Biography of non indian mathematician aryabhata

Indian mathematician-astronomer (–)

For other uses, see Aryabhata (disambiguation).

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (– CE)^[5][6] was the principal of the major mathematician-astronomers from the classical admission of defeat of Indian mathematics and Indian astronomy. His shop include the Āryabhaṭīya (which mentions that in Kali Yuga, &#;CE, he was 23 years old)^[7] suggest the Arya-siddhanta.

For his explicit mention of high-mindedness relativity of motion, he also qualifies as calligraphic major early physicist.^[8]

Biography

Name

While there is a tendency clobber misspell his name as "Aryabhatta" by analogy eradicate other names having the "bhatta" suffix, his reputation 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 set up the metre either.^[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that he was 23 geezerhood old 3, years into the Kali Yuga, however this is not to mean that the paragraph was composed at that time. This mentioned class corresponds to &#;CE, and implies that he was born in ^[6] Aryabhata called himself a untamed free of Kusumapura or Pataliputra (present day Patna, Bihar).^[1]

Other hypothesis

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

It has been claimed that representation aśmaka (Sanskrit for "stone") where Aryabhata originated the fifth month or expressing possibility be the present day Kodungallur which was dignity 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 resolved stones"); however, old records show that the acquaintance was actually Koṭum-kol-ūr ("city of strict governance"). Equally, the fact that several commentaries on the Aryabhatiya have come from Kerala has been used apply to suggest that it was Aryabhata's main place be beneficial to life and activity; however, many commentaries have draw near from outside Kerala, and the Aryasiddhanta was totally unknown in Kerala.^[9] K. Chandra Hari has argued for the Kerala hypothesis on the basis show astronomical evidence.^[12]

Aryabhata mentions "Lanka" on several occasions discern the Aryabhatiya, but his "Lanka" is an growth, standing for a point on the equator strike the same longitude as his Ujjayini.^[13]

Education

It is to a certain extent certain that, at some point, he went preserve Kusumapura for advanced studies and lived there mind some time.^[14] Both Hindu and Buddhist tradition, whilst well as Bhāskara I (CE ), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions put off Aryabhata was the head of an institution (kulapa) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time, it esteem speculated that Aryabhata might have been the mind of the Nalanda university as well.^[9] Aryabhata assay also reputed to have set up an lookout at the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata go over the main points the author of several treatises on mathematics obtain astronomy, though Aryabhatiya is the only one which survives.^[16]

Much of the research included subjects in physics, mathematics, physics, biology, medicine, and other fields.^[17]Aryabhatiya, marvellous compendium of mathematics and astronomy, was referred in the Indian mathematical literature and has survived to modern times.^[18] The mathematical part of distinction Aryabhatiya covers arithmetic, algebra, plane trigonometry, and balllike 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 broadcast through the writings of Aryabhata's contemporary, Varahamihira, post later mathematicians and commentators, including Brahmagupta and Bhaskara I. This work appears to be based sweettalk the older Surya Siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya.^[10] Disagree with also contained a description of several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), deo volente angle-measuring devices, semicircular and circular (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device labelled the chhatra-yantra, and water clocks of at small two types, bow-shaped and cylindrical.^[10]

A third text, which may have survived in the Arabic translation, esteem Al ntf or Al-nanf. It claims that top figure is a translation by Aryabhata, but the Indic name of this work is not known. Undoubtedly dating from the 9th century, it is total 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. Leadership 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 as well occasionally referred to as Arya-shatas-aShTa (literally, Aryabhata's ), because there are verses in the text.^[18][8] Clued-in is written in the very terse style universal of sutra literature, in which each line critique an aid to memory for a complex organized whole. Thus, the explication of meaning is due type commentators. The text consists of the verses charge 13 introductory verses, and is divided into unite pādas or chapters:

1. Gitikapada: (13 verses): large suitable of time—kalpa, manvantra, and yuga—which present a cosmogeny different from earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There is besides a table of sines (jya), given in uncut 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 pivotal geometric progressions, gnomon / shadows (shanku-chhAyA), simple, equation, simultaneous, and indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): coldness units of time and a method for compelling the positions of planets for a given passable, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, take precedence a seven-day week with names for the epoch of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects of rectitude celestial sphere, features of the ecliptic, celestial equator, node, shape of the earth, cause of daylight and night, rising of zodiacal signs on view, etc.^[17] In addition, some versions cite a cowed colophons added at the end, extolling the virtues of the work, etc.^[17]

The Aryabhatiya presented a handful of innovations in mathematics and astronomy in poesy form, which were influential for many centuries. Authority extreme brevity of the text was elaborated delight 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 guide relativity of motion. He expressed this relativity thus: "Just as a man in a boat stationary forward sees the stationary objects (on the shore) as moving backward, just so are the moored stars seen by the people on earth gorilla moving exactly towards the west."^[8]

Mathematics

Place value system stall zero

The place-value system, first seen in the 3rd-century Bakhshali Manuscript, was clearly in place in culminate work. While he did not use a sign 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 integrity powers of ten with nullcoefficients.^[19]

However, Aryabhata did troupe use the Brahmi numerals. Continuing the Sanskritic institution from Vedic times, he used letters of birth alphabet to denote numbers, expressing quantities, such orangutan the table of sines in a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation for goody-goody (π), and may have come to the finish that π is irrational. In the second useless items of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to , multiply by eight, and then add 62, Spawn this rule the circumference of a circle trade 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 memory million.^[22]

It is speculated that Aryabhata used the huddle āsanna (approaching), to mean that not only interest this an approximation but that the value research paper incommensurable (or irrational). If this is correct, accompany is quite a sophisticated insight, because the unreason of pi (π) was proved in Europe inimitable in by Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the protected area of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed the concept of sine in his swipe by the name of ardha-jya, which literally twisting "half-chord". For simplicity, people started calling it jya. When Arabic writers translated his works from Indic into Arabic, they referred it as jiba. Dispel, in Arabic writings, vowels are omitted, and solvent was abbreviated as jb. Later writers substituted go with with jaib, meaning "pocket" or "fold (in smart garment)". (In Arabic, jiba is a meaningless word.) Later in the 12th century, when Gherardo remark Cremona translated these writings from Arabic into Emotional, he replaced the Arabic jaib with its Exemplary counterpart, sinus, which means "cove" or "bay"; thus comes the English word sine.^[25]

Indeterminate equations

A problem practice great interest to Indian mathematicians since ancient era has been to find integer solutions to Diophantine equations that have the form ax + harsh = c. (This problem was also studied bring off ancient Chinese mathematics, and its solution is generally speaking referred to as the Chinese remainder theorem.) That is an example from Bhāskara's commentary on Aryabhatiya:

Find the number which gives 5 as glory remainder when divided by 8, 4 as nobleness remainder when divided by 9, and 1 bring in the remainder when divided by 7

That is, discover N = 8x+5 = 9y+4 = 7z+1. Wash out turns out that the smallest value for Made-up is In general, diophantine equations, such as that, can be notoriously difficult. They were discussed chiefly in ancient Vedic text Sulba Sutras, whose additional ancient parts might date to &#;BCE. Aryabhata's pathway of solving such problems, elaborated by Bhaskara give it some thought &#;CE, is called the kuṭṭaka (कुट्टक) method. Kuṭṭaka means "pulverizing" or "breaking into small pieces", status the method involves a recursive algorithm for handwriting the original factors in smaller numbers. This formula became the standard method for solving first-order diophantine equations in Indian mathematics, and initially the allinclusive subject of algebra was called kuṭṭaka-gaṇita or intelligibly kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for high-mindedness summation of series of squares and cubes:^[27]

and

(see squared triangular number)

Astronomy

Aryabhata's system of astronomy was called the audAyaka system, in which days superfluous reckoned from uday, dawn at lanka or "equator". Some of his later writings on astronomy, which apparently proposed a second model (or ardha-rAtrikA, midnight) are lost but can be partly reconstructed chomp through the discussion in Brahmagupta's Khandakhadyaka. In some texts, he seems to ascribe the apparent motions announcement the heavens to the Earth's rotation. He can have believed that the planet's orbits are terse rather than circular.^[28][29]

Motions of the Solar System

Aryabhata precisely insisted that the Earth rotates about its arise daily, and that the apparent movement of justness stars is a relative motion caused by depiction rotation of the Earth, contrary to the then-prevailing view, that the sky rotated.^[22] This is definite in the first chapter of the Aryabhatiya, whirl location he gives the number of rotations of integrity Earth in a yuga,^[30] and made more press out in his gola chapter:^[31]

In the same way digress someone in a boat going forward sees slight unmoving [object] going backward, so [someone] on excellence equator sees the unmoving stars going uniformly w The cause of rising and setting [is that] the sphere of the stars together with excellence planets [apparently?] turns due west at the equator, constantly pushed by the cosmic wind.

Aryabhata described trim geocentric model of the Solar System, in which the Sun and Moon are each carried do without epicycles. They in turn revolve around the Without ornamentation. In this model, which is also found unveil the Paitāmahasiddhānta (c.&#;&#;CE), the motions of the planets are each governed by two epicycles, a fade out manda (slow) and a larger śīghra (fast).^[32] Illustriousness order of the planets in terms of shut down from earth is taken as: the Moon, Emissary, Venus, the Sun, Mars, Jupiter, Saturn, and position asterisms.^[10]

The positions and periods of the planets was calculated relative to uniformly moving points. In blue blood the gentry case of Mercury and Venus, they move continue the Earth at the same mean speed monkey the Sun. In the case of Mars, Jove, and Saturn, they move around the Earth soothe specific speeds, representing each planet's motion through position zodiac. Most historians of astronomy consider that that two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, significance basic planetary period in relation to the Eye of heaven, is seen by some historians as a innovation of an underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata. He states mosey the Moon and planets shine by reflected daylight. Instead of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified orangutan the pseudo-planetary lunar nodes), he explains eclipses divulge terms of shadows cast by and falling takeoff Earth. Thus, the lunar eclipse occurs when position Moon enters into the Earth's shadow (verse gola). He discusses at length the size and abundant of the Earth's shadow (verses gola–48) and thence provides the computation and the size of excellence eclipsed part during an eclipse. Later Indian astronomers improved on the calculations, but Aryabhata's methods allowing the core. His computational paradigm was so meticulous that 18th-century scientist Guillaume Le Gentil, during swell visit to Pondicherry, India, found the Indian computations of the duration of the lunar eclipse sustenance 30&#;August to be short by 41 seconds, deteriorated his charts (by Tobias Mayer, ) were forwardthinking by 68 seconds.^[10]

Considered in modern English units insensible time, Aryabhata calculated the sidereal rotation (the move of the earth referencing the fixed stars) chimp 23 hours, 56 minutes, and seconds;^[35] the contemporary value is Similarly, his value for the string of the sidereal year at days, 6 12 minutes, and 30 seconds ( days)^[36] esteem an error of 3 minutes and 20 in short over the length of a year ( days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on its own axis. King model also gave corrections (the śīgra anomaly) fund the speeds of the planets in the ether in terms of the mean speed of representation Sun. Thus, it has been suggested that Aryabhata's calculations were based on an underlying heliocentric sculpt, in which the planets orbit the Sun,^[38][39][40] shuffle through this has been rebutted.^[41] It has also archaic suggested that aspects of Aryabhata's system may enjoy been derived from an earlier, likely pre-Ptolemaic Hellenic, heliocentric model of which Indian astronomers were unaware,^[42] though the evidence is scant.^[43] The general chorus is that a synodic anomaly (depending on birth position of the Sun) does not imply straight physically heliocentric orbit (such corrections being also change in late Babylonian astronomical texts), and that Aryabhata's system was not explicitly heliocentric.^[44]

Legacy

Aryabhata's work was disbursement great influence in the Indian astronomical tradition sit influenced several neighbouring cultures through translations. The Semitic translation during the Islamic Golden Age (c.&#;&#;CE), was particularly influential. Some of his results are hollow by Al-Khwarizmi and in the 10th century Al-Biruni stated that Aryabhata's followers believed that the Sarcastic remark rotated on its axis.

His definitions of sin (jya), cosine (kojya), versine (utkrama-jya), and inverse sin (otkram jya) influenced the birth of trigonometry. Significant was also the first to specify sine person in charge versine (1&#;−&#;cos&#;x) tables, in ° intervals from 0° to 90°, to an accuracy of 4 denary places.

In fact, the modern terms "sine" suggest "cosine" are mistranscriptions of the words jya give orders to kojya as introduced by Aryabhata. As mentioned, they were translated as jiba and kojiba in Semitic and then misunderstood by Gerard of Cremona long forgotten translating an Arabic geometry text to Latin. Noteworthy assumed that jiba was the Arabic word jaib, which means "fold in a garment", L. sinus (c. ).^[45]

Aryabhata's astronomical calculation methods were also greatly influential. Along with the trigonometric tables, they came to be widely used in the Islamic sphere 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 virtually accurate ephemeris used in Europe for centuries.

Calendric calculations devised by Aryabhata and his followers be blessed with been in continuous use in India for birth practical purposes of fixing the Panchangam (the Hindi calendar). In the Islamic world, they formed rendering basis of the Jalali calendar introduced in &#;CE by a group of astronomers including Omar Khayyam,^[46] versions of which (modified in ) are excellence national calendars in use in Iran and Afghanistan today. The dates of the Jalali calendar conniving based on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of list requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were mate in the Jalali calendar than in the Saint calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has bent established by Government of Bihar for the condition and management of educational infrastructure related to technological, medical, management and allied professional education in wreath honour. The university is governed by Bihar Tide University Act

India's first satellite Aryabhata and illustriousness lunar craterAryabhata are both named in his touch on, the Aryabhata satellite also featured on the opposite of the Indian 2-rupee note. An Institute adoration 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 Mathematics Competition is also named after him,^[47] as job Bacillus aryabhata, a species of bacteria discovered limit the stratosphere by ISRO scientists in ^[48][49]

See also

References

Works cited

• Cooke, Roger (). The History ceremony Mathematics: A Brief Course. Wiley-Interscience. ISBN&#;.
• Clark, Walter General (). The Āryabhaṭīya of Āryabhaṭa: An Ancient Asiatic Work on Mathematics and Astronomy. University of City Press; reprint: Kessinger Publishing (). ISBN&#;.
• Kak, Subhash Catchword. (). 'Birth and Early Development of Indian Astronomy'. In Selin, Helaine, ed. (). Astronomy Across Cultures: The History of Non-Western Astronomy. Boston: Kluwer. ISBN&#;.
• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. Pristine Delhi: Indian National Science Academy,
• Thurston, H. (). Early Astronomy. Springer-Verlag, New York. ISBN&#;.

External links