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Encyclopedia > Aryabhata
Statue of Aryabhatta on the grounds of IUCAA, Pune.
Statue of Aryabhatta on the grounds of IUCAA, Pune.

Āryabhaa (Devanāgarī: आर्यभट) (b. 476 AD – 550) is the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Aryabhatiya (499) and Arya-Siddhanta. Aryabhata, Indian astronomer, lived 476 – 550, author of the Aryabhatiya. ... Image File history File links Download high-resolution version (951x1361, 193 KB) [edit] Summary This image of a public statue in IUCAA Pune was photographed in May 2006 by myself, and I release all rights. ... Image File history File links Download high-resolution version (951x1361, 193 KB) [edit] Summary This image of a public statue in IUCAA Pune was photographed in May 2006 by myself, and I release all rights. ... The Inter-University Centre for Astronomy and Astrophysics (IUCAA) is an autonomus institution set up by the University Grants Commission to promote nucleation and growth of active groups in astronomy and astrophysics in Indian universities. ... , Pune (IPA: , Marathi: पुणे) is a city located in the western Indian state of Maharashtra. ... () is an abugida script used to write several Indo-Aryan languages, including Sanskrit, Hindi, Gujarati,Marathi, Sindhi, Bihari, Bhili, Marwari, Konkani, Bhojpuri, Pahari (Garhwali and Kumaoni), Santhali, Nepali, Newari, Tharu and sometimes Kashmiri and Romani. ... Events August - The usurper Basiliscus is deposed and Zeno is restored as Eastern Roman Emperor. ... Events By Place Byzantine Empire Silk reaches Constantinople (approximate date). ... This article is under construction. ... The astronomy and the astrology of Ancient India (Jyotisha) is based upon sidereal calculations. ... Ä€ryabhatÄ«ya, an astronomical treastise, is the Magnum Opus and only extant work of the 5th century Indian Mathematician, Aryabhatta. ... Events March 1 - Pope Symmachus makes Antipope Laurentius bishop of Nocera in Campania. ... Siddhanta, a Sanskrit term, roughly translates as the Doctrine or This term Siddhanta is an established theological term within Hinduism which denotes a specific line of theological development within a Hindu religious traditon. ...

Contents

Biography

Aryabhatta was born in the region lying between Narmada and Godavari, which was known as Ashmaka,and is now identified with Maharashtra, though early Buddhist texts describe Ashmaka as being further south, dakShiNApath or the Deccan, while other texts describe the Ashmakas as having fought Alexander, which would put them further north.[1] Other traditions in India claim that he was from Kerala and that he travelled to the North, or that he was a Maga Brahmin from Gujarat. , Maharashtra (Marathi: महाराष्ट्र , IPA  , translation: Great Nation) is Indias third largest state in area and second largest in population after Uttar Pradesh. ... The Deccan Plateau is a vast plateau in India, encompassing most of Central and Southern India. ... Look up Alexander in Wiktionary, the free dictionary. ... , Kerala ( ; Malayalam: കേരളം; ) is a state on the Malabar Coast of southwestern India. ... Bhojaka is a class of Brahmin priests in Western India. ... This article is for the Indian state. ...


However, it is fairly certain that at some point, he went to Kusumapura for higher studies, and that he lived here for some time.[2] Bhāskara I (AD 629) identifies Kusumapura as Pataliputra (modern Patna). He lived there in the dying years of the Gupta empire, the time which is known as the golden age of India, when it was already under Hun attack in the Northeast, during the reign of Buddhagupta and some of the smaller kings before Vishnugupta. For other uses, see Patna (disambiguation). ... Bhāskara, or Bhāskara I, (c. ... Events Jerusalem reconquered by Byzantine Empire from the Persian Empire (September). ... Patna is the capital of the state of Bihar, in north-eastern India. ... The Gupta Empire under Chandragupta II (ruled 375-415) The Gupta Empire was one of the largest political and military empires in the world. ... Many historians consider the Huns (meaning person in Mongolian language) the first Mongolian and Turkic people mentioned in European history. ... People named Vishnugupta: Vishnugupta. ...


His first name “Arya” is a term used for respect, such as "Sri", whereas Bhatta is a typical north Indian name -- found today usually among the “Bania” (or trader) community in Bihar. For other uses, see Bihar (disambiguation). ...


Modern historians say that Aryabhata was born in 478A.D. Their calculations are based on the following sloka in Aryabhatiya. Shastyabdeenam Shadbhiryada
Vyatheethastrayashcha yugapadah
Adhika vimsathirabdaasthedeha
Mamajanmanotheethah

Shadbhih has been taken as shashti by some historians. Then the poem means that Aryabhata was twenty years old in 3600(60 times 60) Kali Era which started in 3102B.C. This calculation will give the year of Aryabhata's birth as 478 A.D. This is wrong for the following reasons.
1.The usage of the word shashti in the above poem is grammatically wrong in Sanskrit.
2.In 478A.D. Kali era was not in vogue. At that time Vikrama and Salivahana eras were widely used. The correct word in the poem is Shadbhih. Aryabhata was 20 years old in 360(6 times 60)Kali Era. This gives Aryabhata's year of birth as 2762B.C., long before the heliocentric theory was even thought of in the West.


Works

Aryabhata is the author of several treatises on mathematics and astronomy, some of which are lost. His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature, and has survived to modern times.


The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary Varahamihira, as well as through later mathematicians and commentators including Brahmagupta and Bhaskara I. This work appears to be based on the older Surya Siddhanta, and uses the midnight-day-reckoning, as opposed to sunrise in Aryabhatiya. This also contained a description of several astronomical instruments, the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semi-circle and circle shaped (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device called chhatra-yantra, and water clocks of at least two types, bow-shaped and cylindrical.[1] Varahamihira (505 – 587) was an Indian astronomer, mathematician, and astrologer born in Ujjain. ... Brahmagupta (ब्रह्मगुप्त) ( ) (589–668) was an Indian mathematician and astronomer. ... Bhāskara, or Bhāskara I, (c. ... This article aims at providing a thorough (but not verse by verse) exposition of most important topics of and problems related to Surya Siddhanta and its comparison with ancient and modern astronomy, together with its use in astrology. ... The cantilever spar of this cable-stay bridge, the Sundial Bridge at Turtle Bay, forms the gnomon of a large garden sundial The gnomon is the part of a sundial that casts the shadow. ... A water clock or clepsydra is a device for measuring time by letting water regularly flow out of a container usually by a tiny aperture. ...


A third text that may have survived in Arabic translation is the Al ntf or Al-nanf, which claims to be a translation of Aryabhata, but the Sanskrit name of this work is not known. Probably dating from the ninth c., it is mentioned by the Persian scholar and chronicler of India, Abū Rayhān al-Bīrūnī.[1] Arabic redirects here. ... (September 15, 973 in Kath, Khwarezm – December 13, 1048 in Ghazni) was a Persian[1][2][3] Muslim polymath[4] of the 11th century, whose experiments and discoveries were as significant and diverse as those of Leonardo da Vinci or Galileo, five hundred years before the Renaissance; al-Biruni was...


Aryabhatiya

Direct details of Aryabhata's work are therefore known only from the Aryabhatiya. The name Aryabhatiya is due to later commentators, Aryabhata himself may not have given it a name; it is referred by his disciple Bhaskara I as Ashmakatantra or the treatise from the Ashmaka. It is also occasionally referred to as Arya-shatas-aShTa, lit., Aryabhata's 108, which is the number of verses in the text. It is written in the very terse style typical of the sutra literature, where each line is an aid to memory for a complex system. Thus, the explication of meaning is due to commentators. The entire text consists of 108 verses, plus an introductory 13, the whole being divided into four pAdas or chapters: Bhāskara, or Bhāskara I, (c. ... Sūtra (sex) (Sanskrit) or Sutta (Pāli) literally means a rope or thread that holds things together, and more metaphorically refers to an aphorism (or line, rule, formula), or a collection of such aphorisms in the form of a manual. ...

  1. gitikApAda: (13 verses) large units of time - kalpa, manvantra, yuga, which present a cosmology that differs from earlier texts such as Lagadha's Vedanga Jyotisha(ca. 1st c. BC). Also includes the table of sines (jya), given in a single verse. For the planetary revolutions during a mahayuga, the number of 4.32mn years is given.
  2. gaNitapAda (33 verses), covering mensuration (kShetra vyAvahAra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), simple, quadratic, simultaneous, and indeterminate equations (kuTTaka)
  3. kAlakriyApAda (25 verses) : different units of time and method of determination of positions of planets for a given day. Calculations concerning the intercalary month (adhikamAsa), kShaya-tithis. Presents a seven-day week, with names for days of week.
  4. golapAda (50 verses): Geometric/trigonometric aspects of the celestial sphere, features of the ecliptic, celestial equator, node, shape of the earth, cause of day and night, rising of zodiacal signs on horizon etc.

In addition, some versions cite a few colophons added at the end, extolling the virtues of the work, etc. The Vedanga Jyotisha, is an Indian text on Jyotisha (Hindu astronomy), redacted by Lagadha (लगध). The text is foundational to the Jyotisha discipline of Vedanga, and is dated to the final centuries BCE.[1] The text describes rules for tracking the motions of the sun and the moon. ... The cantilever spar of this cable-stay bridge, the Sundial Bridge at Turtle Bay, forms the gnomon of a large garden sundial The gnomon is the part of a sundial that casts the shadow. ... In mathematics, a quadratic equation is a polynomial equation of the second degree. ... In Mathematics simultaneous equations are a set of equations containing multiple variables. ... In mathematics, a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. ... Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine and cosine. ... The celestial sphere is divided by the celestial equator. ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ... The celestial equator is a great circle on the imaginary celestial sphere, which could be constructed by inflating the Earths equator until it intersects with said sphere. ... The symbols used in Western Astrology to represent the Astrological signs Both Western and Vedic astrology employ a zodiac which divides the ecliptic into twelve Astrological signs of equal length. ... In publishing, a colophon describes details of the production of a book. ...


The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya, ca. 600) and by Nilakantha Somayaji in his Aryabhatiya Bhasya, (1465). Bhāskara, or Bhāskara I, (c. ... Nilakantha Somayaji (नीलकण्ठ सोमयाजि) (1444-1544), from Kerala, was a major mathematician and astronomer. ...


Mathematics

Place Value system and zero

The number place-value system, first seen in the 3rd century Bakhshali Manuscript was clearly in place in his work.[3] ; he certainly did not use the symbol, but the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients[4]. The place value system is a method of writing numbers with a base 10 numerical system. ... The Bakhshali Manuscript is a mathematical manuscript written on birch bark which was found near the village of Bakhshali in what is now Pakistan in 1881. ... George Ifrah (1947-) was a professor of mathematics, and a historian of mathematics, especially numerals. ...


However, Aryabhata did not use the brahmi numerals; continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities (such as the table of sines) in a mnemonic form[5]. Sanskrit ( , for short ) is a classical language of India, a liturgical language of Hinduism, Buddhism, Sikhism, and Jainism, and one of the 23 official languages of India. ... Map of early Iron Age Vedic India after Witzel (1989). ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... For other uses, see Mnemonic (disambiguation). ...


Pi as Irrational

Aryabhata worked on the approximation for Pi (π), and may have realized that π is irrational. In the second part of the Aryabhatiyam (gaitapāda 10), he writes:[citation needed] When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ...

chaturadhikam śatamaśaguam dvāśaśistathā sahasrāām
Ayutadvayaviśkambhasyāsanno vrîttapariaha.

"Add four to 100, multiply by eight and then add 62,000. By this rule the circumference of a circle of diameter 20,000 can be approached."
Aryabhata interpreted the word āsanna (approaching), appearing just before the last word, as saying that not only that is this an approximation, but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, for the irrationality of pi was proved in Europe only in 1761 by Lambert)[6]. After Aryabhatiya was translated into Arabic (ca. 820 AD) this approximation was mentioned in Al-Khwarizmi's book on algebra[1].

Mensuration and trigonometry

In Ganitapada 6, Aryabhata gives the area of triangle as In philosophy: Irrationality In music: Irrational rhythm In economics: Irrational exuberance In mathematics: Irrational number Proof that e is irrational Quadratic irrational List of integrals of irrational functions See also: rational This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same... Johann Heinrich Lambert Johann Heinrich Lambert (August 26, 1728 – September 25, 1777), was a mathematician, physicist and astronomer. ... Arabic redirects here. ... Soviet postage stamp commemorating the 1200th anniversary of Muhammad al‑Khwarizmi in 1983. ...

tribhujasya phalashariram samadalakoti bhujardhasamvargah

that translates to: for a triangle, the result of a perpendicular with the half-side is the area.[7]

Indeterminate Equations

A problem of great interest to Indian mathematicians since ancient times has been to find integer solutions to equations that have the form ax + b = cy, a topic that has come to be known as diophantine equations. Here is an example from Bhaskara's commentary on Aryabhatiya: : Here is a chronology of the main Indian mathematicians: BC Yajnavalkya, 1800 BC, the author of the altar mathematics of the Shatapatha Brahmana. ... In mathematics, a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. ... Bhaskara (1114-1185), also known as Bhaskara II and Bhaskara Achārya (Bhaskara the teacher), was an Indian mathematician-astronomer. ...

Find the number which gives 5 as the remainder when divided by 8; 4 as the remainder when divided by 9; and 1 as the remainder when divided by 7.

i.e. find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations can be notoriously difficult. Such equations were considered extensively in the ancient Vedic text Sulba Sutras, the more ancient parts of which may date back to 800 BCE. Aryabhata's method of solving such problems, called the kuaka (कूटटक) method. Kuttaka means pulverizing, that is breaking into small pieces, and the method involved a recursive algorithm for writing the original factors in terms of smaller numbers. Today this algorithm, as elaborated by Bhaskara in AD 621, is the standard method for solving first order Diophantine equations, and it is often referred to as the Aryabhata algorithm[8]. The Sulba Sutras or Sulva Sutras are a text of Vedic mathematics. ... (9th century BC - 8th century BC - 7th century BC - other centuries) (800s BC - 790s BC - 780s BC - 770s BC - 760s BC - 750s BC - 740s BC - 730s BC - 720s BC - 710s BC - 700s BC - other decades) (2nd millennium BC - 1st millennium BC - 1st millennium AD) Events Golden age in Armenia Assyria... Events By Place Byzantine Empire Byzantine Emperor Heraclius invades Persia Europe Suinthila succeeds Sisebut as king of the Visigoths. ... Aryabhata algorithm is an algorithm to solve indeterminate Diophantine equations and for residue arithmetic. ...


The diophantine equations are of interest in cryptology, and the RSA Conference, 2006, focused on the kuttaka method and earlier work in the Sulvasutras. Cryptology is an umbrella term for cryptography and cryptanalysis. ... The RSA Conference is a Cryptography-related conference held annually in the San Francisco Bay Area. ... The Shulba Sutras (Sanskrit : string, cord, rope) are sutra texts belonging to the Åšrauta ritual and containing geometry related to fire-altar construction. ...

Astronomy

Aryabhata's system of astronomy was called the audAyaka system (days are reckoned from uday, dawn at lanka, equator). Some of his later writings on astronomy, which apparently proposed a second model (ardha-rAtrikA, midnight), are lost, but can be partly reconstructed from the discussion in Brahmagupta's khanDakhAdyaka. In some texts he seems to ascribe the apparent motions of the heavens to the earth's rotation. Brahmagupta (ब्रह्मगुप्त) ( ) (589–668) was an Indian mathematician and astronomer. ...

Motions of the Solar System

Aryabhata appears to have believed that the earth rotates about its axis. This is made clear in the statement, referring to Lanka , which describes the movement of the stars as a relative motion caused by the rotation of the earth:

Like a man in a boat moving forward sees the stationary objects as moving backward, just so are the stationary stars seen by the people in lankA (i.e. on the equator) as moving exactly towards the West. [achalAni bhAni samapashchimagAni - golapAda.9]

But the next verse describes the motion of the stars and planets as real movements: “The cause of their rising and setting is due to the fact the circle of the asterisms together with the planets driven by the provector wind, constantly moves westwards at Lanka”.


Lanka (lit. Sri Lanka) is here a reference point on the equator, which was taken as the equivalent to the reference meridian for astronomical calculations.


Aryabhata described a geocentric model of the solar system, in which the Sun and Moon are each carried by epicycles which in turn revolve around the Earth. In this model, which is also found in the Paitāmahasiddhānta (ca. AD 425), the motions of the planets are each governed by two epicycles, a smaller manda (slow) epicycle and a larger śīghra (fast) epicycle. [9] The order of the planets in terms of distance from earth are taken as: the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms[1]. The geocentric model (in Greek: geo = earth and centron = centre) of the universe is a paradigm which places the Earth at its center. ... In the Ptolemaic system of astronomy, the epicycle (literally: on the cycle in Greek) was a geometric model to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. ... This article is about Earths moon. ... [[Link titleBold text // ]] This article is about the planet. ... For other uses, see Venus (disambiguation). ... Sol redirects here. ... Adjectives: Martian Atmosphere Surface pressure: 0. ... For other uses, see Jupiter (disambiguation). ... This article is about the planet. ... Asterism has several meanings: In astronomy, it refers to a constellation_like group of stars; see asterism (astronomy) In gemmology, it is an optical phenomenon; see asterism (gemmology) In typography, it refers to a symbol; see asterism (typography) This is a disambiguation page — a navigational aid which lists other pages...


The positions and periods of the planets were calculated relative to uniformly moving points, which in the case of Mercury and Venus, move around the Earth at the same speed as the mean Sun and in the case of Mars, Jupiter, and Saturn move around the Earth at specific speeds representing each planet's motion through the zodiac. Most historians of astronomy consider that this two epicycle model reflects elements of pre-Ptolemaic Greek astronomy.[10] Another element in Aryabhata's model, the śīghrocca, the basic planetary period in relation to the Sun, is seen by some historians as a sign of an underlying heliocentric model.[11] A recreation of the famous Library of Alexandria Greek astronomy is the astronomy of those who spoke Greek in classical antiquity. ... In astronomy, heliocentrism is the theory that the Sun is at the center of the Universe and/or the Solar System. ...

Eclipses

He states that the Moon and planets shine by reflected sunlight. Instead of the prevailing cosmogyny where eclipses were caused by pseudo-planetary nodes Rahu and Ketu, he explains eclipses in terms of shadows cast by and falling on earth. Thus the lunar eclipse occurs when the moon enters into the earth-shadow (verse gola.37), and discusses at length the size and extent of this earth-shadow (verses gola.38-48), and then the computation, and the size of the eclipsed part during eclipses. Subsequent Indian astronomers improved on these calculations, but his methods provided the core. This computational paradigm was so accurate that the 18th century scientist Guillaume le Gentil, during a visit to Pondicherry, found the Indian computations of the duration of the lunar eclipse of 1765-08-30 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.[1]. This article is about Earths moon. ... In Hindu mythology, Rahu is a snake that swallows the sun or the moon causing eclipses. ... In Hindu mythology, Ketu is generally referred to as a shadow planet. ... Guillaume Joseph Hyacinthe Jean-Baptiste Le Gentil de la Galaisière (September 12, 1725 – October 22, 1792) was a French astronomer. ... Time lapse movie of the 3 March 2007 lunar eclipse A lunar eclipse occurs whenever the Moon passes through some portion of the Earth’s shadow. ... Year 1765 (MDCCLXV) was a common year starting on Tuesday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Saturday of the 11-day slower Julian calendar). ... is the 242nd day of the year (243rd in leap years) in the Gregorian calendar. ... 1752 was a leap year starting on Saturday (see link for calendar). ...


Aryabhata's computation of Earth's circumference as 24,835 miles, which was only 0.2% smaller than the actual value of 24,902 miles. This approximation might have improved on the computation by the Greek mathematician Eratosthenes (c.200 BC), whose exact computation is not known in modern units. The circumference is the distance around a closed curve. ... This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman). ... The eastern hemisphere in 200 BC. Antiochus IIIs forces continue their invasion of Coele Syria, defeating the Egyptian general Scopas at Panion near the source of the Jordan River, and thus gaining control of Palestine. ...

Sidereal periods

Considered in modern English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referenced the fixed stars) as 23 hours 56 minutes and 4.1 seconds; the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days 6 hours 12 minutes 30 seconds is an error of 3 minutes 20 seconds over the length of a year. The notion of sidereal time was known in most other astronomical systems of the time, but this computation was likely the most accurate in the period. Solar rotation varies because the sun is composed of a gaseous plasma, and therefore lacks a fixed rotation rate. ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ...

Heliocentrism

Āryabhata claims that the Earth turns on its own axis and some elements of his planetary epicyclic models rotate at the same speed as the motion of the planet around the Sun. This has suggested to some interpreters that Āryabhata's calculations were based on an underlying heliocentric model in which the planets orbit the Sun.[12][13] A detailed rebuttal to this heliocentric interpretation is in a review which describes B. L. van der Waerden's book as "show[ing] a complete misunderstanding of Indian planetary theory [that] is flatly contradicted by every word of Āryabhata's description,"[14] although some concede that Āryabhata's system stems from an earlier heliocentric model of which he was unaware.[15] It has even been claimed that he considered the planet's paths to be elliptical, although no primary evidence for this has been cited.[16] Though Aristarchus of Samos (3rd century BC) and sometimes Heraclides of Pontus (4th century BC) are usually credited with knowing the heliocentric theory, the version of Greek astronomy known in ancient India, Paulisa Siddhanta (possibly by a Paul of Alexandria) makes no reference to a Heliocentric theory. Heliocentric Solar System Heliocentrism (lower panel) in comparison to the geocentric model (upper panel) In astronomy, heliocentrism is the theory that the sun is at the center of the Universe and/or the Solar System. ... Bartel Leendert van der Waerden (February 2, 1903, Amsterdam, Netherlands – January 12, 1996, Zürich, Switzerland) was a Dutch mathematician. ... For other uses, see Ellipse (disambiguation). ... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. ... Heraclides Ponticus (387 - 312 BCE), also known as Heraklides, was a Greek philosopher who lived and died at Heraclea, now Eregli, Turkey. ... A recreation of the famous Library of Alexandria Greek astronomy is the astronomy of those who spoke Greek in classical antiquity. ... The Paulisa Siddhanta (literally, Doctrine of Paul) is an Indian astronomical treatise, based on the works of the Western scholar Paul of Alexandria (c. ... Paulus Alexandrinus was an astrological author from the late Roman Empire. ... This article is about the city in Egypt. ...

Legacy

Aryabhata's work was of great influence in the Indian astronomical tradition, and influenced several neighbouring cultures through translations. The Arabic translation during the Islamic Golden Age (ca. 820), was particularly influential. Some of his results are cited by Al-Khwarizmi, and he is referred to by the 10th century Arabic scholar Al-Biruni, who states that Āryabhata's followers believed the Earth to rotate on its axis. Arabic redirects here. ... During the Islamic Golden Age, usually dated from the 8th century to the 13th century,[1] engineers, scholars and traders of the Islamic world contributed enormously to the arts, agriculture, economics, industry, literature, navigation, philosophy, sciences, and technology, both by preserving and building upon earlier traditions and by adding many... Tahir, the son of a slave, is rewarded with the governorship of Khurasan because he have supported the caliphate. ... Soviet postage stamp commemorating the 1200th anniversary of Muhammad al‑Khwarizmi in 1983. ... A statue of Biruni adorns the southwest entrance of Laleh Park in Tehran. ...


His definitions of sine, as well as cosine (kojya), versine (ukramajya), and inverse sine (otkram jya), influenced the birth of trigonometry. He was also the first to specify sine and versine (1 - cosx) tables, in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places. In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... Wikibooks has a book on the topic of Trigonometry All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Trigonometry (from Greek trigōnon triangle + metron measure[1]), informally called trig, is a branch of mathematics that deals with... The versed sine, also called the versine and, in Latin, the sinus versus (flipped sine) or the sagitta (arrow), is a trigonometric function versin(θ) (sometimes further abbreviated vers) defined by the equation: versin(θ) = 1 − cos(θ) = 2 sin2(θ / 2) There are also three corresponding functions: the...


In fact, the modern names "sine" and "cosine", are a mis-transcription of the words jya and kojya as introduced by Aryabhata. They were transcribed as jiba and kojiba in Arabic. They were then misinterpreted by Gerard of Cremona while translating an Arabic geometry text to Latin; he took jiba to be the Arabic word jaib, which means "fold in a garment", L. sinus (c.1150)[17]. Arabic redirects here. ... Gerard of Cremona (Italian: Gerardo da Cremona; Latin: Gerardus Cremonensis; c. ... For other uses, see Latin (disambiguation). ... Events Åhus, Sweden gains city privileges City of Airdrie, Scotland founded King Sverker I of Sweden is deposed and succeeded by Eric IX of Sweden. ...


Aryabhata's astronomical calculation methods were also very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world, and were used to compute many Arabic astronomical tables (zijes). In particular, the astronomical tables in the work of the Arabic Spain scientist Al-Zarqali (11th c.), were translated into Latin as the Tables of Toledo (12th c.), and remained the most accurate Ephemeris used in Europe for centuries. Arabic can mean: From or related to Arabia From or related to the Arabs The Arabic language; see also Arabic grammar The Arabic alphabet, used for expressing the languages of Arabic, Persian, Malay ( Jawi), Kurdish, Panjabi, Pashto, Sindhi and Urdu, among others. ... ZÄ«j is the generic name applied to books in Arabic, Persian, and some other languages that tabulate parameters used for astronomical calculations of the positions of the Sun, Moon, stars, and planets. ... Al-Andalus is the Arabic name given the Iberian Peninsula by its Muslim conquerors; it refers to both the Caliphate proper and the general period of Muslim rule (711–1492). ... For other meanings, see Arzachel (disambiguation) Al-Zarqali (in full Abu Ishaq Ibrahim ibn Yahya Al-Zarqali, Arzachel to Latin Europe), (1028–1087 CE), was a leading Arab mathematician and the foremost astronomer of his time. ... Gerard of Cremona edited for Latin readers the Tables of Toledo, the most accurate compilation of astronomical data ever seen in Europe at the time. ... An ephemeris (plural: ephemerides) (from the Greek word ephemeros = daily) is a device giving the positions of astronomical objects in the sky. ...


Calendric calculations worked out by Aryabhata and followers have been in continuous use in India for the practical purposes of fixing the Panchanga, or Hindu calendar, These were also transmitted to the Islamic world, and formed the basis for the Jalali calendar introduced 1073 by a group of astronomers including Omar Khayyam[18], versions of which (modified in 1925) are the national calendars in use in Iran and Afghanistan today. The Jalali calendar determines its dates based on actual solar transit, as in Aryabhata (and earlier Siddhanta calendars). This type of calendar requires an Ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were lower in the Jalali calendar than in the Gregorian calendar. Pancanga (pronounced Panchanga) is the Hindu almanac, which follows traditional Vedic cosmology, and presents important astronomical data in tabulated form. ... A page from the Hindu calendar 1871-72. ... The Persian calendar is official in Iran and in some surrounding nations, such as Afghanistan and some Central Asian nations. ... Events Cardinal Hildebrand elevated to papacy as Pope Gregory VII, succeeding Pope Alexander II Emperor Shirakawa ascends the throne of Japan Rabbi Yitchaki Alfassi finishes writing the Rif, an important work of Jewish law. ... Tomb of Omar Khayam, Neishapur, Iran. ... Year 1925 (MCMXXV) was a common year starting on Thursday (link will display the full calendar) of the Gregorian calendar. ... Siddhanta, a Sanskrit term, roughly translates as the Doctrine or This term Siddhanta is an established theological term within Hinduism which denotes a specific line of theological development within a Hindu religious traditon. ... An ephemeris (plural: ephemerides) (from the Greek word ephemeros = daily) is a device giving the positions of astronomical objects in the sky. ... The Persian calendar is official in Iran and in some surrounding nations, such as Afghanistan and some Central Asian nations. ... For the calendar of religious holidays and periods, see liturgical year. ...


India's first satellite Aryabhata, was named after him. Aryabhata was Indias first satellite, named after the great Indian astronomer of the same name. ...


The lunar crater Aryabhata is named in his honour. Wikipedia does not yet have an article with this exact name. ... Aryabhata is the remnant of a lunar impact crater located in the eastern Mare Tranquillitatis. ...


The interschool Aryabhatta Maths Competition is named after him.[19]

See also

References

  1. ^ a b c d e f Ansari, S. M. R. (March 1977). "Aryabhatta I, His Life and His Contributions". Bulletin of the Astronomical Society of India 5 (1): pp. 10-18. Retrieved on 2007-07-21. 
  2. ^ Cooke (1997). "The Mathematics of the Hindus", , 204. “Aryabhata himself (one of at least two mathematicians bearing that name) lived in the late fifth and the early sixth centuries at Kusumapura (now Pataliutra, a village near the city of Patna) and wrote a book called Aryabhatiya.” 
  3. ^ P. Z. Ingerman, 'Panini-Backus form', Communications of the ACM 10 (3)(1967), p.137
  4. ^ A universal history of numbers: From prehistory to the invention of the computer (1998). G Ifrah. John Wiley & Sons. 
  5. ^ Dutta, Bibhutibhushan & Avadhesh Narayan Singh (1962), History of Hindu Mathematics, Asia Publishing House, Bombay, ISBN 81-86050-86-8 (reprint)
  6. ^ Indian Mathematics and Astronomy: Some Landmarks, (1994/1998). S. Balachandra Rao. Jnana Deep Publications,. ISBN ISBN 81-7371-205-0. 
  7. ^ Roger Cooke (1997). "The Mathematics of the Hindus", History of Mathematics: A Brief Course. Wiley-Interscience. ISBN 0471180823. “Aryabhata gave the correct rule for the area of a triangle and an incorrect rule for the volume of a pyramid. (He claimed that the volume was half the height times the area of the base).” 
  8. ^ Amartya K Dutta, Diophantine equations: The Kuttaka, Resonance, October 2002. Also see earlier overview: Mathematics in Ancient India,.
  9. ^ Pingree, David (1996), "Astronomy in India", written at London, in Walker, Christopher, Astronomy before the Telescope, British Museum Press, 123-142, ISBN 0-7141-1746-3 pp. 127-9.
  10. ^ Otto Neugebauer, "The Transmission of Planetary Theories in Ancient and Medieval Astronomy," Scripta Mathematica, 22(1956): 165-192; reprinted in Otto Neugebauer, Astronomy and History: Selected Essays, New York: Springer-Verlag, 1983, pp. 129-156. ISBN 0-387-90844-7
  11. ^ Hugh Thurston, Early Astronomy, New York: Springer-Verlag, 1996, pp. 178-189. ISBN 0-387-94822-8
  12. ^ The concept of Indian heliocentrism has been advocated by B. L. van der Waerden, Das heliozentrische System in der griechischen, persischen und indischen Astronomie. Naturforschenden Gesellschaft in Zürich. Zürich:Kommissionsverlag Leeman AG, 1970.
  13. ^ B. L. van der Waerden, "The Heliocentric System in Greek, Persian and Hindu Astronomy", in David A. King and George Saliba, ed., From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E. S. Kennedy, Annals of the New York Academy of Science, 500 (1987), pp. 529-534.
  14. ^ Noel Swerdlow, "Review: A Lost Monument of Indian Astronomy," Isis, 64 (1973): 239-243.
  15. ^ Dennis Duke, "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models." Archive for History of Exact Sciences 59 (2005): 563–576, n. 4[1].
  16. ^ J. J. O'Connor and E. F. Robertson, Aryabhata the Elder, MacTutor History of Mathematics archive:

    "He believes that the Moon and planets shine by reflected sunlight, incredibly he believes that the orbits of the planets are ellipses." Āryabhatīya, an astronomical treastise, is the Magnum Opus and only extant work of the 5th century Indian Mathematician, Aryabhatta. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 202nd day of the year (203rd in leap years) in the Gregorian calendar. ... David Edwin Pingree (1933-2005), late University Professor and Professor of History of Mathematics and Classics at Brown University, was one of Americas foremost historians of the exact sciences in antiquity. ... Scripta Mathematica was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ...

  17. ^ Douglas Harper (2001). Online Etymology Dictionary. Retrieved on 2007-07-14.
  18. ^ "Omar Khayyam". The Columbia Encyclopedia, Sixth Edition.. (2001-05). Retrieved on 2007-06-10. 
  19. ^ "Maths can be fun", The Hindu, 2006-02-03. Retrieved on 2007-07-06. 

Other References

  • Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN 0471180823. 
  • Walter Eugene Clark, The Āryabhaṭīya of Āryabhaṭa, An Ancient Indian Work on Mathematics and Astronomy, University of Chicago Press (1930); reprint: Kessinger Publishing (2006), ISBN 978-1425485993.
  • Kak, Subhash C. (2000). 'Birth and Early Development of Indian Astronomy'. In Selin, Helaine (2000), Astronomy Across Cultures: The History of Non-Western Astronomy, Kluwer, Boston, ISBN 0-7923-6363-9
  • Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Indian National Science Academy, 1976.
  • Thurston, H. (1994), Early Astronomy, Springer-Verlag, New York, ISBN 0-387-94107-X

External links


  Results from FactBites:
 
Vidyapatha :: Indian Scientists : India's Largest Portal on Educational Information (487 words)
The young astronomer was Aryabhata and the treatise was Aryabhatiya.
Aryabhata was the first to deduce that the earth is round and that it rotates on its own axis, creating day and night.
It was in appreciation of his contributions to astronomy and mathematics that India's first satellite was named Aryabhata.
  More results at FactBites »

 
 

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I hate copy cats
20th May 2010
Liar liar pants on fire! You copied this all from wikipedia.org, but then also YOUR FONT SIZE IS VERY SMALL

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