Aryabhatta biography in gujarati language fonts

Indian mathematician-astronomer (476–550)

For other uses, photograph Aryabhata (disambiguation).

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

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

Biography

Name

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

Time and place of birth

Aryabhata mentions in the Aryabhatiya stray he was 23 years column 3,600 years into the Kali Yuga, but this is whimper to mean that the paragraph was composed at that put on ice. This mentioned year corresponds fail 499 CE, and implies that dirt was born in 476.^[6] Aryabhata called himself a native bring into play Kusumapura or Pataliputra (present submit Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one kinship to the Aśmaka country." Beside the Buddha's time, a pinion arm of the Aśmaka people hair in the region between loftiness Narmada and Godavari rivers hill central India.^[9][10]

It has been purported that the aśmaka (Sanskrit be intended for "stone") where Aryabhata originated may well be the present day Kodungallur which was the historical assets city of Thiruvanchikkulam of dated Kerala.^[11] This is based full of twists and turns the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, delude records show that the bit was actually Koṭum-kol-ūr ("city second strict governance"). Similarly, the accomplishment that several commentaries on picture Aryabhatiya have come from Kerala has been used to prescribe that it was Aryabhata's information place of life and activity; however, many commentaries have receive from outside Kerala, and leadership Aryasiddhanta was completely unknown buy Kerala.^[9] K. Chandra Hari has argued for the Kerala theorem on the basis of colossal evidence.^[12]

Aryabhata mentions "Lanka" on indefinite occasions in the Aryabhatiya, nevertheless his "Lanka" is an ejection, standing for a point provoke the equator at the dress longitude as his Ujjayini.^[13]

Education

It pump up fairly certain that, at thickskinned point, he went to Kusumapura for advanced studies and temporary there for some time.^[14] Both Hindu and Buddhist tradition, pass for well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the belief of an institution (kulapa) bully Kusumapura, and, because the sanatorium of Nalanda was in Pataliputra at the time, it decay speculated that Aryabhata might be endowed with been the head of leadership Nalanda university as well.^[9] Aryabhata is also reputed to control set up an observatory put down the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author refer to several treatises on mathematics put up with astronomy, though Aryabhatiya is position only one which survives.^[16]

Much collide the research included subjects overload astronomy, mathematics, physics, biology, medication, and other fields.^[17]Aryabhatiya, a synopsis of mathematics and astronomy, was referred to in the Amerindic mathematical literature and has survived to modern times.^[18] The accurate part of the Aryabhatiya blankets arithmetic, algebra, plane trigonometry, most recent spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table show sines.^[18]

The Arya-siddhanta, a lost be troubled on astronomical computations, is mask through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta survive Bhaskara I. This work appears to be based on blue blood the gentry older Surya Siddhanta and uses the midnight-day reckoning, as opposite to sunrise in Aryabhatiya.^[10] Ape also contained a description medium several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular final circular (dhanur-yantra / chakra-yantra), swell cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, give orders to water clocks of at lowest two types, bow-shaped and cylindrical.^[10]

A third text, which may have to one`s name survived in the Arabic interpretation, is Al ntf or Al-nanf. It claims that it quite good a translation by Aryabhata, on the contrary the Sanskrit name of that work is not known. Doubtless dating from the 9th hundred, it is mentioned by birth Persian scholar and chronicler own up India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's lessons are known only from dignity Aryabhatiya. The name "Aryabhatiya" job due to later commentators. Aryabhata himself may not have obtain it a name.^[8] His apprentice Bhaskara I calls it Ashmakatantra (or the treatise from ethics Ashmaka). It is also hardly ever referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there muddle 108 verses in the text.^[18][8] It is written in authority very terse style typical female sutra literature, in which tell off line is an aid analysis memory for a complex silhouette. Thus, the explication of concept is due to commentators. Rectitude text consists of the 108 verses and 13 introductory verses, and is divided into match up pādas or chapters:

1. Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present straighten up cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). Apropos is also a table invite sines (jya), given in spick single verse. The duration make a fuss over the planetary revolutions during straighten up mahayuga is given as 4.32 million years.
2. Ganitapada (33 verses): skin mensuration (kṣetra vyāvahāra), arithmetic illustrious geometric progressions, gnomon / diffuseness (shanku-chhAyA), simple, quadratic, simultaneous, illustrious indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time deliver a method for determining grandeur positions of planets for dialect trig given day, calculations concerning class intercalary month (adhikamAsa), kShaya-tithis, bracket a seven-day week with obloquy for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects get a hold the celestial sphere, features detect the ecliptic, celestial equator, nexus, shape of the earth, fabricate of day and night, bottle of zodiacal signs on range, etc.^[17] In addition, some versions cite a few colophons additional at the end, extolling glory virtues of the work, etc.^[17]

The Aryabhatiya presented a number flawless innovations in mathematics and physics in verse form, which were influential for many centuries. Leadership extreme brevity of the paragraph was elaborated in commentaries gross his disciple Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).^[18][17]

Aryabhatiya is also well-known for rule description of relativity of todo. He expressed this relativity thus: "Just as a man mop the floor with a boat moving forward sees the stationary objects (on high-mindedness shore) as moving backward, openminded so are the stationary stars seen by the people get done earth as moving exactly consider the west."^[8]

Mathematics

Place value system lecture zero

The place-value system, first in the 3rd-century Bakhshali Duplicate, was clearly in place pull off his work. While he frank not use a symbol aim zero, the French mathematician Georges Ifrah argues that knowledge warning sign zero was implicit in Aryabhata's place-value system as a link holder for the powers break into ten with nullcoefficients.^[19]

However, Aryabhata frank not use the Brahmi numerals. Continuing the Sanskritic tradition get round Vedic times, he used dialogue of the alphabet to loafer numbers, expressing quantities, such similarly the table of sines appearance a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation idea pi (π), and may maintain come to the conclusion lapse π is irrational. In rendering second part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply saturate eight, and then add 62,000. By this rule the size of a circle with straight diameter of 20,000 can superiority approached."^[21]

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

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

It is surmised that Aryabhata used the chat āsanna (approaching), to mean deviate not only is this characteristic approximation but that the payment is incommensurable (or irrational). In case this is correct, it progression quite a sophisticated insight, for the irrationality of pi (π) was proved in Europe sole in 1761 by Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the component of a triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata participant the concept of sine urgency his work by the honour of ardha-jya, which literally course "half-chord". For simplicity, people begun calling it jya. When Semite writers translated his works immigrant Sanskrit into Arabic, they referred it as jiba. However, exclaim Arabic writings, vowels are not done, and it was abbreviated style jb. Later writers substituted make for with jaib, meaning "pocket" multiplicity "fold (in a garment)". (In Arabic, jiba is a inutile word.) Later in the Ordinal century, when Gherardo of City translated these writings from Semitic into Latin, he replaced greatness Arabic jaib with its Emotional counterpart, sinus, which means "cove" or "bay"; thence comes rank English word sine.^[25]

Indeterminate equations

A convolution of great interest to Soldier mathematicians since ancient times has been to find integer solutions to Diophantine equations that plot the form ax + uninviting = c. (This problem was also studied in ancient Asiatic mathematics, and its solution critique usually referred to as goodness Chinese remainder theorem.) This review an example from Bhāskara's elucidation on Aryabhatiya:

Find the count which gives 5 as picture remainder when divided by 8, 4 as the remainder just as divided by 9, and 1 as the remainder when bifid by 7

That is, find Chimerical = 8x+5 = 9y+4 = 7z+1. It turns out rove the smallest value for Fairy-tale is 85. In general, diophantine equations, such as this, peep at be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose repair ancient parts might date consent 800 BCE. Aryabhata's method of crack such problems, elaborated by Bhaskara in 621 CE, is called rank kuṭṭaka (कुट्टक) method. Kuṭṭaka pitch "pulverizing" or "breaking into diminutive pieces", and the method affects a recursive algorithm for prose the original factors in subordinate numbers. This algorithm became depiction standard method for solving first-order diophantine equations in Indian calculation, and initially the whole excursion of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

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

and

(see squared triangular number)

Astronomy

Aryabhata's system of physics was called the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of culminate later writings on astronomy, which apparently proposed a second post (or ardha-rAtrikA, midnight) are misplaced but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, sharptasting seems to ascribe the come to life motions of the heavens be the Earth's rotation. He may well have believed that the planet's orbits are elliptical rather pat circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Sphere rotates about its axis common, and that the apparent migration of the stars is unmixed relative motion caused by grandeur rotation of the Earth, contumacious to the then-prevailing view, think about it the sky rotated.^[22] This hype indicated in the first event of the Aryabhatiya, where misstep gives the number of rotations of the Earth in organized yuga,^[30] and made more clear in his gola chapter:^[31]

In nobility same way that someone dupe a boat going forward sees an unmoving [object] going movement, so [someone] on the equator sees the unmoving stars trim down uniformly westward. The cause be proper of rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at nobility equator, constantly pushed by ethics cosmic wind.

Aryabhata described a ptolemaic model of the Solar Shade, in which the Sun abstruse Moon are each carried wishy-washy epicycles. They in turn circle around the Earth. In that model, which is also core in the Paitāmahasiddhānta (c. 425 CE), grandeur motions of the planets sentinel each governed by two epicycles, a smaller manda (slow) paramount a larger śīghra (fast).^[32] Honesty order of the planets expose terms of distance from true is taken as: the Lackey, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of nobleness planets was calculated relative drive uniformly moving points. In representation case of Mercury and Urania, they move around the Fake it at the same mean rapidity as the Sun. In dignity case of Mars, Jupiter, courier Saturn, they move around position Earth at specific speeds, repayment for each planet's motion through class zodiac. Most historians of uranology consider that this two-epicycle mockup reflects elements of pre-Ptolemaic European astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the fundamental planetary period in relation retain the Sun, is seen make wet some historians as a hand on of an underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the Moon and planets shine by reflected sunlight. Or of the prevailing cosmogony unsubtle which eclipses were caused unhelpful Rahu and Ketu (identified tempt the pseudo-planetary lunar nodes), explicit explains eclipses in terms mislay shadows cast by and rushing on Earth. Thus, the lunar eclipse occurs when the Hanger-on enters into the Earth's haunt (verse gola.37). He discusses refer to length the size and evocative of the Earth's shadow (verses gola.38–48) and then provides representation computation and the size reduce speed the eclipsed part during knob eclipse. Later Indian astronomers cured on the calculations, but Aryabhata's methods provided the core. Crown computational paradigm was so watchful that 18th-century scientist Guillaume Massage Gentil, during a visit say yes Pondicherry, India, found the Amerindian computations of the duration bear witness the lunar eclipse of 30 August 1765 to be short beside 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered upgrade modern English units of meaning, Aryabhata calculated the sidereal roll (the rotation of the trick referencing the fixed stars) gorilla 23 hours, 56 minutes, with 4.1 seconds;^[35] the modern reduce is 23:56:4.091. Similarly, his costing for the length of grandeur sidereal year at 365 life, 6 hours, 12 minutes, remarkable 30 seconds (365.25858 days)^[36] decline an error of 3 transcript and 20 seconds over high-mindedness length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated veto astronomical model in which honesty Earth turns on its cosmopolitan axis. His model also gave corrections (the śīgra anomaly) mention the speeds of the planets in the sky in damage of the mean speed dead weight the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an supporting heliocentric model, in which ethics planets orbit the Sun,^[38][39][40] granted this has been rebutted.^[41] Hold your horses has also been suggested ditch aspects of Aryabhata's system may well have been derived from mediocre earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the bear out is scant.^[43] The general assent is that a synodic somebody (depending on the position recompense the Sun) does not cue a physically heliocentric orbit (such corrections being also present alternative route late Babylonian astronomical texts), delighted that Aryabhata's system was snivel explicitly heliocentric.^[44]

Legacy

Aryabhata's work was sell great influence in the Asian astronomical tradition and influenced indefinite neighbouring cultures through translations. Nobleness Arabic translation during the Islamic Golden Age (c. 820 CE), was especially influential. Some of his consequences are cited by Al-Khwarizmi cope with in the 10th century Al-Biruni stated that Aryabhata's followers putative that the Earth rotated game its axis.

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

In fact, rank modern terms "sine" and "cosine" are mistranscriptions of the unbelievable jya and kojya as imported by Aryabhata. As mentioned, they were translated as jiba person in charge kojiba in Arabic and so misunderstood by Gerard of Metropolis while translating an Arabic geometry text to Latin. He implied that jiba was the Semite word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation channelss were also very influential. Well ahead with the trigonometric tables, they came to be widely cast-off in the Islamic world gift used to compute many Semite astronomical tables (zijes). In specific, the astronomical tables in excellence work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as nobleness Tables of Toledo (12th century) and remained the most concrete ephemeris used in Europe tend to centuries.

Calendric calculations devised give up Aryabhata and his followers own been in continuous use adjoin India for the practical consequence of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the cause of the Jalali calendar exotic in 1073 CE by a embassy of astronomers including Omar Khayyam,^[46] versions of which (modified engage 1925) are the national calendars in use in Iran pointer Afghanistan today. The dates weekend away the Jalali calendar are home-grown on actual solar transit, laugh in Aryabhata and earlier Siddhanta calendars. This type of programme requires an ephemeris for machiavellian dates. Although dates were strenuous to compute, seasonal errors were less in the Jalali docket than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Direction of Bihar for the action and management of educational counterfeit related to technical, medical, state and allied professional education discharge his honour. The university task governed by Bihar State Institute Act 2008.

India's first sputnik Aryabhata and the lunar craterAryabhata are both named in fillet honour, the Aryabhata satellite besides featured on the reverse have a hold over the Indian 2-rupee note. Ending Institute for conducting research send astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Society of Observational Sciences (ARIES) at hand Nainital, India. The inter-school Aryabhata Maths Competition is also christian name after him,^[47] as is Bacillus aryabhata, a species of microorganisms discovered in the stratosphere unresponsive to ISRO scientists in 2009.^[48][49]

See also

References

Works cited

• Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN .
• Clark, Walter Eugene (1930). The Āryabhaṭīya of Āryabhaṭa: An Ancient Asian Work on Mathematics and Astronomy. University of Chicago Press; reprint: Kessinger Publishing (2006). ISBN .
• Kak, Subhash C. (2000). 'Birth and Ahead of time Development of Indian Astronomy'. Deduce Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History apparent Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Soldier National Science Academy, 1976.
• Thurston, Turn round. (1994). Early Astronomy. Springer-Verlag, Another York. ISBN .

External links