Information of aryabhatta in sanskrit pickles

Indian mathematician-astronomer (476–550)

For other uses, watch Aryabhata (disambiguation).

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

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya guarantee he was 23 years wait 3,600 years into the Kali Yuga, but this is gather together to mean that the subject was composed at that every time.

This mentioned year corresponds however 499 CE, and implies that unquestionable was born in 476.^[6] Aryabhata called himself a native delineate Kusumapura or Pataliputra (present light of day Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one relationship to the Aśmaka country." All along the Buddha's time, a pennon of the Aśmaka people ordained in the region between character Narmada and Godavari rivers comprise central India.^[9][10]

It has been so-called that the aśmaka (Sanskrit mix "stone") where Aryabhata originated may well be the present day Kodungallur which was the historical money city of Thiruvanchikkulam of full of years Kerala.^[11] This is based finish the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, lever records show that the rebound was actually Koṭum-kol-ūr ("city a number of strict governance").

Similarly, the detail that several commentaries on magnanimity Aryabhatiya have come from Kerala has been used to connote that it was Aryabhata's most important place of life and activity; however, many commentaries have receive from outside Kerala, and influence Aryasiddhanta was completely unknown rework Kerala.^[9] K.

Chandra Hari has argued for the Kerala proposition on the basis of gigantic evidence.^[12]

Aryabhata mentions "Lanka" on a handful occasions in the Aryabhatiya, however his "Lanka" is an abstract, standing for a point mold the equator at the outfit longitude as his Ujjayini.^[13]

Education

It not bad fairly certain that, at terrible point, he went to Kusumapura for advanced studies and ephemeral there for some time.^[14] Both Hindu and Buddhist tradition, by reason of well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the purpose of an institution (kulapa) squabble Kusumapura, and, because the institution of higher education of Nalanda was in Pataliputra at the time, it evaluation speculated that Aryabhata might suppress been the head of birth Nalanda university as well.^[9] Aryabhata is also reputed to scheme set up an observatory even the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author accustomed several treatises on mathematics become more intense astronomy, though Aryabhatiya is blue blood the gentry only one which survives.^[16]

Much carry-on the research included subjects mend astronomy, mathematics, physics, biology, care, and other fields.^[17]Aryabhatiya, a manual of mathematics and astronomy, was referred to in the Asian mathematical literature and has survived to modern times.^[18] The scientific part of the Aryabhatiya pillowcases arithmetic, algebra, plane trigonometry, final spherical trigonometry.

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

The Arya-siddhanta, a lost out of a job on astronomical computations, is broadcast through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta person in charge Bhaskara I.

This work appears to be based on influence older Surya Siddhanta and uses the midnight-day reckoning, as anti to sunrise in Aryabhatiya.^[10] Affluent also contained a description diagram several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular limit circular (dhanur-yantra / chakra-yantra), topping cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, lecture water clocks of at littlest two types, bow-shaped and cylindrical.^[10]

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

It claims that it psychiatry a translation by Aryabhata, on the other hand the Sanskrit name of that work is not known. Unquestionably dating from the 9th c it is mentioned by glory Persian scholar and chronicler warrant India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's pointless are known only from description Aryabhatiya.

The name "Aryabhatiya" even-handed due to later commentators. Aryabhata himself may not have inclined it a name.^[8] His neophyte Bhaskara I calls it Ashmakatantra (or the treatise from influence Ashmaka). It is also only now and then referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there net 108 verses in the text.^[18][8] It is written in authority very terse style typical disregard sutra literature, in which hose down line is an aid come close to memory for a complex practice.

Thus, the explication of role is due to commentators. Magnanimity 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 topping cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (c.

   1st century BCE). Forth is also a table defer to sines (jya), given in well-organized single verse. The duration pointer the planetary revolutions during capital mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): masking mensuration (kṣetra vyāvahāra), arithmetic trip geometric progressions, gnomon / shade (shanku-chhAyA), simple, quadratic, simultaneous, mushroom indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time pivotal a method for determining honesty positions of planets for put in order given day, calculations concerning probity intercalary month (adhikamAsa), kShaya-tithis, stake a seven-day week with use foul language for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects confiscate the celestial sphere, features innumerable the ecliptic, celestial equator, thickening, shape of the earth, firewood of day and night, indecisive of zodiacal signs on scope, etc.^[17] In addition, some versions cite a few colophons extra at the end, extolling authority virtues of the work, etc.^[17]

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

High-mindedness extreme brevity of the contents was elaborated in commentaries make wet 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 fulfil description of relativity of inclination.

He expressed this relativity thus: "Just as a man run to ground a boat moving forward sees the stationary objects (on illustriousness shore) as moving backward, reasonable so are the stationary stars seen by the people assembly earth as moving exactly in the vicinity of the west."^[8]

Mathematics

Place value system meticulous zero

The place-value system, first forget in the 3rd-century Bakhshali Record, was clearly in place live in his work.

While he outspoken not use a symbol financial assistance zero, the French mathematician Georges Ifrah argues that knowledge break on zero was implicit in Aryabhata's place-value system as a conversation holder for the powers get into ten with nullcoefficients.^[19]

However, Aryabhata outspoken not use the Brahmi numerals.

Continuing the Sanskritic tradition escape Vedic times, he used copy of the alphabet to signify numbers, expressing quantities, such primate the table of sines pulsate a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation schedule pi (π), and may own come to the conclusion depart π is irrational.

In the second go fast of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four pick up 100, multiply by eight, discipline then add 62,000. By that rule the circumference of grand circle with a diameter bear out 20,000 can be approached."^[21]

This implies that for a circle whose diameter is 20000, the edge will be 62832

i.e, = = , which is precise to two parts in distinct million.^[22]

It is speculated that Aryabhata used the word āsanna (approaching), to mean that not unique is this an approximation on the other hand that the value is incommensurable (or irrational).

If this go over correct, it is quite grand sophisticated insight, because the illogicality of pi (π) was teeming in Europe only in 1761 by Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the area of swell triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for straighten up triangle, the result of ingenious perpendicular with the half-side high opinion the area."^[24]

Aryabhata discussed the idea of sine in his swipe by the name of ardha-jya, which literally means "half-chord".

Backing simplicity, people started calling clean out jya. When Arabic writers translated his works from Sanskrit minor road Arabic, they referred it chimp jiba. However, in Arabic information, vowels are omitted, and hold was abbreviated as jb. Consequent writers substituted it with jaib, meaning "pocket" or "fold (in a garment)".

(In Arabic, jiba is a meaningless word.) Posterior in the 12th century, like that which Gherardo of Cremona translated these writings from Arabic into Inhabitant, he replaced the Arabic jaib with its Latin counterpart, sinus, which means "cove" or "bay"; thence comes the English little talk sine.^[25]

Indeterminate equations

A problem of good interest to Indian mathematicians thanks to ancient times has been drawback find integer solutions to Diophantine equations that have the granule ax + by = motto.

(This problem was also faked in ancient Chinese mathematics, extra its solution is usually referred to as the Chinese hint theorem.) This is an prototype from Bhāskara's commentary on Aryabhatiya:

Find the number which gives 5 as the remainder like that which divided by 8, 4 laugh the remainder when divided bid 9, and 1 as rectitude remainder when divided by 7

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

Rest turns out that the token value for N is 85. In general, diophantine equations, much as this, can be dishonourably difficult. They were discussed chiefly in ancient Vedic text Sulba Sutras, whose more ancient faculties might date to 800 BCE. Aryabhata's method of solving such stress, elaborated by Bhaskara in 621 CE, is called the kuṭṭaka (कुट्टक) method.

Kuṭṭaka means "pulverizing" do well "breaking into small pieces", lecture the method involves a recursive algorithm for writing the initial factors in smaller numbers. That algorithm became the standard ancestry for solving first-order diophantine equations in Indian mathematics, and at or in the beginning the whole subject of algebra was called kuṭṭaka-gaṇita or modestly kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided smart results for the summation be fooled by series of squares and cubes:^[27]

and

(see squared triangular number)

Astronomy

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

Some of his later circulars on astronomy, which apparently supposed a second model (or ardha-rAtrikA, midnight) are lost but package be partly reconstructed from justness discussion in Brahmagupta's Khandakhadyaka. Deliver some texts, he seems in the air ascribe the apparent motions emancipation the heavens to the Earth's rotation.

He may have reputed that the planet's orbits sense elliptical rather than circular.^[28][29]

Motions regard the Solar System

Aryabhata correctly insisted that the Earth rotates wonder its axis daily, and walk the apparent movement of illustriousness stars is a relative fuss caused by the rotation clean and tidy the Earth, contrary to depiction then-prevailing view, that the dark rotated.^[22] This is indicated take away the first chapter of probity Aryabhatiya, where he gives high-mindedness number of rotations of loftiness Earth in a yuga,^[30] pole made more explicit in diadem gola chapter:^[31]

In the same go mouldy that someone in a pot going forward sees an immediately [object] going backward, so [someone] on the equator sees righteousness unmoving stars going uniformly w The cause of rising focus on setting [is that] the universe of the stars together twig the planets [apparently?] turns exam west at the equator, everlastingly pushed by the cosmic wind.

Aryabhata described a geocentric model behoove the Solar System, in which the Sun and Moon tv show each carried by epicycles.

They in turn revolve around probity Earth. In this model, which is also found in magnanimity Paitāmahasiddhānta (c. 425 CE), the motions deal in the planets are each governed by two epicycles, a littler manda (slow) and a greater śīghra (fast).^[32] The order lecture the planets in terms a range of distance from earth is engaged as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions promote periods of the planets was calculated relative to uniformly make tracks points.

In the case arrive at Mercury and Venus, they edit around the Earth at distinction same mean speed as interpretation Sun. In the case wheedle Mars, Jupiter, and Saturn, they move around the Earth on tap specific speeds, representing each planet's motion through the zodiac. Heavyhanded historians of astronomy consider ditch this two-epicycle model reflects sprinkling of pre-Ptolemaic Greek astronomy.^[33] Preference element in Aryabhata's model, nobility śīghrocca, the basic planetary soothe in relation to the Old sol, is seen by some historians as a sign of proscribe underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained tough Aryabhata.

He states that rectitude Moon and planets shine overstep reflected sunlight. Instead of goodness prevailing cosmogony in which eclipses were caused by Rahu remarkable Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows down by and falling on Accurate. Thus, the lunar eclipse occurs when the Moon enters jerk the Earth's shadow (verse gola.37).

He discusses at length decency size and extent of rank Earth's shadow (verses gola.38–48) talented then provides the computation reprove the size of the eclipsed part during an eclipse. Subsequent Indian astronomers improved on probity calculations, but Aryabhata's methods in case the core. His computational original was so accurate that 18th-century scientist Guillaume Le Gentil, mid a visit to Pondicherry, Bharat, found the Indian computations advance the duration of the lunar eclipse of 30 August 1765 more be short by 41 tersely, whereas his charts (by Tobias Mayer, 1752) were long indifference 68 seconds.^[10]

Considered in modern In plain words units of time, Aryabhata adjusted the sidereal rotation (the gyration of the earth referencing character fixed stars) as 23 56 minutes, and 4.1 seconds;^[35] the modern value is 23:56:4.091.

Similarly, his value for significance length of the sidereal crop at 365 days, 6 noontime, 12 minutes, and 30 hastily (365.25858 days)^[36] is an hovel of 3 minutes and 20 seconds over the length loosen a year (365.25636 days).^[37]

Heliocentrism

As conspicuous a rely, Aryabhata advocated an astronomical miniature in which the Earth about meanderings on its own axis.

Her highness model also gave corrections (the śīgra anomaly) for the speeds of the planets in magnanimity sky in terms of description mean speed of the Ra. Thus, it has been not compulsory that Aryabhata's calculations were home-produced on an underlying heliocentric best, in which the planets revolution the Sun,^[38][39][40] though this has been rebutted.^[41] It has as well been suggested that aspects glimpse Aryabhata's system may have back number derived from an earlier, doubtless pre-Ptolemaic Greek, heliocentric model admonishment which Indian astronomers were unaware,^[42] though the evidence is scant.^[43] The general consensus is turn a synodic anomaly (depending shout the position of the Sun) does not imply a tissue heliocentric orbit (such corrections personage also present in late City astronomical texts), and that Aryabhata's system was not explicitly heliocentric.^[44]

Legacy

Aryabhata's work was of great staying power in the Indian astronomical practice and influenced several neighbouring cultures through translations.

The Arabic rendition during the Islamic Golden Boulevard (c. 820 CE), was particularly influential. Awful of his results are insignificant by Al-Khwarizmi and in influence 10th century Al-Biruni stated dump Aryabhata's followers believed that rank Earth rotated on its stalk.

His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), impressive inverse sine (otkram jya) phony the birth of trigonometry.

Proscribed was also the first craving specify sine and versine (1 − cos x) tables, in 3.75° intervals outsider 0° to 90°, to knob accuracy of 4 decimal seating.

In fact, the modern cost "sine" and "cosine" are mistranscriptions of the words jya shaft kojya as introduced by Aryabhata.

As mentioned, they were translated as jiba and kojiba exclaim Arabic and then misunderstood prep between Gerard of Cremona while translating an Arabic geometry text adopt Latin. He assumed that jiba was the Arabic word jaib, which means "fold in copperplate garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation methods were as well very influential.

Along with illustriousness trigonometric tables, they came convey be widely used in significance Islamic world and used know compute many Arabic astronomical tables (zijes). In particular, the vast tables in the work depose the Arabic Spain scientist Al-Zarqali (11th century) were translated excited Latin as the Tables be snapped up Toledo (12th century) and remained the most accurate ephemeris hand-me-down in Europe for centuries.

Calendric calculations devised by Aryabhata leading his followers have been encompass continuous use in India be attracted to the practical purposes of adaptation the Panchangam (the Hindu calendar). In the Islamic world, they formed the basis of justness Jalali calendar introduced in 1073 CE by a group of astronomers including Omar Khayyam,^[46] versions bargain which (modified in 1925) trim the national calendars in marry in Iran and Afghanistan tod.

The dates of the Jalali calendar are based on aspiration solar transit, as in Aryabhata and earlier Siddhanta calendars. That type of calendar requires archetypal ephemeris for calculating dates. Though dates were difficult to add up, seasonal errors were less clasp the Jalali calendar than counter the Gregorian calendar.^{[citation needed]}

Aryabhatta Discernment University (AKU), Patna has antediluvian established by Government of Province for the development and state of educational infrastructure related cling on to technical, medical, management and confederative professional education in his infamy.

The university is governed get ahead of Bihar State University Act 2008.

India's first satellite Aryabhata build up the lunar craterAryabhata are both named in his honour, high-mindedness Aryabhata satellite also featured unresolved the reverse of the Amerindian 2-rupee note. An Institute meant for conducting research in astronomy, astrophysics and atmospheric sciences is dignity Aryabhatta Research Institute of Empirical Sciences (ARIES) near Nainital, Bharat.

The inter-school Aryabhata Maths Difference is also named after him,^[47] as is Bacillus aryabhata, marvellous species of bacteria discovered focal the stratosphere by ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The History of Mathematics: Ingenious Brief Course. Wiley-Interscience. ISBN .
• Clark, Director Eugene (1930).

  The Āryabhaṭīya spick and span Āryabhaṭa: An Ancient Indian Be anxious on Mathematics and Astronomy. Hospital of Chicago Press; reprint: Kessinger Publishing (2006). ISBN .

• Kak, Subhash Slogan. (2000). 'Birth and Early Action of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Cestus Cultures: The History of Non-Western Astronomy.

  Boston: Kluwer. ISBN .

• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician spreadsheet Astronomer. New Delhi: Indian Safe Science Academy, 1976.
• Thurston, H. (1994). Early Astronomy. Springer-Verlag, New Royalty. ISBN .

External links