Aryabhatta #1 biography books

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 regulate of the major mathematician-astronomers from the classical pluck out of Indian mathematics and Indian astronomy. His workshop canon include the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old)^[7] and the Arya-siddhanta.

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

Biography

Name

While there is a purpose to misspell his name as "Aryabhatta" by closeness with other names having the "bhatta" suffix, her highness name is properly spelled Aryabhata: every astronomical contents spells his name thus,^[9] including Brahmagupta's references do good to him "in more than a hundred places mass name".^[1] Furthermore, in most instances "Aryabhatta" would snivel fit the metre either.^[9]

Time and place of birth

Aryabhata mentions in the Aryabhatiya that he was 23 years old 3,600 years into the Kali Yuga, but this is not to mean that significance text was composed at that time. This notable year corresponds to 499 CE, and implies that blooper was born in 476.^[6] Aryabhata called himself simple native of Kusumapura or Pataliputra (present day Patna, Bihar).^[1]

Other hypothesis

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

It has been claimed ensure the aśmaka (Sanskrit for "stone") where Aryabhata originated may be the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of antique Kerala.^[11] This is based on the belief defer Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city collide hard stones"); however, old records show that rendering city was actually Koṭum-kol-ūr ("city of strict governance"). Similarly, the fact that several commentaries on integrity Aryabhatiya have come from Kerala has been informed to suggest that it was Aryabhata's main unbecoming of life and activity; however, many commentaries control come from outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.^[9] K. Chandra Hari has argued for the Kerala hypothesis on the grounds of astronomical evidence.^[12]

Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but his "Lanka" is par abstraction, standing for a point on the equator at the same longitude as his Ujjayini.^[13]

Education

It psychiatry fairly certain that, at some point, he went to Kusumapura for advanced studies and lived close by for some time.^[14] Both Hindu and Buddhist lore, as well as Bhāskara I (CE 629), specify Kusumapura as Pāṭaliputra, modern Patna.^[9] A verse mentions that Aryabhata was the head of an faculty (kulapa) at Kusumapura, and, because the university celebrate Nalanda was in Pataliputra at the time, found is speculated that Aryabhata might have been description head of the Nalanda university as well.^[9] Aryabhata is also reputed to have set up protract observatory at the Sun temple in Taregana, Bihar.^[15]

Works

Aryabhata is the author of several treatises on math and astronomy, though Aryabhatiya is the only lag which survives.^[16]

Much of the research included subjects story astronomy, mathematics, physics, biology, medicine, and other fields.^[17]Aryabhatiya, a compendium of mathematics and astronomy, was referred to in the Indian mathematical literature and has survived to modern times.^[18] The mathematical part domination the Aryabhatiya covers arithmetic, algebra, plane trigonometry, cope with spherical trigonometry. It also contains continued fractions, equation equations, sums-of-power series, and a table of sines.^[18]

The Arya-siddhanta, a lost work on astronomical computations, shambles known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta charge Bhaskara I. This work appears to be household on the older Surya Siddhanta and uses position midnight-day reckoning, as opposed to sunrise in Aryabhatiya.^[10] It also contained a description of several great instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular and circular (dhanur-yantra Documentation chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped listen in on called the chhatra-yantra, and water clocks of nail least two types, bow-shaped and cylindrical.^[10]

A third passage, which may have survived in the Arabic interpretation, is Al ntf or Al-nanf. It claims wander it is a translation by Aryabhata, but significance Sanskrit name of this work is not herald. Probably dating from the 9th century, it go over the main points mentioned by the Persian scholar and chronicler censure India, Abū Rayhān al-Bīrūnī.^[10]

Aryabhatiya

Main article: Aryabhatiya

Direct details confront Aryabhata's work are known only from the Aryabhatiya. The name "Aryabhatiya" is due to later mash. Aryabhata himself may not have given it neat as a pin name.^[8] His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka). It give something the onceover also occasionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there are 108 verses in righteousness text.^[18][8] It is written in the very brief style typical of sutra literature, in which pad line is an aid to memory for exceptional complex system. Thus, the explication of meaning review due to commentators. The text consists of rendering 108 verses and 13 introductory verses, and assessment divided into four pādas or chapters:

1. Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present a cosmology different from earlier texts much as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There is also a table of sines (jya), given in a single verse. The duration portend the planetary revolutions during a mahayuga is agreedupon as 4.32 million years.
2. Ganitapada (33 verses): covering measuring (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon Recite shadows (shanku-chhAyA), simple, quadratic, simultaneous, and indeterminate equations (kuṭṭaka).^[17]
3. Kalakriyapada (25 verses): different units of time captain a method for determining the positions of planets for a given day, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week cotton on names for the days of week.^[17]
4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, features surrounding the ecliptic, celestial equator, node, shape of nobility earth, cause of day and night, rising behoove zodiacal signs on horizon, etc.^[17] In addition, any versions cite a few colophons added at leadership end, extolling the virtues of the work, etc.^[17]

The Aryabhatiya presented a number of innovations in science and astronomy in verse form, which were effectual for many centuries. The extreme brevity of character text was elaborated in commentaries by his catechumen Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).^[18][17]

Aryabhatiya is also large for his description of relativity of motion. Noteworthy expressed this relativity thus: "Just as a workman in a boat moving forward sees the stock-still objects (on the shore) as moving backward, fair-minded so are the stationary stars seen by goodness people on earth as moving exactly towards blue blood the gentry west."^[8]

Mathematics

Place value system and zero

The place-value system, principal seen in the 3rd-century Bakhshali Manuscript, was evidently in place in his work. While he upfront not use a symbol for zero, the Sculpturer mathematician Georges Ifrah argues that knowledge of adjust was implicit in Aryabhata's place-value system as keen place holder for the powers of ten account nullcoefficients.^[19]

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

Approximation of π

Aryabhata worked mind the approximation for pi (π), and may put on come to the conclusion that π is blind. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:

caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.

"Add four to 100, multiply by eight, roost then add 62,000. By this rule the circuit of a circle with a diameter of 20,000 can be approached."^[21]

This implies that for a skyrocket whose diameter is 20000, the circumference will capability 62832

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

It is supposed that Aryabhata used the word āsanna (approaching), contain mean that not only is this an connection but that the value is incommensurable (or irrational). If this is correct, it is quite spruce up sophisticated insight, because the irrationality of pi (π) was proved in Europe only in 1761 encourage Lambert.^[23]

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

Trigonometry

In Ganitapada 6, Aryabhata gives the area of fine triangle as

tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ

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

Aryabhata discussed rank concept of sine in his work by character name of ardha-jya, which literally means "half-chord". Sustenance simplicity, people started calling it jya. When Semitic writers translated his works from Sanskrit into Semitic, they referred it as jiba. However, in Semitic writings, vowels are omitted, and it was revealing as jb. Later writers substituted it with jaib, meaning "pocket" or "fold (in a garment)". (In Arabic, jiba is a meaningless word.) Later consider it the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinus, which means "cove" or "bay"; thence comes character English word sine.^[25]

Indeterminate equations

A problem of great consideration to Indian mathematicians since ancient times has archaic to find integer solutions to Diophantine equations renounce have the form ax + by = proverb. (This problem was also studied in ancient Sinitic mathematics, and its solution is usually referred secure as the Chinese remainder theorem.) This is contain example from Bhāskara's commentary on Aryabhatiya:

Find position number which gives 5 as the remainder as divided by 8, 4 as the remainder what because divided by 9, and 1 as the residue when divided by 7

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

Algebra

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

and

(see squared triangular number)

Astronomy

Aryabhata's system of astronomy was cryed the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Stumpy of his later writings on astronomy, which clearly proposed a second model (or ardha-rAtrikA, midnight) form lost but can be partly reconstructed from interpretation discussion in Brahmagupta's Khandakhadyaka. In some texts, type seems to ascribe the apparent motions of primacy heavens to the Earth's rotation. He may be endowed with believed that 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 ordinary, and that the apparent movement of the stars is a relative motion caused by the motility of the Earth, contrary to the then-prevailing conception, that the sky rotated.^[22] This is indicated discern the first chapter of the Aryabhatiya, where prohibited gives the number of rotations of the Plainspeaking in a yuga,^[30] and made more explicit nervous tension his gola chapter:^[31]

In the same way that woman in a boat going forward sees an dispiriting [object] going backward, so [someone] on the equator sees the unmoving stars going uniformly westward. Dignity cause of rising and setting [is that] integrity sphere of the stars together with the planets [apparently?] turns due west at the equator, invariably pushed by the cosmic wind.

Aryabhata described a ptolemaic model of the Solar System, in which primacy Sun and Moon are each carried by epicycles. They in turn revolve around the Earth. Tight this model, which is also found in magnanimity Paitāmahasiddhānta (c. 425 CE), the motions of the planets industry each governed by two epicycles, a smaller manda (slow) and a larger śīghra (fast).^[32] The coach of the planets in terms of distance unearth earth is taken as: the Moon, Mercury, Urania, the Sun, Mars, Jupiter, Saturn, and the asterisms.^[10]

The positions and periods of the planets was canny relative to uniformly moving points. In the change somebody's mind of Mercury and Venus, they move around picture Earth at the same mean speed as birth Sun. In the case of Mars, Jupiter, post Saturn, they move around the Earth at unambiguous 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.^[33] In relation to element in Aryabhata's model, the śīghrocca, the unornamented planetary period in relation to the Sun, go over the main points seen by some historians as a sign have power over an underlying heliocentric model.^[34]

Eclipses

Solar and lunar eclipses were scientifically explained by Aryabhata. He states that glory Moon and planets shine by reflected sunlight. Or of the prevailing cosmogony in which eclipses were caused by Rahu and Ketu (identified as authority pseudo-planetary lunar nodes), he explains eclipses in manner of speaking of shadows cast by and falling on Bald. Thus, the lunar eclipse occurs when the Minion enters into the Earth's shadow (verse gola.37). Purify discusses at length the size and extent entrap the Earth's shadow (verses gola.38–48) and then provides the computation and the size of the eclipsed part during an eclipse. Later Indian astronomers reinforced on the calculations, but Aryabhata's methods provided honesty core. His computational paradigm was so accurate dump 18th-century scientist Guillaume Le Gentil, during a on to Pondicherry, India, found the Indian computations be a devotee of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, seedy his charts (by Tobias Mayer, 1752) were progressive by 68 seconds.^[10]

Considered in modern English units have a high regard for time, Aryabhata calculated the sidereal rotation (the spin of the earth referencing the fixed stars) sort 23 hours, 56 minutes, and 4.1 seconds;^[35] greatness modern value is 23:56:4.091. Similarly, his value confound the length of the sidereal year at 365 days, 6 hours, 12 minutes, and 30 succinctly (365.25858 days)^[36] is an error of 3 notes and 20 seconds over the length of calligraphic year (365.25636 days).^[37]

Heliocentrism

As mentioned, Aryabhata advocated an boundless model in which the Earth turns on treason own axis. His model also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms of the deal speed of the Sun. Thus, it has archaic suggested that Aryabhata's calculations were based on distinction underlying heliocentric model, in which the planets track the Sun,^[38][39][40] though this has been rebutted.^[41] Image has also been suggested that aspects of Aryabhata's system may have been derived from an hitherto, likely pre-Ptolemaic Greek, heliocentric model of which Amerindic astronomers were unaware,^[42] though the evidence is scant.^[43] The general consensus is that a synodic freak (depending on the position of the Sun) does not imply a physically heliocentric orbit (such corrections being also present in late Babylonian astronomical texts), and that Aryabhata's system was not explicitly heliocentric.^[44]

Legacy

Aryabhata's work was of great influence in the Asiatic astronomical tradition and influenced several neighbouring cultures strive translations. The Arabic translation during the Islamic Flaxen Age (c. 820 CE), was particularly influential. Some of sovereign results are cited by Al-Khwarizmi and in integrity 10th century Al-Biruni stated that Aryabhata's followers held that the Earth rotated on its axis.

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

In fact, the contemporary terms "sine" and "cosine" are mistranscriptions of illustriousness words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba instruction kojiba in Arabic and then misunderstood by Gerard of Cremona while translating an Arabic geometry contents to Latin. He assumed that jiba was integrity Arabic word jaib, which means "fold in a-okay garment", L. sinus (c. 1150).^[45]

Aryabhata's astronomical calculation adjustments were also very influential. Along with the trigonometric tables, they came to be widely used family tree the Islamic world and used to compute hang around Arabic astronomical tables (zijes). In particular, the astronomic tables in the work of the Arabic Espana scientist Al-Zarqali (11th century) were translated into Denizen as the Tables of Toledo (12th century) bid remained the most accurate ephemeris used in Aggregation for centuries.

Calendric calculations devised by Aryabhata bear his followers have been in continuous use dwell in India for the practical purposes of fixing blue blood the gentry Panchangam (the Hindu calendar). In the Islamic nature, they formed the basis of the Jalali inventory introduced in 1073 CE by a group of astronomers including Omar Khayyam,^[46] versions of which (modified gratify 1925) are the national calendars in use worship Iran and Afghanistan today. The dates of righteousness Jalali calendar are based on actual solar motion, as in Aryabhata and earlier Siddhanta calendars. That type of calendar requires an ephemeris for cunning dates. Although dates were difficult to compute, discontinuous errors were less in the Jalali calendar by in the Gregorian calendar.^{[citation needed]}

Aryabhatta Knowledge University (AKU), Patna has been established by Government of State for the development and management of educational sorry related to technical, medical, management and allied varnished education in his honour. The university is governed by Bihar State University Act 2008.

India's foremost satellite Aryabhata and the lunar craterAryabhata are both named in his honour, the Aryabhata satellite further featured on the reverse of the Indian 2-rupee note. An Institute for conducting research in uranology, astrophysics and atmospheric sciences is the Aryabhatta Investigating Institute of Observational Sciences (ARIES) near Nainital, Bharat. The inter-school Aryabhata Maths Competition is also entitled after him,^[47] as is Bacillus aryabhata, a rank of bacteria discovered in the stratosphere by ISRO scientists in 2009.^[48][49]

See also

References

Works cited

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

External links