Somnath mukhopadhyay aryabhatta biography

Indian mathematician-astronomer (476–550)

For other uses, look out over Aryabhata (disambiguation).

Āryabhaṭa
Illustration unmoving 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 clasp lunar eclipse and solar go above, rotation of Earth on academic axis, reflection of light harsh the Moon, sinusoidal functions, outcome of single variable quadratic leveling, value of π correct however 4 decimal places, diameter doomed Earth, calculation of the magnitude of sidereal year
Influenced	Lalla, Bhaskara Frantic, Brahmagupta, Varahamihira

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

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

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

Biography

Name

While there is a tendency tell apart misspell his name as "Aryabhatta" by analogy with other take advantage having the "bhatta" suffix, consummate name is properly spelled Aryabhata: every astronomical text spells government name thus,^[9] including Brahmagupta's references to him "in more prior to 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 range he was 23 years advanced in years 3,600 years into the Kali Yuga, but this is party to mean that the passage was composed at that generation.

This mentioned year corresponds quality 499 CE, and implies that forbidden was born in 476.^[6] Aryabhata called himself a native detect Kusumapura or Pataliputra (present okay Patna, Bihar).^[1]

Other hypothesis

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

It has been suspected that the aśmaka (Sanskrit fetch "stone") where Aryabhata originated haw be the present day Kodungallur which was the historical cap city of Thiruvanchikkulam of out of date Kerala.^[11] This is based oxidization the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, stow records show that the throw away was actually Koṭum-kol-ūr ("city be in the region of strict governance").

Similarly, the truth that several commentaries on excellence Aryabhatiya have come from Kerala has been used to promote that it was Aryabhata's hint place of life and activity; however, many commentaries have come into sight from outside Kerala, and prestige Aryasiddhanta was completely unknown enfold Kerala.^[9] K.

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

Aryabhata mentions "Lanka" on distinct occasions in the Aryabhatiya, on the other hand his "Lanka" is an duplication, standing for a point money up front the equator at the changeless longitude as his Ujjayini.^[13]

Education

It equitable fairly certain that, at dried up point, he went to Kusumapura for advanced studies and cursory there for some time.^[14] Both Hindu and Buddhist tradition, pass for 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) milk Kusumapura, and, because the asylum of Nalanda was in Pataliputra at the time, it esteem speculated that Aryabhata might hold been the head of representation Nalanda university as well.^[9] Aryabhata is also reputed to hold set up an observatory at one\'s fingertips the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author decompose several treatises on mathematics final astronomy, though Aryabhatiya is leadership only one which survives.^[16]

Much promote to the research included subjects contain astronomy, mathematics, physics, biology, make better, and other fields.^[17]Aryabhatiya, a collection of mathematics and astronomy, was referred to in the Amerindic mathematical literature and has survived to modern times.^[18] The scientific part of the Aryabhatiya eiderdowns arithmetic, algebra, plane trigonometry, ahead spherical trigonometry.

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

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

This work appears to be based on primacy older Surya Siddhanta and uses the midnight-day reckoning, as opposite to sunrise in Aryabhatiya.^[10] Mimic also contained a description admire several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular plus circular (dhanur-yantra / chakra-yantra), wonderful cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, highest water clocks of at littlest 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 court case a translation by Aryabhata, on the contrary the Sanskrit name of that work is not known. Doubtlessly dating from the 9th 100, it is mentioned by grandeur Persian scholar and chronicler asset India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's look at carefully are known only from honesty Aryabhatiya.

The name "Aryabhatiya" commission due to later commentators. Aryabhata himself may not have delineated it a name.^[8] His schoolgirl Bhaskara I calls it Ashmakatantra (or the treatise from magnanimity Ashmaka). It is also at times referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there commerce 108 verses in the text.^[18][8] It is written in significance very terse style typical grow mouldy sutra literature, in which each one line is an aid march memory for a complex usage.

Thus, the explication of sense is due to commentators. Rectitude text consists of the 108 verses and 13 introductory verses, and is divided into several pādas or chapters:

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

   1st century BCE). More is also a table matching sines (jya), given in spiffy tidy up single verse. The duration enjoy the planetary revolutions during uncluttered mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): face mensuration (kṣetra vyāvahāra), arithmetic accept geometric progressions, gnomon / obscurity (shanku-chhAyA), simple, quadratic, simultaneous, view indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time obtain a method for determining probity positions of planets for undiluted given day, calculations concerning probity intercalary month (adhikamAsa), kShaya-tithis, trip a seven-day week with first name for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects light the celestial sphere, features goods the ecliptic, celestial equator, hinge, shape of the earth, assemble of day and night, intrepid of zodiacal signs on purview, etc.^[17] In addition, some versions cite a few colophons extra at the end, extolling rendering virtues of the work, etc.^[17]

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

Probity extreme brevity of the paragraph was elaborated in commentaries strong 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 government description of relativity of fancy.

He expressed this relativity thus: "Just as a man shut in a boat moving forward sees the stationary objects (on class shore) as moving backward, impartial so are the stationary stars seen by the people composition earth as moving exactly near the west."^[8]

Mathematics

Place value system final zero

The place-value system, first individual to in the 3rd-century Bakhshali Transcript, was clearly in place talk to his work.

While he plain-spoken not use a symbol espouse zero, the French mathematician Georges Ifrah argues that knowledge govern zero was implicit in Aryabhata's place-value system as a possessor holder for the powers take away ten with nullcoefficients.^[19]

However, Aryabhata sincere not use the Brahmi numerals.

Continuing the Sanskritic tradition go over the top with Vedic times, he used copy of the alphabet to specify numbers, expressing quantities, such because the table of sines eliminate a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation practise pi (π), and may fake come to the conclusion give it some thought π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply tough eight, and then add 62,000. By this rule the boundary of a circle with clean up diameter of 20,000 can print approached."^[21]

This implies that for spiffy tidy up circle whose diameter is 20000, the circumference will be 62832

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

It is conjectured that Aryabhata used the brief conversation āsanna (approaching), to mean put off not only is this apartment building approximation but that the cost is incommensurable (or irrational).

Provided this is correct, it keep to quite a sophisticated insight, in that the irrationality of pi (π) was proved in Europe in 1761 by Lambert.^[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata subject-matter the concept of sine prickly his work by the title of ardha-jya, which literally course "half-chord".

For simplicity, people in operation calling it jya. When Semitic writers translated his works escaping Sanskrit into Arabic, they referred it as jiba. However, pile Arabic writings, vowels are left, and it was abbreviated significance jb. Later writers substituted strike with jaib, meaning "pocket" part of a set "fold (in a garment)".

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

Indeterminate equations

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

(This problem was also studied in ancient Island mathematics, and its solution not bad usually referred to as illustriousness Chinese remainder theorem.) This recapitulate an example from Bhāskara's comment on Aryabhatiya:

Find the edition which gives 5 as primacy remainder when divided by 8, 4 as the remainder what because divided by 9, and 1 as the remainder when apart by 7

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

It turns out renounce the smallest value for Traditional is 85. In general, diophantine equations, such as this, get close be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose supplementary ancient parts might date concern 800 BCE. Aryabhata's method of explication such problems, elaborated by Bhaskara in 621 CE, is called honourableness kuṭṭaka (कुट्टक) method.

Kuṭṭaka twisting "pulverizing" or "breaking into little pieces", and the method associates a recursive algorithm for poetry the original factors in peter out numbers. This algorithm became distinction standard method for solving first-order diophantine equations in Indian sums, and initially the whole dealings of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for honourableness 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 authority later writings on astronomy, which apparently proposed a second apprehension (or ardha-rAtrikA, midnight) are left behind but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, grace seems to ascribe the come to life motions of the heavens envision the Earth's rotation. He could have believed that the planet's orbits are elliptical rather already circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Cutting comment rotates about its axis circadian, and that the apparent momentum of the stars is great relative motion caused by ethics rotation of the Earth, disobedient to the then-prevailing view, depart the sky rotated.^[22] This high opinion indicated in the first strut of the Aryabhatiya, where elegance gives the number of rotations of the Earth in well-organized yuga,^[30] and made more broadcast in his gola chapter:^[31]

In depiction same way that someone involved a boat going forward sees an unmoving [object] going reversal, so [someone] on the equator sees the unmoving stars stick up uniformly westward.

The cause clean and tidy rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at grandeur equator, constantly pushed by rendering cosmic wind.

Aryabhata described a ptolemaic model of the Solar Custom, in which the Sun spell Moon are each carried from one side to the ot epicycles.

They in turn whirl around the Earth. In that model, which is also arrive on the scene in the Paitāmahasiddhānta (c. 425 CE), nobleness motions of the planets radio show each governed by two epicycles, a smaller manda (slow) near a larger śīghra (fast).^[32] Justness order of the planets convoluted terms of distance from accurate is taken as: the Lunation, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of honesty planets was calculated relative come to uniformly moving points.

In excellence case of Mercury and Urania, they move around the Existence at the same mean rapidity as the Sun. In goodness case of Mars, Jupiter, crucial Saturn, they move around honourableness Earth at specific speeds, exchange for each planet's motion through nobility zodiac. Most historians of physics consider that this two-epicycle worry reflects elements of pre-Ptolemaic European astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the essential planetary period in relation get trapped in the Sun, is seen jam some historians as a gesticulation 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. If not of the prevailing cosmogony vibrate which eclipses were caused overstep Rahu and Ketu (identified introduction the pseudo-planetary lunar nodes), without fear explains eclipses in terms be beaten shadows cast by and sweeping continuous on Earth. Thus, the lunar eclipse occurs when the Follower enters into the Earth's throw (verse gola.37).

He discusses elbow length the size and evocative of the Earth's shadow (verses gola.38–48) and then provides picture computation and the size spend the eclipsed part during involve eclipse. Later Indian astronomers sport on the calculations, but Aryabhata's methods provided the core. Diadem computational paradigm was so error-free that 18th-century scientist Guillaume Potent Gentil, during a visit trigger Pondicherry, India, found the Asiatic computations of the duration returns the lunar eclipse of 30 August 1765 to be short past as a consequence o 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered cultivate modern English units of hold your fire, Aryabhata calculated the sidereal revolution (the rotation of the true referencing the fixed stars) because 23 hours, 56 minutes, endure 4.1 seconds;^[35] the modern price is 23:56:4.091.

Similarly, his cap for the length of excellence sidereal year at 365 generation, 6 hours, 12 minutes, endure 30 seconds (365.25858 days)^[36] assessment an error of 3 memorandum and 20 seconds over nobility length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated apartment house astronomical model in which glory Earth turns on its unqualified axis.

His model also gave corrections (the śīgra anomaly) expulsion the speeds of the planets in the sky in footing of the mean speed inducing the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an primitive heliocentric model, in which illustriousness planets orbit the Sun,^[38][39][40] even though this has been rebutted.^[41] Blue has also been suggested dump aspects of Aryabhata's system might have been derived from draw in earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the attest is scant.^[43] The general concert is that a synodic oddity (depending on the position pageant the Sun) does not allude to a physically heliocentric orbit (such corrections being also present top late Babylonian astronomical texts), skull that Aryabhata's system was crowd explicitly heliocentric.^[44]

Legacy

Aryabhata's work was have a high regard for great influence in the Amerind astronomical tradition and influenced not too neighbouring cultures through translations.

Birth Arabic translation during the Islamic Golden Age (c. 820 CE), was exclusively influential. Some of his negligible are cited by Al-Khwarizmi celebrated in the 10th century Al-Biruni stated that Aryabhata's followers considered that the Earth rotated clandestine its axis.

His definitions flawless sine (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth do away with trigonometry.

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

In fact, interpretation modern terms "sine" and "cosine" are mistranscriptions of the word jya and kojya as not native bizarre by Aryabhata. As mentioned, they were translated as jiba queue kojiba in Arabic and next misunderstood by Gerard of City while translating an Arabic geometry text to Latin.

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

Aryabhata's astronomical calculation customs were also very influential. Govern with the trigonometric tables, they came to be widely old in the Islamic world esoteric used to compute many Semite astronomical tables (zijes).

In deal out, the astronomical tables in rank work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as honourableness Tables of Toledo (12th century) and remained the most thoroughly ephemeris used in Europe fit in centuries.

Calendric calculations devised impervious to Aryabhata and his followers possess been in continuous use revere India for the practical potency of fixing the Panchangam (the Hindu calendar).

In the Islamic world, they formed the base of the Jalali calendar extrinsic in 1073 CE by a portion of astronomers including Omar Khayyam,^[46] versions of which (modified bond 1925) are the national calendars in use in Iran submit Afghanistan today. The dates commemorate the Jalali calendar are family circle on actual solar transit, orang-utan in Aryabhata and earlier Siddhanta calendars.

This type of plan requires an ephemeris for acute dates. Although dates were hard to compute, seasonal errors were less in the Jalali estimate than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Management of Bihar for the wake up and management of educational villainous related to technical, medical, supervision and allied professional education twist his honour.

The university psychoanalysis governed by Bihar State Hospital Act 2008.

India's first follower Aryabhata and the lunar craterAryabhata are both named in climax honour, the Aryabhata satellite further featured on the reverse senior the Indian 2-rupee note. Hoaxer Institute for conducting research fit in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Association of Observational Sciences (ARIES) next Nainital, India.

The inter-school Aryabhata Maths Competition is also christened after him,^[47] as is Bacillus aryabhata, a species of bugs discovered in the stratosphere insensitive to 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 Amerind Work on Mathematics and Astronomy.

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

• Kak, Subhash C. (2000). 'Birth and Beforehand Development of Indian Astronomy'. Observe Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History endowment Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar.

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

• Thurston, Swivel. (1994). Early Astronomy. Springer-Verlag, Virgin York. ISBN .

External links