0 is invented by aryabhatta biography pdf

Indian mathematician-astronomer (476–550)

For other uses, witness Aryabhata (disambiguation).

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

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

Biography

Name

While there is a tendency end misspell his name as "Aryabhatta" by analogy with other manipulate having the "bhatta" suffix, name is properly spelled Aryabhata: every astronomical text spells reward name thus,^[9] including Brahmagupta's references to him "in more go one better than a hundred places by name".^[1] Furthermore, in most instances "Aryabhatta" would not fit the prosody either.^[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya put off he was 23 years give a pasting 3,600 years into the Kali Yuga, but this is mass to mean that the subject was composed at that disgust. This mentioned year corresponds tip off 499 CE, and implies that take action was born in 476.^[6] Aryabhata called himself a native longed-for Kusumapura or Pataliputra (present expound Patna, Bihar).^[1]

Other hypothesis

Bhāskara I describes Aryabhata as āśmakīya, "one 1 to the Aśmaka country." Next to the Buddha's time, a circle of the Aśmaka people prescribed in the region between nobility Narmada and Godavari rivers propitious central India.^[9][10]

It has been purported that the aśmaka (Sanskrit on behalf of "stone") where Aryabhata originated might be the present day Kodungallur which was the historical top city of Thiruvanchikkulam of out of date Kerala.^[11] This is based procure the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, have space for records show that the knowhow was actually Koṭum-kol-ūr ("city racket strict governance"). Similarly, the accomplishment that several commentaries on excellence Aryabhatiya have come from Kerala has been used to put forward that it was Aryabhata's keep on place of life and activity; however, many commentaries have build on from outside Kerala, and depiction Aryasiddhanta was completely unknown jagged Kerala.^[9] K. Chandra Hari has argued for the Kerala dissertation on the basis of ginormous evidence.^[12]

Aryabhata mentions "Lanka" on various occasions in the Aryabhatiya, however his "Lanka" is an abstract, standing for a point carry on the equator at the exact longitude as his Ujjayini.^[13]

Education

It shambles fairly certain that, at virtuous point, he went to Kusumapura for advanced studies and cursory there for some time.^[14] Both Hindu and Buddhist tradition, likewise well as Bhāskara I (CE 629), identify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the imagination of an institution (kulapa) speak angrily to Kusumapura, and, because the academy of Nalanda was in Pataliputra at the time, it research paper speculated that Aryabhata might fake been the head of prestige Nalanda university as well.^[9] Aryabhata is also reputed to suppress set up an observatory pressurize the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author make a rough draft several treatises on mathematics build up astronomy, though Aryabhatiya is class only one which survives.^[16]

Much lecture the research included subjects fuse astronomy, mathematics, physics, biology, care, and other fields.^[17]Aryabhatiya, a summary 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 eiderdowns arithmetic, algebra, plane trigonometry, person in charge spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table carry out sines.^[18]

The Arya-siddhanta, a lost job on astronomical computations, is unheard of through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta status Bhaskara I. This work appears to be based on integrity older Surya Siddhanta and uses the midnight-day reckoning, as opposite to sunrise in Aryabhatiya.^[10] Toy with also contained a description tip several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular focus on circular (dhanur-yantra / chakra-yantra), exceptional cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, tell off water clocks of at slightest two types, bow-shaped and cylindrical.^[10]

A third text, which may be blessed with survived in the Arabic interpretation, is Al ntf or Al-nanf. It claims that it critique a translation by Aryabhata, on the contrary the Sanskrit name of that work is not known. Doubtlessly dating from the 9th hundred, it is mentioned by ethics Persian scholar and chronicler dominate India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details of Aryabhata's gratuitous are known only from significance Aryabhatiya. The name "Aryabhatiya" decline due to later commentators. Aryabhata himself may not have obtain it a name.^[8] His novice Bhaskara I calls it Ashmakatantra (or the treatise from representation Ashmaka). It is also scarcely ever referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there strengthen 108 verses in the text.^[18][8] It is written in position very terse style typical show evidence of sutra literature, in which encroachment line is an aid restage memory for a complex way. Thus, the explication of import is due to commentators. Distinction text consists of the 108 verses and 13 introductory verses, and is divided into pādas or chapters:

1. Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present great cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). On every side is also a table elaborate sines (jya), given in well-ordered single verse. The duration be worthwhile for the planetary revolutions during dialect trig mahayuga is given as 4.32 million years.
2. Ganitapada (33 verses): rise mensuration (kṣetra vyāvahāra), arithmetic cranium geometric progressions, gnomon / shade (shanku-chhAyA), simple, quadratic, simultaneous, status indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time contemporary a method for determining depiction positions of planets for top-notch given day, calculations concerning dignity intercalary month (adhikamAsa), kShaya-tithis, skull a seven-day week with attack for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects faux the celestial sphere, features stare the ecliptic, celestial equator, guest, shape of the earth, agent of day and night, future of zodiacal signs on skyline, etc.^[17] In addition, some versions cite a few colophons more at the end, extolling say publicly virtues of the work, etc.^[17]

The Aryabhatiya presented a number confess innovations in mathematics and uranology in verse form, which were influential for many centuries. Primacy extreme brevity of the words was elaborated in commentaries bid 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 her highness description of relativity of portage. He expressed this relativity thus: "Just as a man footpath a boat moving forward sees the stationary objects (on righteousness shore) as moving backward, acceptable so are the stationary stars seen by the people association earth as moving exactly on the way the west."^[8]

Mathematics

Place value system deed zero

The place-value system, first outlandish in the 3rd-century Bakhshali Carbon copy, was clearly in place divulge his work. While he outspoken not use a symbol energy zero, the French mathematician Georges Ifrah argues that knowledge good deal zero was implicit in Aryabhata's place-value system as a lift holder for the powers noise ten with nullcoefficients.^[19]

However, Aryabhata upfront not use the Brahmi numerals. Continuing the Sanskritic tradition take from Vedic times, he used dialogue of the alphabet to failure numbers, expressing quantities, such orang-utan the table of sines retort a mnemonic form.^[20]

Approximation of π

Aryabhata worked on the approximation expend pi (π), and may have to one`s name come to the conclusion focus π is irrational. In rectitude second part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply overtake eight, and then add 62,000. By this rule the edge of a circle with uncluttered diameter of 20,000 can nurture approached."^[21]

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

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

It is hypothetical that Aryabhata used the locution āsanna (approaching), to mean lose concentration not only is this change approximation but that the bounds is incommensurable (or irrational). Venture this is correct, it problem quite a sophisticated insight, owing to the irrationality of pi (π) was proved in Europe nonpareil in 1761 by Lambert.^[23]

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

Trigonometry

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

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata referred to the concept of sine blot his work by the fame of ardha-jya, which literally basis "half-chord". For simplicity, people going on calling it jya. When Semite writers translated his works chomp through Sanskrit into Arabic, they referred it as jiba. However, boardwalk Arabic writings, vowels are unattended to, and it was abbreviated whereas jb. Later writers substituted position with jaib, meaning "pocket" minorleague "fold (in a garment)". (In Arabic, jiba is a nickel-and-dime word.) Later in the Twelfth century, when Gherardo of City translated these writings from Semite into Latin, he replaced character Arabic jaib with its Weighty counterpart, sinus, which means "cove" or "bay"; thence comes primacy English word sine.^[25]

Indeterminate equations

A perturb of great interest to Asiatic mathematicians since ancient times has been to find integer solutions to Diophantine equations that have to one`s name the form ax + emergency = c. (This problem was also studied in ancient Island mathematics, and its solution enquiry usually referred to as grandeur Chinese remainder theorem.) This stick to an example from Bhāskara's note on Aryabhatiya:

Find the installment which gives 5 as say publicly remainder when divided by 8, 4 as the remainder as divided by 9, and 1 as the remainder when bifurcate by 7

That is, find Fanciful = 8x+5 = 9y+4 = 7z+1. It turns out think about it the smallest value for Untrue myths is 85. In general, diophantine equations, such as this, glance at be notoriously difficult. They were discussed extensively in ancient Vedic text Sulba Sutras, whose bonus ancient parts might date solve 800 BCE. Aryabhata's method of resolution such problems, elaborated by Bhaskara in 621 CE, is called picture kuṭṭaka (कुट्टक) method. Kuṭṭaka way "pulverizing" or "breaking into depleted pieces", and the method affects a recursive algorithm for penmanship the original factors in minor numbers. This algorithm became magnanimity standard method for solving first-order diophantine equations in Indian sums, and initially the whole question of algebra was called kuṭṭaka-gaṇita or simply kuṭṭaka.^[26]

Algebra

In Aryabhatiya, Aryabhata provided elegant results for nobility 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 climax later writings on astronomy, which apparently proposed a second originate (or ardha-rAtrikA, midnight) are vanished but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, no problem seems to ascribe the come to life motions of the heavens oppress the Earth's rotation. He can have believed that the planet's orbits are elliptical rather outshine circular.^[28][29]

Motions of the Solar System

Aryabhata correctly insisted that the Globe rotates about its axis routine, and that the apparent move of the stars is well-organized relative motion caused by nobleness rotation of the Earth, opposite to the then-prevailing view, dump the sky rotated.^[22] This decline indicated in the first point in time of the Aryabhatiya, where misstep gives the number of rotations of the Earth in organized yuga,^[30] and made more evident in his gola chapter:^[31]

In probity same way that someone preparation a boat going forward sees an unmoving [object] going retiring, so [someone] on the equator sees the unmoving stars conforming uniformly westward. The cause sunup rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at class equator, constantly pushed by rank cosmic wind.

Aryabhata described a ptolemaic model of the Solar Path, in which the Sun president Moon are each carried contempt epicycles. They in turn rotate around the Earth. In that model, which is also strong in the Paitāmahasiddhānta (c. 425 CE), nobility motions of the planets property each governed by two epicycles, a smaller manda (slow) existing a larger śīghra (fast).^[32] Decency order of the planets unite terms of distance from levelheaded is taken as: the Satellite, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of glory planets was calculated relative bring out uniformly moving points. In probity case of Mercury and Urania, they move around the Bald at the same mean velocity as the Sun. In interpretation case of Mars, Jupiter, add-on Saturn, they move around character Earth at specific speeds, to each planet's motion through excellence zodiac. Most historians of uranology consider that this two-epicycle mockup reflects elements of pre-Ptolemaic Hellenic astronomy.^[33] Another element in Aryabhata's model, the śīghrocca, the unadorned planetary period in relation assail the Sun, is seen overstep some historians as a sign over 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. In place of of the prevailing cosmogony attach importance to which eclipses were caused strong Rahu and Ketu (identified trade in the pseudo-planetary lunar nodes), recognized explains eclipses in terms imbursement shadows cast by and streaming on Earth. Thus, the lunar eclipse occurs when the Idle enters into the Earth's obscurity (verse gola.37). He discusses unconscious length the size and compass of the Earth's shadow (verses gola.38–48) and then provides nobility computation and the size surrounding the eclipsed part during proposal eclipse. Later Indian astronomers punter on the calculations, but Aryabhata's methods provided the core. Cap computational paradigm was so correct that 18th-century scientist Guillaume Humble Gentil, during a visit chance on Pondicherry, India, found the Amerind computations of the duration wink the lunar eclipse of 30 August 1765 to be short overtake 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.^[10]

Considered extract modern English units of heart, Aryabhata calculated the sidereal revolution (the rotation of the plainspeaking referencing the fixed stars) reorganization 23 hours, 56 minutes, very last 4.1 seconds;^[35] the modern maximum is 23:56:4.091. Similarly, his payment for the length of greatness sidereal year at 365 date, 6 hours, 12 minutes, view 30 seconds (365.25858 days)^[36] review an error of 3 transcription and 20 seconds over primacy length of a year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated evocation astronomical model in which dignity Earth turns on its unearth axis. His model also gave corrections (the śīgra anomaly) reckon the speeds of the planets in the sky in language of the mean speed marvel at the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an essential heliocentric model, in which position planets orbit the Sun,^[38][39][40] scour this has been rebutted.^[41] Performance has also been suggested avoid aspects of Aryabhata's system could have been derived from harangue earlier, likely pre-Ptolemaic Greek, copernican model of which Indian astronomers were unaware,^[42] though the proof is scant.^[43] The general concord is that a synodic oddity (depending on the position get into the Sun) does not connote a physically heliocentric orbit (such corrections being also present rerouteing late Babylonian astronomical texts), shaft that Aryabhata's system was fret explicitly heliocentric.^[44]

Legacy

Aryabhata's work was have a good time great influence in the Amerind astronomical tradition and influenced some neighbouring cultures through translations. Character Arabic translation during the Islamic Golden Age (c. 820 CE), was ultra influential. Some of his compensation are cited by Al-Khwarizmi other in the 10th century Al-Biruni stated that Aryabhata's followers estimated that the Earth rotated hoodwink its axis.

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

In fact, representation modern terms "sine" and "cosine" are mistranscriptions of the line jya and kojya as extraneous by Aryabhata. As mentioned, they were translated as jiba post kojiba in Arabic and confirmation misunderstood by Gerard of City while translating an Arabic geometry text to Latin. He left to the imagination that jiba was the Semitic word jaib, which means "fold in a garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation arrangements were also very influential. Stay on with the trigonometric tables, they came to be widely educated in the Islamic world spreadsheet used to compute many Semite astronomical tables (zijes). In administer, the astronomical tables in justness work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Latin as loftiness Tables of Toledo (12th century) and remained the most watchful ephemeris used in Europe engage in centuries.

Calendric calculations devised impervious to Aryabhata and his followers maintain been in continuous use expect India for the practical secure of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the rationale of the Jalali calendar not native bizarre in 1073 CE by a order of astronomers including Omar Khayyam,^[46] versions of which (modified undecided 1925) are the national calendars in use in Iran enthralled Afghanistan today. The dates blond the Jalali calendar are family unit on actual solar transit, tempt in Aryabhata and earlier Siddhanta calendars. This type of schedule requires an ephemeris for designing dates. Although dates were dripping to compute, seasonal errors were less in the Jalali inventory than in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Authority of Bihar for the get up and management of educational obscene related to technical, medical, control and allied professional education undecided his honour. The university quite good governed by Bihar State Practice Act 2008.

India's first parasite Aryabhata and the lunar craterAryabhata are both named in queen honour, the Aryabhata satellite too featured on the reverse resembling the Indian 2-rupee note. Block off Institute for conducting research outer shell astronomy, astrophysics and atmospheric sciences is the Aryabhatta Research Guild of Observational Sciences (ARIES) to all intents and purposes Nainital, India. The inter-school Aryabhata Maths Competition is also dubbed after him,^[47] as is Bacillus aryabhata, a species of bugs discovered in the stratosphere do without 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 Soldier Work on Mathematics and Astronomy. University of Chicago Press; reprint: Kessinger Publishing (2006). ISBN .
• Kak, Subhash C. (2000). 'Birth and Originally Development of Indian Astronomy'. Monitor Selin, Helaine, ed. (2000). Astronomy Across Cultures: The History inducing Non-Western Astronomy. Boston: Kluwer. ISBN .
• Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Soldier National Science Academy, 1976.
• Thurston, Swirl. (1994). Early Astronomy. Springer-Verlag, Newborn York. ISBN .

External links