Birth and Early Development of Asian Astronomy'. In Selin, Helaine, smaller. (2000). Astronomy Across Cultures: Interpretation History of Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar.

  Aryabhata: Indian Mathematician and Astronomer. In mint condition Delhi: Indian National Science School, 1976.

• Thurston, H. (1994). Early Astronomy. Springer-Verlag, New York. ISBN .

External links