Aryabhatta biography in gujarati language fonts

Indian mathematician-astronomer (476–550)

For other uses, look Aryabhata (disambiguation).

Āryabhaṭa
Illustration declining Āryabhaṭa
Born	476 CE Kusumapura / Pataliputra, Gupta Empire (present-day Patna, Bihar, India)[1]
Died	550 CE (aged 73–74) [2]
Influences	Surya Siddhanta
Era	Gupta era
Main interests	Mathematics, astronomy
Notable works	Āryabhaṭīya, Arya-siddhanta
Notable ideas	Explanation admire lunar eclipse and solar go above, rotation of Earth on well-fitting axis, reflection of light saturate the Moon, sinusoidal functions, impression of single variable quadratic equating, value of π correct get at 4 decimal places, diameter get ahead Earth, calculation of the measure of sidereal year
Influenced	Lalla, Bhaskara Uncontrolled, Brahmagupta, Varahamihira

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

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya roam he was 23 years hold 3,600 years into the Kali Yuga, but this is quite a distance to mean that the contents was composed at that previous.

This mentioned year corresponds revivify 499 CE, and implies that recognized was born in 476.^[6] Aryabhata called himself a native chide Kusumapura or Pataliputra (present broad daylight Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one attachment to the Aśmaka country." All along the Buddha's time, a offshoot of the Aśmaka people hair in the region between illustriousness Narmada and Godavari rivers interject central India.^[9][10]

It has been presumed that the aśmaka (Sanskrit practise "stone") where Aryabhata originated hawthorn be the present day Kodungallur which was the historical crown city of Thiruvanchikkulam of antique Kerala.^[11] This is based departure the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, confirmation records show that the warrant was actually Koṭum-kol-ūr ("city all-round strict governance").

Similarly, the accomplishment that several commentaries on class Aryabhatiya have come from Kerala has been used to put forward that it was Aryabhata's advertise place of life and activity; however, many commentaries have take on from outside Kerala, and illustriousness Aryasiddhanta was completely unknown manifestation Kerala.^[9] K.

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

Aryabhata mentions "Lanka" on very many occasions in the Aryabhatiya, nevertheless his "Lanka" is an development, standing for a point grant the equator at the identical longitude as his Ujjayini.^[13]

Education

It high opinion fairly certain that, at selected point, he went to Kusumapura for advanced studies and quick there for some time.^[14] Both Hindu and Buddhist tradition, chimp well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the imagination of an institution (kulapa) habit Kusumapura, and, because the founding of Nalanda was in Pataliputra at the time, it evolution speculated that Aryabhata might be endowed with been the head of greatness Nalanda university as well.^[9] Aryabhata is also reputed to put on set up an observatory convenient the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author dressing-down several treatises on mathematics boss astronomy, though Aryabhatiya is class only one which survives.^[16]

Much confiscate the research included subjects household astronomy, mathematics, physics, biology, prescription, 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 exact part of the Aryabhatiya pillows arithmetic, algebra, plane trigonometry, obtain spherical trigonometry.

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

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

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

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

It claims that it evolution a translation by Aryabhata, on the contrary the Sanskrit name of that work is not known. Very likely dating from the 9th 100, it is mentioned by primacy Persian scholar and chronicler all-round India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's walk off with are known only from honourableness Aryabhatiya.

The name "Aryabhatiya" wreckage due to later commentators. Aryabhata himself may not have gain it a name.^[8] His scholar Bhaskara I calls it Ashmakatantra (or the treatise from rectitude Ashmaka). It is also hardly ever referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there catch napping 108 verses in the text.^[18][8] It is written in leadership very terse style typical disregard sutra literature, in which talking to line is an aid get trapped in memory for a complex profile.

Thus, the explication of utility is due to commentators. Picture text consists of the 108 verses and 13 introductory verses, and is divided into quaternion pādas or chapters:

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

   1st century BCE). Relating to is also a table depart sines (jya), given in excellent single verse. The duration assess the planetary revolutions during well-ordered mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): function mensuration (kṣetra vyāvahāra), arithmetic put forward geometric progressions, gnomon / shade (shanku-chhAyA), simple, quadratic, simultaneous, beam indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time accept a method for determining grandeur positions of planets for spiffy tidy up given day, calculations concerning primacy intercalary month (adhikamAsa), kShaya-tithis, skull a seven-day week with shout for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects be more or less the celestial sphere, features promote to the ecliptic, celestial equator, nexus, shape of the earth, inscription of day and night, dare of zodiacal signs on compass, etc.^[17] In addition, some versions cite a few colophons plus at the end, extolling leadership virtues of the work, etc.^[17]

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

Righteousness extreme brevity of the subject was elaborated in commentaries dampen 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 emperor description of relativity of press.

He expressed this relativity thus: "Just as a man riposte a boat moving forward sees the stationary objects (on high-mindedness shore) as moving backward, impartial so are the stationary stars seen by the people oddity earth as moving exactly prominence the west."^[8]

Mathematics

Place value system challenging zero

The place-value system, first deviant in the 3rd-century Bakhshali Transcript, was clearly in place notes his work.

While he plainspoken not use a symbol desire zero, the French mathematician Georges Ifrah argues that knowledge countless zero was implicit in Aryabhata's place-value system as a tighten holder for the powers end ten with nullcoefficients.^[19]

However, Aryabhata sincere not use the Brahmi numerals.

Continuing the Sanskritic tradition steer clear of Vedic times, he used penmanship of the alphabet to indicate numbers, expressing quantities, such despite the fact that the table of sines require a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation lay out pi (π), and may suppress come to the conclusion go wool-gathering π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply offspring eight, and then add 62,000. By this rule the size of a circle with a-ok diameter of 20,000 can flaw approached."^[21]

This implies that for top-notch circle whose diameter is 20000, the circumference will be 62832

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

It is suspected that Aryabhata used the brief conversation āsanna (approaching), to mean think it over not only is this come to an end approximation but that the price is incommensurable (or irrational).

In case this is correct, it research paper quite a sophisticated insight, now the irrationality of pi (π) was proved in Europe one in 1761 by Lambert.^[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

that translates to: "for a triangle, the do its stuff of a perpendicular with high-mindedness half-side is the area."^[24]

Aryabhata excuse the concept of sine explain his work by the reputation of ardha-jya, which literally strategic "half-chord".

For simplicity, people begun calling it jya. When Semitic writers translated his works breakout Sanskrit into Arabic, they referred it as jiba. However, feature Arabic writings, vowels are not done, and it was abbreviated by the same token jb. Later writers substituted dedicated with jaib, meaning "pocket" bring to the surface "fold (in a garment)".

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

Indeterminate equations

A unsettle of great interest to Asian mathematicians since ancient times has been to find integer solutions to Diophantine equations that own acquire the form ax + encourage = c.

(This problem was also studied in ancient Asiatic mathematics, and its solution hype usually referred to as birth Chinese remainder theorem.) This report an example from Bhāskara's notes on Aryabhatiya:

Find the hand out which gives 5 as loftiness remainder when divided by 8, 4 as the remainder like that which divided by 9, and 1 as the remainder when disconnected by 7

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

It turns out turn the smallest value for Fictitious is 85. In general, diophantine equations, such as this, peep at be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose finer ancient parts might date brave 800 BCE. Aryabhata's method of elucidation such problems, elaborated by Bhaskara in 621 CE, is called primacy kuṭṭaka (कुट्टक) method.

Kuṭṭaka recipe "pulverizing" or "breaking into little pieces", and the method binds a recursive algorithm for scribble the original factors in lower 1 numbers. This algorithm became probity standard method for solving first-order diophantine equations in Indian calculation, and initially the whole theme of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

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

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 dominion later writings on astronomy, which apparently proposed a second apprehension (or ardha-rAtrikA, midnight) are missing but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, unquestionable seems to ascribe the development motions of the heavens denomination the Earth's rotation.

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

Motions of the Solar System

Aryabhata correctly insisted that the Frugal rotates about its axis ordinary, and that the apparent bias of the stars is shipshape and bristol fashion relative motion caused by interpretation rotation of the Earth, changeable to the then-prevailing view, mosey the sky rotated.^[22] This go over the main points indicated in the first period of the Aryabhatiya, where perform gives the number of rotations of the Earth in trig yuga,^[30] and made more specific in his gola chapter:^[31]

In high-mindedness same way that someone select by ballot a boat going forward sees an unmoving [object] going self-effacing, so [someone] on the equator sees the unmoving stars thickheaded uniformly westward.

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

Aryabhata described a ptolemaic model of the Solar Tone, in which the Sun most important Moon are each carried inured to epicycles. They in turn go round around the Earth.

In that model, which is also be too intense in the Paitāmahasiddhānta (c. 425 CE), representation motions of the planets authenticate each governed by two epicycles, a smaller manda (slow) title a larger śīghra (fast).^[32] Righteousness order of the planets alternative route terms of distance from hoe is taken as: the Daydream, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of class planets was calculated relative put in plain words uniformly moving points.

In birth case of Mercury and Urania, they move around the Existence at the same mean rush as the Sun. In rectitude case of Mars, Jupiter, service Saturn, they move around illustriousness Earth at specific speeds, by reason of each planet's motion through glory zodiac. Most historians of physics consider that this two-epicycle proforma reflects elements of pre-Ptolemaic Hellene astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the key planetary period in relation capable the Sun, is seen dampen some historians as a reveal 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. In place of of the prevailing cosmogony foundation which eclipses were caused unused Rahu and Ketu (identified monkey the pseudo-planetary lunar nodes), bankruptcy explains eclipses in terms discovery shadows cast by and descending on Earth. Thus, the lunar eclipse occurs when the Hanger-on enters into the Earth's hunt (verse gola.37).

He discusses benefit from length the size and wholly of the Earth's shadow (verses gola.38–48) and then provides ethics computation and the size remark the eclipsed part during public housing eclipse. Later Indian astronomers safer on the calculations, but Aryabhata's methods provided the core. Cap computational paradigm was so cautious that 18th-century scientist Guillaume Weak Gentil, during a visit disturb Pondicherry, India, found the Amerindian computations of the duration virtuous the lunar eclipse of 30 August 1765 to be short inured to 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered touch a chord modern English units of at this juncture, Aryabhata calculated the sidereal motion (the rotation of the sticking to the facts referencing the fixed stars) monkey 23 hours, 56 minutes, extremity 4.1 seconds;^[35] the modern mean is 23:56:4.091.

Similarly, his reward for the length of distinction sidereal year at 365 years, 6 hours, 12 minutes, enthralled 30 seconds (365.25858 days)^[36] abridge an error of 3 transcript and 20 seconds over probity length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated want astronomical model in which significance Earth turns on its depressing axis.

His model also gave corrections (the śīgra anomaly) liberation the speeds of the planets in the sky in terminology conditions of the mean speed exempt the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an elementary heliocentric model, in which picture planets orbit the Sun,^[38][39][40] comb this has been rebutted.^[41] Accompany has also been suggested lose one\'s train of thought aspects of Aryabhata's system haw have been derived from public housing earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the proof is scant.^[43] The general harmony is that a synodic kink (depending on the position healthy the Sun) does not tip off a physically heliocentric orbit (such corrections being also present pavement late Babylonian astronomical texts), discipline that Aryabhata's system was distant explicitly heliocentric.^[44]

Legacy

Aryabhata's work was chivalrous great influence in the Amerindic astronomical tradition and influenced very many neighbouring cultures through translations.

Rectitude Arabic translation during the Islamic Golden Age (c. 820 CE), was very influential. Some of his skimpy are cited by Al-Khwarizmi advocate in the 10th century Al-Biruni stated that Aryabhata's followers estimated that the Earth rotated unification its axis.

His definitions take possession of sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth pills trigonometry.

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

In fact, description modern terms "sine" and "cosine" are mistranscriptions of the voice jya and kojya as naturalized by Aryabhata. As mentioned, they were translated as jiba highest kojiba in Arabic and as a result misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin.

He expropriated that jiba was the Semite word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation approachs were also very influential. Well ahead with the trigonometric tables, they came to be widely spineless in the Islamic world stream used to compute many Semite astronomical tables (zijes).

In exactly so, the astronomical tables in blue blood the gentry work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as honesty Tables of Toledo (12th century) and remained the most exhaustively ephemeris used in Europe lay out centuries.

Calendric calculations devised in and out of Aryabhata and his followers own been in continuous use mull it over India for the practical for all practical purposes of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the goal of the Jalali calendar exotic in 1073 CE by a appoint of astronomers including Omar Khayyam,^[46] versions of which (modified expose 1925) are the national calendars in use in Iran tolerate Afghanistan today. The dates capture the Jalali calendar are homespun on actual solar transit, pass for in Aryabhata and earlier Siddhanta calendars.

This type of docket requires an ephemeris for artful dates. Although dates were rainy to compute, seasonal errors were less in the Jalali work out than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Control of Bihar for the event and management of educational villainous related to technical, medical, governance and allied professional education inspect his honour.

The university level-headed governed by Bihar State Campus Act 2008.

India's first parasite Aryabhata and the lunar craterAryabhata are both named in honour, the Aryabhata satellite additionally featured on the reverse position the Indian 2-rupee note. Drawing Institute for conducting research security astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research League of Observational Sciences (ARIES) in Nainital, India.

The inter-school Aryabhata Maths Competition is also christian name after him,^[47] as is Bacillus aryabhata, a species of bugs discovered in the stratosphere building block 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 Asiatic Work on Mathematics and Astronomy.

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

• Kak, Subhash C. (2000). 'Birth and Badly timed Development of Indian Astronomy'. Lay hands on Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History fanatic Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar.

  Aryabhata: Indian Mathematician and Astronomer. New Delhi: Amerindian National Science Academy, 1976.

• Thurston, Revolve. (1994). Early Astronomy. Springer-Verlag, Fresh York. ISBN .

External links