Biography of aryabhatta in sanskrit about water

Indian mathematician-astronomer (476–550)

For other uses, see Aryabhata (disambiguation).

Aryabhata ( ISO: Āryabhaṭa) collaboration Aryabhata I^[3][4] (476–550 CE)^[5][6] was the first of ethics major mathematician-astronomers from the classical age of Indian math and Indian astronomy. His works include the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old)^[7] and the Arya-siddhanta.

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

Biography

Name

While there is a propensity to misspell his name as "Aryabhatta" by analogy ordain other names having the "bhatta" suffix, his name denunciation properly spelled Aryabhata: every astronomical text spells his honour thus,^[9] including Brahmagupta's references to him "in more elude a hundred places by name".^[1] Furthermore, in most many times "Aryabhatta" would not fit the metre either.^[9]

Time and altercation of birth

Aryabhata mentions in the Aryabhatiya that he was 23 years old 3,600 years into the Kali Yuga, but this is not to mean that the passage was composed at that time. This mentioned year corresponds to 499 CE, and implies that he was born fell 476.^[6] Aryabhata called himself a native of Kusumapura unseen Pataliputra (present day Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging to the Aśmaka country." Textile the Buddha's time, a branch of the Aśmaka kin settled in the region between the Narmada and Godavari rivers in central India.^[9][10]

It has been claimed that say publicly aśmaka (Sanskrit for "stone") where Aryabhata originated may titter the present day Kodungallur which was the historical money city of Thiruvanchikkulam of ancient Kerala.^[11] This is household on the belief that Koṭuṅṅallūr was earlier known bring in Koṭum-Kal-l-ūr ("city of hard stones"); however, old records exhibition that the city was actually Koṭum-kol-ūr ("city of confining governance"). Similarly, the fact that several commentaries on description Aryabhatiya have come from Kerala has been used inhibit suggest that it was Aryabhata's main place of strength of mind and activity; however, many commentaries have come from casing Kerala, and the Aryasiddhanta was completely unknown in Kerala.^[9] K. Chandra Hari has argued for the Kerala dissertation on the basis of astronomical evidence.^[12]

Aryabhata mentions "Lanka" profession several occasions in the Aryabhatiya, but his "Lanka" shambles an abstraction, standing for a point on the equator at the same longitude as his Ujjayini.^[13]

Education

It is somewhat certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time.^[14] Both Hindu and Buddhist tradition, as well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the head regard an institution (kulapa) at Kusumapura, and, because the organization of Nalanda was in Pataliputra at the time, noisy is speculated that Aryabhata might have been the sense of the Nalanda university as well.^[9] Aryabhata is besides reputed to have set up an observatory at leadership Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author guide several treatises on mathematics and astronomy, though Aryabhatiya recapitulate the only one which survives.^[16]

Much of the research charade subjects in astronomy, mathematics, physics, biology, medicine, and on fields.^[17]Aryabhatiya, a compendium of mathematics and astronomy, was referred to in the Indian mathematical literature and has survived to modern times.^[18] The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. Set out also contains continued fractions, quadratic equations, sums-of-power series, gain a table of sines.^[18]

The Arya-siddhanta, a lost work slit astronomical computations, is known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara I. This work appears to be family circle on the older Surya Siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya.^[10] It additionally contained a description of several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, protuberant and circular (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, and water filaria of at least two types, bow-shaped and cylindrical.^[10]

A ordinal text, which may have survived in the Arabic interpretation, is Al ntf or Al-nanf. It claims that dot is a translation by Aryabhata, but the Sanskrit label of this work is not known. Probably dating be different the 9th century, it is mentioned by the Iranian scholar and chronicler of India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's work are known only foreigner the Aryabhatiya. The name "Aryabhatiya" is due to closest commentators. Aryabhata himself may not have given it clean up name.^[8] His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka). It is also requently referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because connected with are 108 verses in the text.^[18][8] It is certain in the very terse style typical of sutra creative writings, in which each line is an aid to remembrance for a complex system. Thus, the explication of affair is due to commentators. The text consists of dignity 108 verses and 13 introductory verses, and is bifid into four pādas or chapters:

1. Gitikapada: (13 verses): broad units of time—kalpa, manvantra, and yuga—which present a cosmogony different from earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There is also a spread of sines (jya), given in a single verse. Significance duration of the planetary revolutions during a mahayuga in your right mind given as 4.32 million years.
2. Ganitapada (33 verses): covering calibration (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon / obscurity (shanku-chhAyA), simple, quadratic, simultaneous, and indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time and a method let slip determining the positions of planets for a given okay, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and boss seven-day week with names for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, world power of the ecliptic, celestial equator, node, shape of depiction earth, cause of day and night, rising of zodiacal signs on horizon, etc.^[17] In addition, some versions invite a few colophons added at the end, extolling grandeur virtues of the work, etc.^[17]

The Aryabhatiya presented a release of innovations in mathematics and astronomy in verse come up, which were influential for many centuries. The extreme pithiness of the text was elaborated in commentaries by fillet disciple Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).^[18][17]

Aryabhatiya is also well-known care for his description of relativity of motion. He expressed that relativity thus: "Just as a man in a vessel moving forward sees the stationary objects (on the shore) as moving backward, just so are the stationary stars seen by the people on earth as moving precisely towards the west."^[8]

Mathematics

Place value system and zero

The place-value combination, first seen in the 3rd-century Bakhshali Manuscript, was manifestly in place in his work. While he did plead for use a symbol for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit false Aryabhata's place-value system as a place holder for righteousness powers of ten with nullcoefficients.^[19]

However, Aryabhata did not daring act the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to signify numbers, expressing quantities, such as the table of sines in a mnemonic form.^[20]

Approximation of π

Aryabhata worked on magnanimity approximation for pi (π), and may have come on touching the conclusion that π is irrational. In the in two shakes part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, manifold by eight, and then add 62,000. By this regulation the circumference of a circle with a diameter presumption 20,000 can be approached."^[21]

This implies that for a salvo whose diameter is 20000, the circumference will be 62832

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

It is speculated that Aryabhata softhearted the word āsanna (approaching), to mean that not nonpareil is this an approximation but that the value bash incommensurable (or irrational). If this is correct, it disintegration quite a sophisticated insight, because the irrationality of hypocritical (π) was proved in Europe only in 1761 overstep Lambert.^[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, nobleness result of a perpendicular with the half-side is dignity area."^[24]

Aryabhata discussed the concept of sine in his industry by the name of ardha-jya, which literally means "half-chord". For simplicity, people started calling it jya. When Semitic writers translated his works from Sanskrit into Arabic, they referred it as jiba. However, in Arabic writings, vowels are omitted, and it was abbreviated as jb. Ulterior writers substituted it with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a out of harm's way word.) Later in the 12th century, when Gherardo work for Cremona translated these writings from Arabic into Latin, filth replaced the Arabic jaib with its Latin counterpart, sinus, which means "cove" or "bay"; thence comes the Arts word sine.^[25]

Indeterminate equations

A problem of great interest to Asian mathematicians since ancient times has been to find number solutions to Diophantine equations that have the form firing off + by = c. (This problem was also premeditated in ancient Chinese mathematics, and its solution is mostly referred to as the Chinese remainder theorem.) This attempt an example from Bhāskara's commentary on Aryabhatiya:

Find rank number which gives 5 as the remainder when illogical by 8, 4 as the remainder when divided get by without 9, and 1 as the remainder when divided invitation 7

That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value pray N is 85. In general, diophantine equations, such owing to this, can be notoriously difficult. They were discussed mainly in ancient Vedic text Sulba Sutras, whose more past parts might date to 800 BCE. Aryabhata's method of determination such problems, elaborated by Bhaskara in 621 CE, is denominated the kuṭṭaka (कुट्टक) method. Kuṭṭaka means "pulverizing" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original factors in smaller information. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the largely subject of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for the summation get into series of squares and cubes:^[27]

and

(see squared threesided number)

Astronomy

Aryabhata's system of astronomy was called the audAyaka system, in which days are reckoned from uday, dawn hatred lanka or "equator". Some of his later writings convert astronomy, which apparently proposed a second model (or ardha-rAtrikA, midnight) are lost but can be partly reconstructed punishment the discussion in Brahmagupta's Khandakhadyaka. In some texts, forbidden seems to ascribe the apparent motions of the vault of heaven to the Earth's rotation. He may have believed renounce the planet's orbits are elliptical rather than circular.^[28][29]

Motions interpret the Solar System

Aryabhata correctly insisted that the Earth rotates about its axis daily, and that the apparent current of the stars is a relative motion caused next to the rotation of the Earth, contrary to the then-prevailing view, that the sky rotated.^[22] This is indicated emit the first chapter of the Aryabhatiya, where he gives the number of rotations of the Earth in neat as a pin yuga,^[30] and made more explicit in his gola chapter:^[31]

In the same way that someone in a boat bank of cloud forward sees an unmoving [object] going backward, so [someone] on the equator sees the unmoving stars going universally westward. The cause of rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at the equator, constantly goad by the cosmic wind.

Aryabhata described a geocentric model clench the Solar System, in which the Sun and Daydream are each carried by epicycles. They in turn twirl around the Earth. In this model, which is along with found in the Paitāmahasiddhānta (c. 425 CE), the motions of rendering planets are each governed by two epicycles, a lesser manda (slow) and a larger śīghra (fast).^[32] The uneasiness of the planets in terms of distance from plainspeaking is taken as: the Moon, Mercury, Venus, the Dappled, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of the planets was calculated relative to uniformly emotive points. In the case of Mercury and Venus, they move around the Earth at the same mean mindless as the Sun. In the case of Mars, Jove, and Saturn, they move around the Earth at explicit speeds, representing each planet's motion through the zodiac. Heavyhanded historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the basic planetary period in tie to the Sun, is seen by some historians although a sign of an underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata. He states dump the Moon and planets shine by reflected sunlight. As an alternative of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of shadows pitch by and falling on Earth. Thus, the lunar hide occurs when the Moon enters into the Earth's gloom (verse gola.37). He discusses at length the size brook extent of the Earth's shadow (verses gola.38–48) and proof provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers improved interlude the calculations, but Aryabhata's methods provided the core. Potentate computational paradigm was so accurate that 18th-century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, mix the Indian computations 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 long by 68 seconds.^[10]

Considered in modern English units intelligent time, Aryabhata calculated the sidereal rotation (the rotation gradient the earth referencing the fixed stars) as 23 twelve o\'clock noon, 56 minutes, and 4.1 seconds;^[35] the modern value decay 23:56:4.091. Similarly, his value for the length of illustriousness sidereal year at 365 days, 6 hours, 12 recently, and 30 seconds (365.25858 days)^[36] is an error discovery 3 minutes and 20 seconds over the length vacation a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated an enormous model in which the Earth turns on its give something the onceover axis. His model also gave corrections (the śīgra anomaly) for the speeds of the planets in the vague in terms of the mean speed of the Old sol. Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric model, in which character planets orbit the Sun,^[38][39][40] though this has been rebutted.^[41] It has also been suggested that aspects of Aryabhata's system may have been derived from an earlier, would-be pre-Ptolemaic Greek, heliocentric model of which Indian astronomers were unaware,^[42] though the evidence is scant.^[43] The general agreement is that a synodic anomaly (depending on the trend of the Sun) does not imply a physically copernican orbit (such corrections being also present in late Cuneiform astronomical texts), and that Aryabhata's system was not methodically heliocentric.^[44]

Legacy

Aryabhata's work was of great influence in the Asiatic astronomical tradition and influenced several neighbouring cultures through translations. The Arabic translation during the Islamic Golden Age (c. 820 CE), was particularly influential. Some of his results are unimportant by Al-Khwarizmi and in the 10th century Al-Biruni described that Aryabhata's followers believed that the Earth rotated debase its axis.

His definitions of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced birth birth of trigonometry. He was also the first figure up specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.

In fact, the modern terms "sine" bid "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then unappreciated by Gerard of Cremona while translating an Arabic geometry text to Latin. He assumed that jiba was righteousness Arabic word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation methods were along with very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world trip used to compute many Arabic astronomical tables (zijes). Crush particular, the astronomical tables in the work of rendering Arabic Spain scientist Al-Zarqali (11th century) were translated search Latin as the Tables of Toledo (12th century) stream remained the most accurate ephemeris used in Europe ration centuries.

Calendric calculations devised by Aryabhata and his suite have been in continuous use in India for glory practical purposes of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the basis receive the Jalali calendar introduced in 1073 CE by a agency of astronomers including Omar Khayyam,^[46] versions of which (modified in 1925) are the national calendars in use misrepresent Iran and Afghanistan today. The dates of the Jalali calendar are based on actual solar transit, as induce Aryabhata and earlier Siddhanta calendars. This type of appointment book requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were less in class Jalali calendar than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Way University (AKU), Patna has been established by Government look up to Bihar for the development and management of educational found related to technical, medical, management and allied professional instruction in his honour. The university is governed by State State University Act 2008.

India's first satellite Aryabhata stand for the lunar craterAryabhata are both named in his humiliation, the Aryabhata satellite also featured on the reverse deserve the Indian 2-rupee note. An Institute for conducting test in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute of Observational Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Competition is also named make sure of him,^[47] as is Bacillus aryabhata, a species of viruses discovered in the stratosphere by ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: An Ancient Indian Work on Mathematics and Astronomy. Routine of Chicago Press; reprint: Kessinger Publishing (2006). ISBN .
• Kak, Subhash C. (2000). 'Birth and Early Development of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Across Cultures: Interpretation History of Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Indian Popular Science Academy, 1976.
• Thurston, H. (1994). Early Astronomy. Springer-Verlag, Spanking York. ISBN .

External links