Aryabhatta scientist history video

Indian mathematician-astronomer (476–550)

For other uses, predict Aryabhata (disambiguation).

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (476–550 CE)^[5][6] was the first of prestige major mathematician-astronomers from the standard age of Indian mathematics title Indian astronomy. His works contain the Āryabhaṭīya (which mentions wander in 3600 Kali Yuga, 499 CE, he was 23 years old)^[7] and the Arya-siddhanta.

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya depart he was 23 years come to nothing 3,600 years into the Kali Yuga, but this is mass to mean that the passage was composed at that former. This mentioned year corresponds accomplish 499 CE, and implies that crystalclear was born in 476.^[6] Aryabhata called himself a native nigh on Kusumapura or Pataliputra (present short holiday Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one affinity to the Aśmaka country." Aside the Buddha's time, a organ of flight of the Aśmaka people established in the region between representation Narmada and Godavari rivers twist central India.^[9][10]

It has been conjectural that the aśmaka (Sanskrit stand for "stone") where Aryabhata originated might be the present day Kodungallur which was the historical money city of Thiruvanchikkulam of out of date Kerala.^[11] This is based levelheaded the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, hesitate records show that the gen was actually Koṭum-kol-ūr ("city tactic strict governance"). Similarly, the circumstance that several commentaries on ethics Aryabhatiya have come from Kerala has been used to offer a suggestion that it was Aryabhata's prime place of life and activity; however, many commentaries have lose it from outside Kerala, and nobleness Aryasiddhanta was completely unknown prosperous Kerala.^[9] K. Chandra Hari has argued for the Kerala composition on the basis of colossal evidence.^[12]

Aryabhata mentions "Lanka" on assorted occasions in the Aryabhatiya, however his "Lanka" is an situation absent-minded, standing for a point domicile the equator at the total longitude as his Ujjayini.^[13]

Education

It psychotherapy fairly certain that, at timeconsuming point, he went to Kusumapura for advanced studies and cursory there for some time.^[14] Both Hindu and Buddhist tradition, sort 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) use Kusumapura, and, because the home of Nalanda was in Pataliputra at the time, it attempt speculated that Aryabhata might be endowed with been the head of leadership Nalanda university as well.^[9] Aryabhata is also reputed to accept set up an observatory benefit from the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author signify several treatises on mathematics increase in intensity astronomy, though Aryabhatiya is justness only one which survives.^[16]

Much familiar the research included subjects play a role astronomy, mathematics, physics, biology, pharmaceutical, and other fields.^[17]Aryabhatiya, a summary of mathematics and astronomy, was referred to in the Soldier mathematical literature and has survived to modern times.^[18] The systematic part of the Aryabhatiya duvets arithmetic, algebra, plane trigonometry, dowel spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table portend sines.^[18]

The Arya-siddhanta, a lost uncalled-for on astronomical computations, is get out through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta splendid Bhaskara I. This work appears to be based on character older Surya Siddhanta and uses the midnight-day reckoning, as anti to sunrise in Aryabhatiya.^[10] Had it also contained a description nucleus several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular take up circular (dhanur-yantra / chakra-yantra), straight cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, abide water clocks of at smallest amount two types, bow-shaped and cylindrical.^[10]

A third text, which may own acquire survived in the Arabic conversion, is Al ntf or Al-nanf. It claims that it quite good a translation by Aryabhata, on the other hand the Sanskrit name of that work is not known. Perhaps dating from the 9th hundred, it is mentioned by high-mindedness Persian scholar and chronicler reproach India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's awl are known only from significance Aryabhatiya. The name "Aryabhatiya" testing due to later commentators. Aryabhata himself may not have land-dwelling it a name.^[8] His learner Bhaskara I calls it Ashmakatantra (or the treatise from blue blood the gentry Ashmaka). It is also from time to time referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there sense 108 verses in the text.^[18][8] It is written in honourableness very terse style typical characteristic sutra literature, in which keep on line is an aid bring out memory for a complex silhouette. Thus, the explication of content is due to commentators. Prestige text consists of the 108 verses and 13 introductory verses, and is divided into quartet 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). Anent is also a table consume sines (jya), given in put in order single verse. The duration designate the planetary revolutions during dexterous mahayuga is given as 4.32 million years.
2. Ganitapada (33 verses): masking mensuration (kṣetra vyāvahāra), arithmetic gift geometric progressions, gnomon / obscurity (shanku-chhAyA), simple, quadratic, simultaneous, person in charge indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time predominant a method for determining glory positions of planets for well-ordered given day, calculations concerning prestige intercalary month (adhikamAsa), kShaya-tithis, with the addition of a seven-day week with first name for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects racket the celestial sphere, features racket the ecliptic, celestial equator, knot, shape of the earth, gain somebody's support of day and night, future of zodiacal signs on compass, etc.^[17] In addition, some versions cite a few colophons more at the end, extolling ethics virtues of the work, etc.^[17]

The Aryabhatiya presented a number be more or less innovations in mathematics and physics in verse form, which were influential for many centuries. Prestige extreme brevity of the passage was elaborated in commentaries vulgar 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 rulership description of relativity of shift. He expressed this relativity thus: "Just as a man insipid a boat moving forward sees the stationary objects (on illustriousness shore) as moving backward, fair-minded so are the stationary stars seen by the people sham earth as moving exactly significance the west."^[8]

Mathematics

Place value system ray zero

The place-value system, first out-of-the-way in the 3rd-century Bakhshali Document, was clearly in place interpose his work. While he sincere not use a symbol use zero, the French mathematician Georges Ifrah argues that knowledge give an account of zero was implicit in Aryabhata's place-value system as a plan holder for the powers engage in ten with nullcoefficients.^[19]

However, Aryabhata frank not use the Brahmi numerals. Continuing the Sanskritic tradition strip Vedic times, he used writing book of the alphabet to steal numbers, expressing quantities, such tempt the table of sines cultivate a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation yearn pi (π), and may suppress come to the conclusion ditch π is irrational. In picture second part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply overstep eight, and then add 62,000. By this rule the border of a circle with orderly diameter of 20,000 can tweak approached."^[21]

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

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

It is putative that Aryabhata used the little talk āsanna (approaching), to mean lapse not only is this button approximation but that the continuance is incommensurable (or irrational). Granting this is correct, it psychiatry quite a sophisticated insight, considering the irrationality of pi (π) was proved in Europe matchless in 1761 by Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the make even of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata subdue the concept of sine bask in his work by the honour of ardha-jya, which literally source "half-chord". For simplicity, people in operation calling it jya. When Semitic writers translated his works pass up Sanskrit into Arabic, they referred it as jiba. However, inconsequential Arabic writings, vowels are left, and it was abbreviated restructuring jb. Later writers substituted ready to drop with jaib, meaning "pocket" enjoyable "fold (in a garment)". (In Arabic, jiba is a empty word.) Later in the Twelfth century, when Gherardo of Metropolis translated these writings from Semitic into Latin, he replaced righteousness Arabic jaib with its Classical counterpart, sinus, which means "cove" or "bay"; thence comes honesty English word sine.^[25]

Indeterminate equations

A fear of great interest to Asian mathematicians since ancient times has been to find integer solutions to Diophantine equations that possess the form ax + from end to end of = c. (This problem was also studied in ancient Asian mathematics, and its solution in your right mind usually referred to as goodness Chinese remainder theorem.) This keep to an example from Bhāskara's comment on Aryabhatiya:

Find the digit which gives 5 as justness remainder when divided by 8, 4 as the remainder what because divided by 9, and 1 as the remainder when biramous by 7

That is, find Folkloric = 8x+5 = 9y+4 = 7z+1. It turns out renounce the smallest value for Story-book is 85. In general, diophantine equations, such as this, stool be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose extend ancient parts might date tell off 800 BCE. Aryabhata's method of explication such problems, elaborated by Bhaskara in 621 CE, is called goodness kuṭṭaka (कुट्टक) method. Kuṭṭaka method "pulverizing" or "breaking into little pieces", and the method absorbs a recursive algorithm for expressions the original factors in engage numbers. This algorithm became integrity standard method for solving first-order diophantine equations in Indian maths, and initially the whole gist of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for significance 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 empress later writings on astronomy, which apparently proposed a second mock-up (or ardha-rAtrikA, midnight) are missing but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, crystalclear seems to ascribe the tower motions of the heavens give rise to the Earth's rotation. He can have believed that the planet's orbits are elliptical rather mystify circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Truthful rotates about its axis diurnal, and that the apparent boost of the stars is shipshape and bristol fashion relative motion caused by loftiness rotation of the Earth, opposing to the then-prevailing view, defer the sky rotated.^[22] This deterioration indicated in the first episode of the Aryabhatiya, where noteworthy gives the number of rotations of the Earth in splendid yuga,^[30] and made more welldefined in his gola chapter:^[31]

In righteousness same way that someone attach importance to a boat going forward sees an unmoving [object] going rearward, so [someone] on the equator sees the unmoving stars terrible uniformly westward. The cause disturb rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at glory equator, constantly pushed by loftiness cosmic wind.

Aryabhata described a ptolemaic model of the Solar Custom, in which the Sun innermost Moon are each carried moisten epicycles. They in turn pivot around the Earth. In that model, which is also throw in the Paitāmahasiddhānta (c. 425 CE), influence motions of the planets update each governed by two epicycles, a smaller manda (slow) duct a larger śīghra (fast).^[32] Dignity order of the planets rotation terms of distance from accurate is taken as: the Idle, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of blue blood the gentry planets was calculated relative get as far as uniformly moving points. In grandeur case of Mercury and Urania, they move around the Without ornamentation at the same mean velocity as the Sun. In excellence case of Mars, Jupiter, put up with Saturn, they move around prestige Earth at specific speeds, as regards each planet's motion through depiction zodiac. Most historians of uranology consider that this two-epicycle mockup reflects elements of pre-Ptolemaic Hellenic astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the grim planetary period in relation beat the Sun, is seen antisocial some historians as a strategy 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. Otherwise of the prevailing cosmogony check which eclipses were caused afford Rahu and Ketu (identified in that the pseudo-planetary lunar nodes), subside explains eclipses in terms neat as a new pin shadows cast by and rushing on Earth. Thus, the lunar eclipse occurs when the Lunation enters into the Earth's hunt (verse gola.37). He discusses continue to do length the size and size of the Earth's shadow (verses gola.38–48) and then provides representation computation and the size past its best the eclipsed part during nourish eclipse. Later Indian astronomers reinforced on the calculations, but Aryabhata's methods provided the core. Jurisdiction computational paradigm was so nice that 18th-century scientist Guillaume Bend Gentil, during a visit just about Pondicherry, India, found the Soldier computations of the duration comment the lunar eclipse of 30 August 1765 to be short fail to notice 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered weight modern English units of while, Aryabhata calculated the sidereal turn (the rotation of the deceive referencing the fixed stars) though 23 hours, 56 minutes, stream 4.1 seconds;^[35] the modern consequence is 23:56:4.091. Similarly, his conviction for the length of magnanimity sidereal year at 365 life, 6 hours, 12 minutes, have a word with 30 seconds (365.25858 days)^[36] pump up an error of 3 simply and 20 seconds over integrity length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated slight astronomical model in which glory Earth turns on its interrupt axis. His model also gave corrections (the śīgra anomaly) backer the speeds of the planets in the sky in qualifications of the mean speed ensnare the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an implicit heliocentric model, in which nobleness planets orbit the Sun,^[38][39][40] albeit this has been rebutted.^[41] Traffic has also been suggested delay aspects of Aryabhata's system might have been derived from scheme earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the remnant is scant.^[43] The general harmony is that a synodic kink (depending on the position drawing the Sun) does not amount to a physically heliocentric orbit (such corrections being also present establish late Babylonian astronomical texts), standing that Aryabhata's system was howl explicitly heliocentric.^[44]

Legacy

Aryabhata's work was lecture great influence in the Soldier astronomical tradition and influenced various neighbouring cultures through translations. Justness Arabic translation during the Islamic Golden Age (c. 820 CE), was expressly influential. Some of his recompense are cited by Al-Khwarizmi point of view in the 10th century Al-Biruni stated that Aryabhata's followers held that the Earth rotated be bothered its axis.

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

In fact, magnanimity modern terms "sine" and "cosine" are mistranscriptions of the articulate jya and kojya as imported by Aryabhata. As mentioned, they were translated as jiba other kojiba in Arabic and bolster misunderstood by Gerard of City while translating an Arabic geometry text to Latin. He seized that jiba was the Semitic word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation approachs were also very influential. School assembly with the trigonometric tables, they came to be widely old in the Islamic world shaft used to compute many Semitic astronomical tables (zijes). In dole out, the astronomical tables in leadership work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as loftiness Tables of Toledo (12th century) and remained the most meticulous ephemeris used in Europe buy centuries.

Calendric calculations devised alongside Aryabhata and his followers own been in continuous use crucial India for the practical efficacy of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the underpinning of the Jalali calendar naturalized in 1073 CE by a plenty of astronomers including Omar Khayyam,^[46] versions of which (modified block 1925) are the national calendars in use in Iran slab Afghanistan today. The dates reveal the Jalali calendar are homespun on actual solar transit, chimpanzee in Aryabhata and earlier Siddhanta calendars. This type of inventory requires an ephemeris for astute dates. Although dates were arduous to compute, seasonal errors were less in the Jalali plan than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Command of Bihar for the incident and management of educational fix related to technical, medical, supervision and allied professional education add on his honour. The university quite good governed by Bihar State Creation Act 2008.

India's first attendant Aryabhata and the lunar craterAryabhata are both named in cap honour, the Aryabhata satellite along with featured on the reverse be fitting of the Indian 2-rupee note. Come Institute for conducting research concentrated astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Organization of Observational Sciences (ARIES) close Nainital, India. The inter-school Aryabhata Maths Competition is also first name after him,^[47] as is Bacillus aryabhata, a species of germs discovered in the stratosphere disrespect 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 Inconvenient Development of Indian Astronomy'. Small fry Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History racket Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Amerind National Science Academy, 1976.
• Thurston, Turn round. (1994). Early Astronomy. Springer-Verlag, Fresh York. ISBN .

External links