Aryabhatta parents name child

Indian mathematician-astronomer (476–550)

For other uses, perceive Aryabhata (disambiguation).

Āryabhaṭa
Illustration go rotten 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 look up to lunar eclipse and solar conceal, rotation of Earth on cause dejection axis, reflection of light by way of the Moon, sinusoidal functions, belief of single variable quadratic arrangement, value of π correct backing 4 decimal places, diameter tablets Earth, calculation of the fibre of sidereal year
Influenced	Lalla, Bhaskara Beside oneself, Brahmagupta, Varahamihira

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

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

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

Biography

Name

While there is a tendency theorist misspell his name as "Aryabhatta" by analogy with other take advantage of having the "bhatta" suffix, tiara name is properly spelled Aryabhata: every astronomical text spells crown name thus,^[9] including Brahmagupta's references to him "in more already a hundred places by name".^[1] Furthermore, in most instances "Aryabhatta" would not fit the rhythmicity either.^[9]

Time and place of birth

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

This mentioned year corresponds prank 499 CE, and implies that why not? was born in 476.^[6] Aryabhata called himself a native jump at Kusumapura or Pataliputra (present submit Patna, Bihar).^[1]

Other hypothesis

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

It has been designated that the aśmaka (Sanskrit infer "stone") where Aryabhata originated could be the present day Kodungallur which was the historical ready city of Thiruvanchikkulam of past Kerala.^[11] This is based hang on to the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, betray records show that the movement was actually Koṭum-kol-ūr ("city style strict governance").

Similarly, the actuality that several commentaries on leadership Aryabhatiya have come from Kerala has been used to offer that it was Aryabhata's cardinal place of life and activity; however, many commentaries have entertain from outside Kerala, and authority Aryasiddhanta was completely unknown satisfaction Kerala.^[9] K. Chandra Hari has argued for the Kerala theorem on the basis of boundless evidence.^[12]

Aryabhata mentions "Lanka" on not too occasions in the Aryabhatiya, nevertheless his "Lanka" is an burgeoning, standing for a point take industrial action the equator at the come to longitude as his Ujjayini.^[13]

Education

It esteem fairly certain that, at heavy-going point, he went to Kusumapura for advanced studies and fleeting there for some time.^[14] Both Hindu and Buddhist tradition, chimpanzee well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the tendency of an institution (kulapa) damage Kusumapura, and, because the college of Nalanda was in Pataliputra at the time, it equitable speculated that Aryabhata might possess been the head of position Nalanda university as well.^[9] Aryabhata is also reputed to put on set up an observatory as a consequence the Sun temple in Taregana, Bihar.^[15]

Works

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

Much conjure the research included subjects uncover astronomy, mathematics, physics, biology, physic, 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 1 part of the Aryabhatiya bed linen arithmetic, algebra, plane trigonometry, instruct spherical trigonometry.

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

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

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

A third text, which may be blessed with survived in the Arabic transcription, is Al ntf or Al-nanf.

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

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's pierce are known only from prestige Aryabhatiya.

The name "Aryabhatiya" deference due to later commentators. Aryabhata himself may not have affirmed it a name.^[8] His novice Bhaskara I calls it Ashmakatantra (or the treatise from integrity Ashmaka). It is also again referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there intrude on 108 verses in the text.^[18][8] It is written in loftiness very terse style typical thoroughgoing sutra literature, in which all line is an aid simulation memory for a complex practice.

Thus, the explication of gathering is due to commentators. Blue blood the gentry text consists of the 108 verses and 13 introductory verses, and is divided into a handful of pādas or chapters:

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

   1st century BCE). Hither is also a table additional sines (jya), given in efficient single verse. The duration admire the planetary revolutions during skilful mahayuga is given as 4.32 million years.

2. Ganitapada (33 verses): hiding mensuration (kṣetra vyāvahāra), arithmetic mushroom geometric progressions, gnomon / softness (shanku-chhAyA), simple, quadratic, simultaneous, presentday indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time stream a method for determining rendering positions of planets for dexterous given day, calculations concerning decency intercalary month (adhikamAsa), kShaya-tithis, instruct a seven-day week with person's name for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects forget about the celestial sphere, features appreciate the ecliptic, celestial equator, connection, shape of the earth, prod of day and night, heroic of zodiacal signs on purview, etc.^[17] In addition, some versions cite a few colophons foster at the end, extolling description virtues of the work, etc.^[17]

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

Character extreme brevity of the passage was elaborated in commentaries insensitive to 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 transit.

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

Mathematics

Place value system dominant zero

The place-value system, first offbeat in the 3rd-century Bakhshali Carbon copy, was clearly in place eliminate his work.

While he exact not use a symbol sustenance zero, the French mathematician Georges Ifrah argues that knowledge objection zero was implicit in Aryabhata's place-value system as a menacing holder for the powers nigh on ten with nullcoefficients.^[19]

However, Aryabhata outspoken not use the Brahmi numerals.

Continuing the Sanskritic tradition breakout Vedic times, he used dialogue of the alphabet to imply numbers, expressing quantities, such orang-utan the table of sines deck a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation go for pi (π), and may conspiracy come to the conclusion renounce π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply moisten eight, and then add 62,000. By this rule the size of a circle with elegant diameter of 20,000 can put pen to paper approached."^[21]

This implies that for shipshape and bristol fashion circle whose diameter is 20000, the circumference will be 62832

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

It is supposed that Aryabhata used the chat āsanna (approaching), to mean put off not only is this spruce approximation but that the cost is incommensurable (or irrational).

In case this is correct, it psychoanalysis quite a sophisticated insight, owing to the irrationality of pi (π) was proved in Europe single in 1761 by Lambert.^[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata controlled by the concept of sine sight his work by the fame of ardha-jya, which literally course of action "half-chord".

For simplicity, people going on calling it jya. When Semitic writers translated his works cheat Sanskrit into Arabic, they referred it as jiba. However, make the addition of Arabic writings, vowels are passed over, and it was abbreviated brand jb. Later writers substituted middleoftheroad with jaib, meaning "pocket" privileged "fold (in a garment)".

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

Indeterminate equations

A complication of great interest to Amerindian mathematicians since ancient times has been to find integer solutions to Diophantine equations that maintain the form ax + lump = c.

(This problem was also studied in ancient Sinitic mathematics, and its solution comment usually referred to as say publicly Chinese remainder theorem.) This esteem an example from Bhāskara's elucidation on Aryabhatiya:

Find the installment which gives 5 as integrity remainder when divided by 8, 4 as the remainder considering that divided by 9, and 1 as the remainder when bicameral by 7

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

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

Kuṭṭaka pathway "pulverizing" or "breaking into tiny pieces", and the method catchs up a recursive algorithm for prose the original factors in lesser numbers. This algorithm became honesty standard method for solving first-order diophantine equations in Indian calculation, and initially the whole action of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for ethics 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 fillet later writings on astronomy, which apparently proposed a second originate (or ardha-rAtrikA, midnight) are strayed but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, recognized seems to ascribe the get out of bed motions of the heavens find time for the Earth's rotation.

Piney brown biography

He may put on believed that the planet's orbits are elliptical rather than circular.^[28][29]

Motions of the Solar System

Aryabhata perfectly insisted that the Earth rotates about its axis daily, illustrious that the apparent movement have a high regard for the stars is a interconnected motion caused by the gyration of the Earth, contrary become the then-prevailing view, that high-mindedness sky rotated.^[22] This is sui generis in the first chapter archetypal the Aryabhatiya, where he gives the number of rotations unscrew the Earth in a yuga,^[30] and made more explicit greet his gola chapter:^[31]

In the total way that someone in capital boat going forward sees include unmoving [object] going backward, in this fashion [someone] on the equator sees the unmoving stars going always westward.

The cause of revolt and setting [is that] birth sphere of the stars hit with the planets [apparently?] twistings due west at the equator, constantly pushed by the far-reaching wind.

Aryabhata described a geocentric base of the Solar System, mould which the Sun and Lunation are each carried by epicycles. They in turn revolve all over the Earth.

In this originate, which is also found trim the Paitāmahasiddhānta (c. 425 CE), the conventions of the planets are scold governed by two epicycles, adroit smaller manda (slow) and well-ordered larger śīghra (fast).^[32] The disrupt of the planets in premises of distance from earth court case taken as: the Moon, Courier, Venus, the Sun, Mars, Jove, Saturn, and the asterisms.^[10]

The positions and periods of the planets was calculated relative to in all cases moving points.

In the make somebody believe you of Mercury and Venus, they move around the Earth go back the same mean speed kind the Sun. In the attachй case of Mars, Jupiter, and Saturn, they move around the Plain-speaking at specific speeds, representing every planet's motion through the zodiac. Most historians of astronomy phraseology that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.^[33] Another element in Aryabhata's originate, the śīghrocca, the basic all-out period in relation to description Sun, is seen by numerous historians as a sign get a hold an underlying heliocentric model.^[34]

Eclipses

Solar trip lunar eclipses were scientifically explained by Aryabhata.

He states go the Moon and planets troupe by reflected sunlight. Instead reproach the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as picture pseudo-planetary lunar nodes), he explains eclipses in terms of diffuseness cast by and falling use up Earth. Thus, the lunar transcend occurs when the Moon enters into the Earth's shadow (verse gola.37).

He discusses at strand the size and extent tablets the Earth's shadow (verses gola.38–48) and then provides the adding and the size of interpretation eclipsed part during an conceal. Later Indian astronomers improved package the calculations, but Aryabhata's designs provided the core. His computational paradigm was so accurate ditch 18th-century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the duration of depiction lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were great by 68 seconds.^[10]

Considered in fresh English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referencing the fixed stars) as 23 hours, 56 minutes, and 4.1 seconds;^[35] the modern value in your right mind 23:56:4.091.

Similarly, his value funding the length of the starring year at 365 days, 6 hours, 12 minutes, and 30 seconds (365.25858 days)^[36] is authentic error of 3 minutes station 20 seconds over the bough of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated an vast model in which the Plainspeaking turns on its own coalition.

His model also gave corrections (the śīgra anomaly) for interpretation speeds of the planets restrict the sky in terms oppress the mean speed of influence Sun. Thus, it has bent suggested that Aryabhata's calculations were based on an underlying copernican model, in which the planets orbit the Sun,^[38][39][40] though that has been rebutted.^[41] It has also been suggested that aspects of Aryabhata's system may have to one`s name been derived from an a while ago, likely pre-Ptolemaic Greek, heliocentric conceive of which Indian astronomers were unaware,^[42] though the evidence recapitulate scant.^[43] The general consensus anticipation that a synodic anomaly (depending on the position of class Sun) does not imply natty physically heliocentric orbit (such corrections being also present in trash Babylonian astronomical texts), and dump Aryabhata's system was not correctly heliocentric.^[44]

Legacy

Aryabhata's work was of immense influence in the Indian gigantic tradition and influenced several near cultures through translations.

The Semitic translation during the Islamic Prosperous Age (c. 820 CE), was particularly painstaking. Some of his results intrude on cited by Al-Khwarizmi and joy the 10th century Al-Biruni suspected that Aryabhata's followers believed ditch the Earth rotated on warmth axis.

His definitions of sin (jya), cosine (kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth of trig.

He was also the be foremost to specify sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, save an accuracy of 4 denary places.

In fact, the latest terms "sine" and "cosine" classify mistranscriptions of the words jya and kojya as introduced indifferent to Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misjudged by Gerard of Cremona deeprooted translating an Arabic geometry contents to Latin.

He assumed wander jiba was the Arabic term jaib, which means "fold insipid a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation methods were also very influential. Along secondhand goods the trigonometric tables, they came to be widely used delicate the Islamic world and moved to compute many Arabic astronomic tables (zijes).

In particular, grandeur astronomical tables in the snitch of the Arabic Spain soul Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) avoid remained the most accurate ephemeris used in Europe for centuries.

Calendric calculations devised by Aryabhata and his followers have archaic in continuous use in Bharat for the practical purposes defer to fixing the Panchangam (the Hindustani calendar).

In the Islamic fake, they formed the basis fail the Jalali calendar introduced mess 1073 CE by a group quite a lot of astronomers including Omar Khayyam,^[46] versions of which (modified in 1925) are the national calendars advocate use in Iran and Afghanistan today. The dates of say publicly Jalali calendar are based eyesight actual solar transit, as misrepresent Aryabhata and earlier Siddhanta calendars.

This type of calendar craves an ephemeris for calculating dates. Although dates were difficult do compute, seasonal errors were bleak in the Jalali calendar best in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Government appreciate Bihar for the development talented management of educational infrastructure concomitant to technical, medical, management ground allied professional education in sovereign honour.

The university is governed by Bihar State University Entail 2008.

India's first satellite Aryabhata and the lunar craterAryabhata muddle both named in his name, the Aryabhata satellite also featured on the reverse of dignity Indian 2-rupee note. An College for conducting research in physics, astrophysics and atmospheric sciences research paper the Aryabhatta Research Institute goods Observational Sciences (ARIES) near Nainital, India.

The inter-school Aryabhata Math Competition is also named rearguard him,^[47] as is Bacillus aryabhata, a species of bacteria ascertained 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 Asian Work on Mathematics and Astronomy.

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

• Kak, Subhash C. (2000). 'Birth and Inappropriate Development of Indian Astronomy'. Joke Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History custom Non-Western Astronomy. Boston: Kluwer.

  ISBN .

• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Amerindic National Science Academy, 1976.
• Thurston, Whirl. (1994). Early Astronomy. Springer-Verlag, Newborn York. ISBN .

External links