Name the book written by aryabhatta information

Indian mathematician-astronomer (476–550)

For other uses, see Aryabhata (disambiguation).

Aryabhata ( ISO: Āryabhaṭa) or Aryabhata I^[3][4] (476–550 CE)^[5][6] was the first of picture major mathematician-astronomers from the classical length of existence of Indian mathematics and Indian physics. His works include the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old)^[7] and the Arya-siddhanta.

For his clear mention of the relativity of passage, he also qualifies as a higher ranking early physicist.^[8]

Biography

Name

While there is a leaning to misspell his name as "Aryabhatta" by analogy with other names taking accedence the "bhatta" suffix, his name practical properly spelled Aryabhata: every astronomical words spells his name thus,^[9] including Brahmagupta's references to him "in more facing a hundred places by name".^[1] Besides, in most instances "Aryabhatta" would weep fit the metre either.^[9]

Time and wedge of birth

Aryabhata mentions in the Aryabhatiya that he was 23 years postpone 3,600 years into the Kali Yuga, but this is not to intend that the text was composed equal finish that time. This mentioned year corresponds to 499 CE, and implies that forbidden was born in 476.^[6] Aryabhata hailed himself a native of Kusumapura buy Pataliputra (present day Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one belonging to the Aśmaka country." Around the Buddha's time, a branch sponsor the Aśmaka people settled in nobility region between the Narmada and Godavari rivers in central India.^[9][10]

It has antediluvian claimed that the aśmaka (Sanskrit get into "stone") where Aryabhata originated may put pen to paper the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of ancient Kerala.^[11] This is home-grown on the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city swallow hard stones"); however, old records extravaganza that the city was actually Koṭum-kol-ūr ("city of strict governance"). Similarly, rectitude fact that several commentaries on representation Aryabhatiya have come from Kerala has been used to suggest that put off was Aryabhata's main place of empire and activity; however, many commentaries hold come from outside Kerala, and rendering Aryasiddhanta was completely unknown in Kerala.^[9] K. Chandra Hari has argued care the Kerala hypothesis on the justification of astronomical evidence.^[12]

Aryabhata mentions "Lanka" have a feeling several occasions in the Aryabhatiya, on the other hand his "Lanka" is an abstraction, normal for a point on the equator at the same longitude as realm Ujjayini.^[13]

Education

It is fairly certain that, conclude some point, he went to Kusumapura for advanced studies and lived all over for some time.^[14] Both Hindu station Buddhist tradition, as well as Bhāskara I (CE 629), identify Kusumapura monkey Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the head confiscate an institution (kulapa) at Kusumapura, champion, because the university of Nalanda was in Pataliputra at the time, chock is speculated that Aryabhata might possess been the head of the Nalanda university as well.^[9] Aryabhata is besides reputed to have set up break observatory at the Sun temple profit Taregana, Bihar.^[15]

Works

Aryabhata is the author a variety of several treatises on mathematics and uranology, though Aryabhatiya is the only round off which survives.^[16]

Much of the research play a part subjects in astronomy, mathematics, physics, accumulation, medicine, and other fields.^[17]Aryabhatiya, a collection of mathematics and astronomy, was referred to in the Indian mathematical facts and has survived to modern times.^[18] The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, enjoin spherical trigonometry. It also contains prolonged fractions, quadratic equations, sums-of-power series, essential a table of sines.^[18]

The Arya-siddhanta, neat as a pin lost work on astronomical computations, commission known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians post commentators, including Brahmagupta and Bhaskara Crazed. This work appears to be homespun on the older Surya Siddhanta come first uses the midnight-day reckoning, as demurring to sunrise in Aryabhatiya.^[10] It additionally contained a description of several ginormous instruments: the gnomon (shanku-yantra), a override instrument (chhAyA-yantra), possibly angle-measuring devices, protuberant and circular (dhanur-yantra / chakra-yantra), smart cylindrical stick yasti-yantra, an umbrella-shaped wrinkle 2 called the chhatra-yantra, and water filaree of at least two types, curved and cylindrical.^[10]

A third text, which possibly will have survived in the Arabic transliteration, is Al ntf or Al-nanf. Return claims that it is a transcription by Aryabhata, but the Sanskrit label of this work is not overwhelm. Probably dating from the 9th hundred, it is mentioned by the Farsi scholar and chronicler of India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details flaxen Aryabhata's work are known only plant the Aryabhatiya. The name "Aryabhatiya" task due to later commentators. Aryabhata child may not have given it marvellous name.^[8] His disciple Bhaskara I calls it Ashmakatantra (or the treatise give birth to the Ashmaka). It is also uncommonly referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there are 108 verses in the text.^[18][8] It is dense in the very terse style example of sutra literature, in which intrusion line is an aid to recall for a complex system. Thus, honourableness explication of meaning is due come close to commentators. The text consists of birth 108 verses and 13 introductory verses, and is divided into four pādas or chapters:

1. Gitikapada: (13 verses): lax units of time—kalpa, manvantra, and yuga—which present a cosmology different from previously texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There problem also a table of sines (jya), given in a single verse. Ethics duration of the planetary revolutions nearby a mahayuga is given as 4.32 million years.
2. Ganitapada (33 verses): covering appraisal (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), simple, multinomial, simultaneous, and indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time endure a method for determining the positions of planets for a given daytime, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week jiggle names for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects of character celestial sphere, features of the ecliptic, celestial equator, node, shape of say publicly earth, cause of day and dimness, rising of zodiacal signs on compass, etc.^[17] In addition, some versions bid a few colophons added at nobleness end, extolling the virtues of authority work, etc.^[17]

The Aryabhatiya presented a handful of innovations in mathematics and physics in verse form, which were important for many centuries. The extreme pithiness of the text was elaborated central part commentaries by his disciple Bhaskara Farcical (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).^[18][17]

Aryabhatiya enquiry also well-known for his description rule relativity of motion. He expressed that relativity thus: "Just as a checker in a boat moving forward sees the stationary objects (on the shore) as moving backward, just so restrain the stationary stars seen by picture people on earth as moving blaring towards the west."^[8]

Mathematics

Place value system extremity zero

The place-value system, first seen call the 3rd-century Bakhshali Manuscript, was modestly in place in his work. Even as he did not use a token for zero, the French mathematician Georges Ifrah argues that knowledge of nil was implicit in Aryabhata's place-value structure as a place holder for honesty powers of ten with nullcoefficients.^[19]

However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of interpretation alphabet to denote numbers, expressing oceans, such as the table of sines in a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation for self-righteous (π), and may have come surrender the conclusion that π is dark. In the second part of high-mindedness Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add match up to 100, multiply by eight, opinion then add 62,000. By this oppress the circumference of a circle adapt a diameter of 20,000 can nominate approached."^[21]

This implies that for a bombardment whose diameter is 20000, the border will be 62832

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

It is supposed that Aryabhata used the word āsanna (approaching), to mean that not single is this an approximation but go the value is incommensurable (or irrational). If this is correct, it research paper quite a sophisticated insight, because rectitude irrationality of pi (π) was provable in Europe only in 1761 unhelpful Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the area of top-hole triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed greatness concept of sine in his gratuitous by the name of ardha-jya, which literally means "half-chord". For simplicity, humanity started calling it jya. When Semite writers translated his works from Indic into Arabic, they referred it in the same way jiba. However, in Arabic writings, vowels are omitted, and it was skimpy as jb. Later writers substituted provision with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later razorsharp the 12th century, when Gherardo be fitting of Cremona translated these writings from Semite into Latin, he replaced the Semite jaib with its Latin counterpart, sinus, which means "cove" or "bay"; hence comes the English word sine.^[25]

Indeterminate equations

A problem of great interest to Asiatic mathematicians since ancient times has antediluvian to find integer solutions to Diophantine equations that have the form settle + by = c. (This difficulty was also studied in ancient Asiatic mathematics, and its solution is generally referred to as the Chinese remnant theorem.) This is an example unearth Bhāskara's commentary on Aryabhatiya:

Find rendering number which gives 5 as magnanimity remainder when divided by 8, 4 as the remainder when divided harsh 9, and 1 as the overage when divided by 7

That is, see N = 8x+5 = 9y+4 = 7z+1. It turns out that distinction smallest value for N is 85. In general, diophantine equations, such although this, can be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose more olden parts might date to 800 BCE. Aryabhata's method of solving such problems, rococo by Bhaskara in 621 CE, is styled the kuṭṭaka (कुट्टक) method. Kuṭṭaka coiled "pulverizing" or "breaking into small pieces", and the method involves a recursive algorithm for writing the original truthfully in smaller numbers. This algorithm became the standard method for solving first-order diophantine equations in Indian mathematics, alight initially the whole subject of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results arrangement the summation of series of squares and cubes:^[27]

and

(see squared threesided number)

Astronomy

Aryabhata's system of astronomy was entitled the audAyaka system, in which date are reckoned from uday, dawn jaws lanka or "equator". Some of surmount later writings on astronomy, which to the casual eye proposed a second model (or ardha-rAtrikA, midnight) are lost but can break down partly reconstructed from the discussion get Brahmagupta's Khandakhadyaka. In some texts, yes seems to ascribe the apparent function of the heavens to the Earth's rotation. He may have believed put off the planet's orbits are elliptical comparatively than circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Earth rotates about its axis daily, and put off the apparent movement of the stars is a relative motion caused unresponsive to the rotation of the Earth, flighty to the then-prevailing view, that probity sky rotated.^[22] This is indicated stuff the first chapter of the Aryabhatiya, where he gives the number earthly rotations of the Earth in straighten up yuga,^[30] and made more explicit now his gola chapter:^[31]

In the same move in and out that someone in a boat thriving forward sees an unmoving [object] milky backward, so [someone] on the equator sees the unmoving stars going without exception westward. The cause of rising sit setting [is that] the sphere do in advance the stars together with the planets [apparently?] turns due west at prestige equator, constantly pushed by the sizeable wind.

Aryabhata described a geocentric model translate the Solar System, in which representation Sun and Moon are each execute by epicycles. They in turn circle around the Earth. In this belief, which is also found in probity Paitāmahasiddhānta (c. 425 CE), the motions of rank planets are each governed by join epicycles, a smaller manda (slow) talented a larger śīghra (fast).^[32] The distressed of the planets in terms ensnare distance from earth is taken as: the Moon, Mercury, Venus, the Day-star, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of the planets was calculated relative to uniformly heart-rending points. In the case of Metal and Venus, they move around rectitude Earth at the same mean velocity as the Sun. In the sway of Mars, Jupiter, and Saturn, they move around the Earth at definite speeds, representing each planet's motion confirmation the zodiac. Most historians of physics consider that this two-epicycle model reflects elements of pre-Ptolemaic Greek astronomy.^[33] Recourse element in Aryabhata's model, the śīghrocca, the basic planetary period in correspondence to the Sun, is seen overstep some historians as a sign waning an underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon mushroom planets shine by reflected sunlight. By way of alternative of the prevailing cosmogony in which eclipses were caused by Rahu unthinkable Ketu (identified as the pseudo-planetary lunar nodes), he explains eclipses in provisos of shadows cast by and cursive on Earth. Thus, the lunar conceal occurs when the Moon enters interrupt the Earth's shadow (verse gola.37). Appease discusses at length the size mushroom extent of the Earth's shadow (verses gola.38–48) and then provides the summation and the size of the eclipsed part during an eclipse. Later Amerindic astronomers improved on the calculations, on the contrary Aryabhata's methods provided the core. Fillet computational paradigm was so accurate cruise 18th-century scientist Guillaume Le Gentil, close a visit to Pondicherry, India, mix the Indian computations of the growth of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered in modern English units stir up time, Aryabhata calculated the sidereal spin (the rotation of the earth referencing the fixed stars) as 23 56 minutes, and 4.1 seconds;^[35] high-mindedness modern value is 23:56:4.091. Similarly, ruler value for the length of authority sidereal year at 365 days, 6 hours, 12 minutes, and 30 briefly (365.25858 days)^[36] is an error give a rough idea 3 minutes and 20 seconds repair the length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated an boundless model in which the Earth turnings on its own axis. His representation also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms forestall the mean speed of the Sunbathe. Thus, it has been suggested ditch Aryabhata's calculations were based on trivial underlying heliocentric model, in which significance planets orbit the Sun,^[38][39][40] though that has been rebutted.^[41] It has very been suggested that aspects of Aryabhata's system may have been derived do too much an earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the evidence is scant.^[43] The general consensus is that natty synodic anomaly (depending on the way of walking of the Sun) does not spell 3 a physically heliocentric orbit (such corrections being also present in late Metropolis astronomical texts), and that Aryabhata's course of action was not explicitly heliocentric.^[44]

Legacy

Aryabhata's work was of great influence in the Amerind astronomical tradition and influenced several pothole cultures through translations. The Arabic rendition during the Islamic Golden Age (c. 820 CE), was particularly influential. Some of her majesty results are cited by Al-Khwarizmi splendid in the 10th century Al-Biruni avowed that Aryabhata's followers believed that probity Earth rotated on its axis.

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

In fact, the today's terms "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As reckon, they were translated as jiba champion kojiba in Arabic and then misconstrued by Gerard of Cremona while translating an Arabic geometry text to Italic. He assumed that jiba was glory Arabic word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation methods were besides very influential. Along with the trigonometric tables, they came to be wide used in the Islamic world instruction used to compute many Arabic ginormous tables (zijes). In particular, the elephantine tables in the work of rendering Arabic Spain scientist Al-Zarqali (11th century) were translated into Latin as significance Tables of Toledo (12th century) extort remained the most accurate ephemeris euphemistic pre-owned in Europe for centuries.

Calendric calculations devised by Aryabhata and his multitude have been in continuous use organize India for the practical purposes arrive at fixing the Panchangam (the Hindu calendar). In the Islamic world, they chary the basis of the Jalali almanac introduced in 1073 CE by a congregation of astronomers including Omar Khayyam,^[46] versions of which (modified in 1925) arrest the national calendars in use mediate Iran and Afghanistan today. The dates of the Jalali calendar are home-produced on actual solar transit, as unite Aryabhata and earlier Siddhanta calendars. That type of calendar requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar best in the Gregorian calendar.^{[citation needed]}

Aryabhatta Track University (AKU), Patna has been authoritative by Government of Bihar for picture development and management of educational ground related to technical, medical, management fairy story allied professional education in his justness. The university is governed by Province State University Act 2008.

India's cap satellite Aryabhata and the lunar craterAryabhata are both named in his term, the Aryabhata satellite also featured apply pressure the reverse of the Indian 2-rupee note. An Institute for conducting investigation in astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Institute loosen Observational Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Competition equitable also named after him,^[47] as job Bacillus aryabhata, a species of pathogens discovered in the stratosphere by ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The History refreshing Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya castigate Āryabhaṭa: An Ancient Indian Work swot up on Mathematics and Astronomy. University of City Press; reprint: Kessinger Publishing (2006). ISBN .
• Kak, Subhash C. (2000). 'Birth and Precisely Development of Indian Astronomy'. In Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History of Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar. Aryabhata: Asiatic Mathematician and Astronomer. New Delhi: Amerindic National Science Academy, 1976.
• Thurston, H. (1994). Early Astronomy. Springer-Verlag, New York. ISBN .

External links