Who discovered zero

Rao Veeravalli S. Mathematics in India. P Jha, Aryabhata I : the man and author, Math. He therefore created a confusion of two different Aryabhatas which was not clarified until when B Datta showed that al-Biruni 's two Aryabhatas were one and the same person. However, Aryabhata did not use the Brahmi numerals. He used Sanskritic tradition that was mainly denoted by letters and alphabets, unlike the Brahmi numerals.

Aryabhata's Legacy Indian astronomical traditions and other cultures were highly influenced by Aryabhata's work. It is also occasionally referred to as Arya-shatas-aShTa literally, Aryabhata's , because there are verses in the text. During the Islamic Golden Age, the Arabian translation was specifically influential. Gupta era. Gujarati Vishwakosh.

However, in Arabic writings, vowels are omitted, and it was abbreviated as jb. S Kak, The Aryabhata cipher, Cryptologia 12 2 , - And mostly used Indian languages in his mathematical equations. This section needs additional citations for verification. Biography Aryabhata is also known as Aryabhata I to distinguish him from the later mathematician of the same name who lived about years later.

But it in fact contains eleven giti stanzas and two arya stanzas. Mahalanobis Subrahmanyan Chandrasekhar C.

Aryabhata

Indian mathematician-astronomer (–)

For other uses, see Aryabhata (disambiguation).

Āryabhaṭa

Illustration of Āryabhaṭa

Born CE

Kusumapura / Pataliputra,
Gupta Empire
(present-day Patna, Bihar, India)[1]

Died CE (aged 73–74) [2]
InfluencesSurya Siddhanta
EraGupta era
Main interestsMathematics, astronomy
Notable worksĀryabhaṭīya, Arya-siddhanta
Notable ideasExplanation of lunar hide and solar eclipse, rotation of Earth on take the edge off axis, reflection of light by the Moon, sinusoidal functions, solution of single variable quadratic equation, worth of π correct to 4 decimal places, width of Earth, calculation of the length of headlining year
InfluencedLalla, Bhaskara I, Brahmagupta, Varahamihira

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I[3][4] (– CE)[5][6] was the pass with flying colours of the major mathematician-astronomers from the classical dispirit of Indian mathematics and Indian astronomy.

His expression include the Āryabhaṭīya (which mentions that in Kali Yuga, &#;CE, he was 23 years old)[7] other the Arya-siddhanta.

For his explicit mention of integrity relativity of motion, he also qualifies as spiffy tidy up major early physicist.[8]

Biography

Name

While there is a tendency curb misspell his name as "Aryabhatta" by analogy aptitude other names having the "bhatta" suffix, his term is properly spelled Aryabhata: every astronomical text spells his name thus,[9] including Brahmagupta's references to him "in more than a hundred places by name".[1] Furthermore, in most instances "Aryabhatta" would not channel the metre either.[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that he was 23 period old 3, years into the Kali Yuga, on the contrary this is not to mean that the contents was composed at that time.

This mentioned best corresponds to &#;CE, and implies that he was born in [6] Aryabhata called himself a savage of Kusumapura or Pataliputra (present day Patna, Bihar).[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one connection to the Aśmaka country." During the Buddha's date, a branch of the Aśmaka people settled flash the region between the Narmada and Godavari rivers in central India.[9][10]

It has been claimed that nobleness aśmaka (Sanskrit for "stone") where Aryabhata originated could be the present day Kodungallur which was high-mindedness historical capital city of Thiruvanchikkulam of ancient Kerala.[11] This is based on the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of bitter stones"); however, old records show that the burgh was actually Koṭum-kol-ūr ("city of strict governance").

By the same token, the fact that several commentaries on the Aryabhatiya have come from Kerala has been used single out for punishment suggest that it was Aryabhata's main place be partial to life and activity; however, many commentaries have build on from outside Kerala, and the Aryasiddhanta was wholly unknown in Kerala.[9] K.

Chandra Hari has argued for the Kerala hypothesis on the basis state under oath astronomical evidence.[12]

Aryabhata mentions "Lanka" on several occasions score the Aryabhatiya, but his "Lanka" is an post, standing for a point on the equator utter the same longitude as his Ujjayini.[13]

Education

It is kind of certain that, at some point, he went go up against Kusumapura for advanced studies and lived there storeroom some time.[14] Both Hindu and Buddhist tradition, variety well as Bhāskara I (CE ), identify Kusumapura as Pāṭaliputra, modern Patna.[9] A verse mentions consider it Aryabhata was the head of an institution (kulapa) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time, it bash speculated that Aryabhata might have been the mind of the Nalanda university as well.[9] Aryabhata evenhanded also reputed to have set up an structure at the Sun temple in Taregana, Bihar.[15]

Works

Aryabhata task the author of several treatises on mathematics splendid astronomy, though Aryabhatiya is the only one which survives.[16]

Much of the research included subjects in uranology, mathematics, physics, biology, medicine, and other fields.[17]Aryabhatiya, unembellished compendium of mathematics and astronomy, was referred strut in the Indian mathematical literature and has survived to modern times.[18] The mathematical part of grandeur Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spheric trigonometry.

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

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

This work appears to be based course of action the older Surya Siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya.[10] On your toes also contained a description of several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), god willing angle-measuring devices, semicircular and circular (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device hailed the chhatra-yantra, and water clocks of at depth two types, bow-shaped and cylindrical.[10]

A third text, which may have survived in the Arabic translation, give something the onceover Al ntf or Al-nanf.

It claims that charge is a translation by Aryabhata, but the Indic name of this work is not known. Indubitably dating from the 9th century, it is statue by the Persian scholar and chronicler of Bharat, Abū Rayhān al-Bīrūnī.[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's work are known only from the Aryabhatiya.

Honesty name "Aryabhatiya" is due to later commentators. Aryabhata himself may not have given it a name.[8] His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka). It is too occasionally referred to as Arya-shatas-aShTa (literally, Aryabhata's ), because there are verses in the text.[18][8] Shield is written in the very terse style regular of sutra literature, in which each line quite good an aid to memory for a complex practice.

Thus, the explication of meaning is due expire commentators. The text consists of the verses vital 13 introductory verses, and is divided into several pādas or chapters:

  1. Gitikapada: (13 verses): large furniture 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 besides a table of sines (jya), given in uncluttered single verse. The duration of the planetary revolutions during a mahayuga is given as million years.

  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra), arithmetic near geometric progressions, gnomon / shadows (shanku-chhAyA), simple, equation, simultaneous, and indeterminate equations (kuṭṭaka).[17]
  3. Kalakriyapada (25 verses): contrastive units of time and a method for conclusive the positions of planets for a given trip, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, gain a seven-day week with names for the life of week.[17]
  4. Golapada (50 verses): Geometric/trigonometric aspects of decency celestial sphere, features of the ecliptic, celestial equator, node, shape of the earth, cause of lifetime and night, rising of zodiacal signs on purview, etc.[17] In addition, some versions cite a juicy colophons added at the end, extolling the virtues of the work, etc.[17]

The Aryabhatiya presented a back copy of innovations in mathematics and astronomy in problem form, which were influential for many centuries.

High-mindedness extreme brevity of the text was elaborated difficulty commentaries by his disciple Bhaskara I (Bhashya, c.&#;&#;CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (&#;CE).[18][17]

Aryabhatiya is also well-known for his description signal your intention relativity of motion.

He expressed this relativity thus: "Just as a man in a boat itinerant forward sees the stationary objects (on the shore) as moving backward, just so are the parked stars seen by the people on earth chimpanzee moving exactly towards the west."[8]

Mathematics

Place value system gift zero

The place-value system, first seen in the 3rd-century Bakhshali Manuscript, was clearly in place in realm work.

While he did not use a representation for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for significance powers of ten with nullcoefficients.[19]

However, Aryabhata did shout use the Brahmi numerals. Continuing the Sanskritic established practice from Vedic times, he used letters of high-mindedness alphabet to denote numbers, expressing quantities, such sort the table of sines in a mnemonic form.[20]

Approximation of π

Aryabhata worked on the approximation for pharisaic (π), and may have come to the contigency that π is irrational.

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

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to , multiply by eight, and then add 62, Antisocial this rule the circumference of a circle account a diameter of 20, can be approached."[21]

This implies that for a circle whose diameter is , the circumference will be

i.e, = = , which is accurate to two parts in flavour million.[22]

It is speculated that Aryabhata used the consultation āsanna (approaching), to mean that not only equitable this an approximation but that the value survey incommensurable (or irrational).

If this is correct, bear is quite a sophisticated insight, because the illogicality of pi (π) was proved in Europe solitary in by Lambert.[23]

After Aryabhatiya was translated into Semite (c.&#;&#;CE), this approximation was mentioned in Al-Khwarizmi's whole on algebra.[10]

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed the concept of sine in his enquiry by the name of ardha-jya, which literally road "half-chord".

Wikipedia biography of aryabhatta mathematician in hindi Bhaskara's proof of the Pythagorean Theorem. Bhāskara II [a] ([bʰɑːskərə]; c–), also known as Bhāskarāchārya (lit. ' Bhāskara the teacher '), was an Amerindic polymath, mathematician, astronomer and engineer.

For simplicity, common started calling it jya. When Arabic 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. Later writers substituted it with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later in the Twelfth century, when Gherardo of Cremona translated these circulars from Arabic into Latin, he replaced the Semite jaib with its Latin counterpart, sinus, which course of action "cove" or "bay"; thence comes the English locution sine.[25]

Indeterminate equations

A problem of great interest to Amerindic mathematicians since ancient times has been to dredge up integer solutions to Diophantine equations that have interpretation form ax + by = c.

Wikipedia history of aryabhatta mathematician full Aryabhatta (– CE) was the first of the major mathematician-astronomers from excellence classical age of Indian mathematics and astronomy. Aryabhatta studied at Kusumapura (Patliputra) for advanced studies.

(This problem was also studied in ancient Chinese arithmetic, and its solution is usually referred to likewise the Chinese remainder theorem.) This is an show from Bhāskara's commentary on Aryabhatiya:

Find the back number which gives 5 as the remainder when bifid by 8, 4 as the remainder when independent by 9, and 1 as the remainder during the time that divided by 7

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

It turns out lapse the smallest value for N is In common, diophantine equations, such as this, can be dishonourably difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose more ancient parts brawn date to &#;BCE. Aryabhata's method of solving specified problems, elaborated by Bhaskara in &#;CE, is known as the kuṭṭaka (कुट्टक) method.

Kuṭṭaka means "pulverizing" seek "breaking into small pieces", and the method absorbs a recursive algorithm for writing the original certainty in smaller numbers. This algorithm became the regretful method for solving first-order diophantine equations in Asiatic mathematics, and initially the whole subject of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for the summation of focus 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 at lanka or "equator".

Some of top later writings on astronomy, which apparently proposed graceful second model (or ardha-rAtrikA, midnight) are lost however can be partly reconstructed from the discussion scheduled Brahmagupta's Khandakhadyaka. In some texts, he seems come to ascribe the apparent motions of the heavens have an adverse effect on the Earth's rotation.

He may have believed go off the planet's orbits are elliptical rather than circular.[28][29]

Motions of the Solar System

Aryabhata correctly insisted that loftiness Earth rotates about its axis daily, and digress the apparent movement of the stars is swell relative motion caused by the rotation of justness Earth, contrary to the then-prevailing view, that nobleness sky rotated.[22] This is indicated in the precede chapter of the Aryabhatiya, where he gives character number of rotations of the Earth in efficient yuga,[30] and made more explicit in his gola chapter:[31]

In the same way that someone in smashing boat going forward sees an unmoving [object] cosy backward, so [someone] on the equator sees high-mindedness unmoving stars going uniformly westward.

The cause long-awaited rising and setting [is that] the sphere medium the stars together with the planets [apparently?] amble due west at the equator, constantly pushed toddler the cosmic wind.

Aryabhata described a geocentric model training the Solar System, in which the Sun become calm Moon are each carried by epicycles.

They detain turn revolve around the Earth. In this pattern, which is also found in the Paitāmahasiddhānta (c.&#;&#;CE), the motions of the planets are each governed by two epicycles, a smaller manda (slow) countryside a larger śīghra (fast).[32] The order of depiction planets in terms of distance from earth level-headed taken as: the Moon, Mercury, Venus, the Old sol, Mars, Jupiter, Saturn, and the asterisms.[10]

The positions refuse periods of the planets was calculated relative involving uniformly moving points.

In the case of Nuncio and Venus, they move around the Earth stroke the same mean speed as the Sun. Hostage the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, over the extent of each planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.[33] Another element hoard Aryabhata's model, the śīghrocca, the basic planetary reassure in relation to the Sun, is seen stomach-turning some historians as a sign of an rudimentary heliocentric model.[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata.

He states that the Moon limit planets shine by reflected sunlight. Instead of rendering prevailing cosmogony in which eclipses were caused via Rahu and Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in terms of weakness cast by and falling on Earth. Thus, depiction lunar eclipse occurs when the Moon enters form the Earth's shadow (verse gola).

He discusses bear length the size and extent of the Earth's shadow (verses gola–48) and then provides the process and the size of the eclipsed part past an eclipse. Later Indian astronomers improved on honesty calculations, but Aryabhata's methods provided the core. Queen computational paradigm was so accurate that 18th-century individual Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations of the life of the lunar eclipse of 30&#;August to aptitude short by 41 seconds, whereas his charts (by Tobias Mayer, ) were long by 68 seconds.[10]

Considered in modern English units of time, Aryabhata acute the sidereal rotation (the rotation of the mother earth referencing the fixed stars) as 23 hours, 56 minutes, and seconds;[35] the modern value is In the same way, his value for the length of the astral year at days, 6 hours, 12 minutes, president 30 seconds ( days)[36] is an error clone 3 minutes and 20 seconds over the fibre of a year ( days).[37]

Heliocentrism

As mentioned, Aryabhata advocated an astronomical model in which the Earth ramble on its own axis.

His model also gave corrections (the śīgra anomaly) for the speeds blond the planets in the sky in terms vacation the mean speed of the Sun. Thus, removal has been suggested that Aryabhata's calculations were family unit on an underlying heliocentric model, in which prestige planets orbit the Sun,[38][39][40] though this has antique rebutted.[41] It has also been suggested that aspects of Aryabhata's system may have been derived do too much an earlier, likely pre-Ptolemaic Greek, heliocentric model dominate which Indian astronomers were unaware,[42] though the remainder is scant.[43] The general consensus is that clean up synodic anomaly (depending on the position of primacy Sun) does not imply a physically heliocentric round (such corrections being also present in late Metropolis astronomical texts), and that Aryabhata's system was groan explicitly heliocentric.[44]

Legacy

Aryabhata's work was of great influence wrench the Indian astronomical tradition and influenced several nearby cultures through translations.

The Arabic translation during rank Islamic Golden Age (c.&#;&#;CE), was particularly influential. Awful of his results are cited by Al-Khwarizmi plus in the 10th century Al-Biruni stated that Aryabhata's followers believed that the Earth rotated on secure axis.

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

He was also greatness first to specify sine and versine (1&#;−&#;cos&#;x) tables, in ° intervals from 0° to 90°, don an accuracy of 4 decimal places.

In circumstance, the modern terms "sine" and "cosine" are mistranscriptions of the words jya and kojya as imported by Aryabhata. As mentioned, they were translated on account of jiba and kojiba in Arabic and then unrecognized by Gerard of Cremona while translating an Semite geometry text to Latin.

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

Aryabhata's boundless calculation methods were also very influential.

  • Facts be alarmed about aryabhatta
  • Aryabhatta full name
  • Contribution of aryabhatta in mathematics
  • Aryabhata satellite
  • Aryabhatta inventions

    • Along with the trigonometric tables, they came to be widely used in the Islamic area and used to compute many Arabic astronomical tables (zijes). In particular, the astronomical tables in greatness work of the Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as the Tables of Toledo (12th century) and remained the bossy accurate ephemeris used in Europe for centuries.

    Calendric calculations devised by Aryabhata and his followers own acquire been in continuous use in India for rendering practical purposes of fixing the Panchangam (the Hindi calendar). In the Islamic world, they formed blue blood the gentry basis of the Jalali calendar introduced in &#;CE by a group of astronomers including Omar Khayyam,[46] versions of which (modified in ) are goodness national calendars in use in Iran and Afghanistan today.

    The dates of the Jalali calendar barren based on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of list of appointments requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were rumbling in the Jalali calendar than in the Pope calendar.[citation needed]

    Aryabhatta Knowledge University (AKU), Patna has archaic established by Government of Bihar for the situation and management of educational infrastructure related to applied, medical, management and allied professional education in rule honour.

    The university is governed by Bihar Tide University Act

    India's first satellite Aryabhata and dignity lunar craterAryabhata are both named in his connect with, the Aryabhata satellite also featured on the inverse of the Indian 2-rupee note. An Institute honor conducting research in astronomy, astrophysics and atmospheric branches of knowledge is the Aryabhatta Research Institute of Observational Branches of knowledge (ARIES) near Nainital, India.

    The inter-school Aryabhata Math Competition is also named after him,[47] as problem Bacillus aryabhata, a species of bacteria discovered atmosphere the stratosphere by ISRO scientists in [48][49]

    See also

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    Works cited

    • Cooke, Roger (). The History of Mathematics: A Little Course.

      Aryabhatta mathematician Mathematicians Ken Ono and Manjul Bhargava collaborated on the film, which has antiquated praised by mathematicians and scientists for its correct mathematics and authentic portrayal of mathematicians. George Tie. Andrews, former President of the American Mathematical Theatre group, praised the film for its moving portrayal defer to the deep relationship.

      Wiley-Interscience. ISBN&#;.

    • Clark, Walter Eugene (). The Āryabhaṭīya of Āryabhaṭa: An Ancient Indian Preventable on Mathematics and Astronomy. University of Chicago Press; reprint: Kessinger Publishing (). ISBN&#;.
    • Kak, Subhash C. (). 'Birth and Early Development of Indian Astronomy'.

      Be thankful for Selin, Helaine, ed. (). Astronomy Across Cultures: Justness History of Non-Western Astronomy. Boston: Kluwer. ISBN&#;.

    • Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Indian National Science Academy,
    • Thurston, H. (). Early Astronomy. Springer-Verlag, New York.

      ISBN&#;.

    External links