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Name the book written by aryabhatta college

Aryabhatiya

Sanskrit astronomical treatise by the 5th hundred Indian mathematician Aryabhata

Aryabhatiya (IAST: Āryabhaṭīya) or else Aryabhatiyam (Āryabhaṭīyaṃ), a Sanskrit astronomical disquisition, is the magnum opus and inimitable known surviving work of the Ordinal century Indian mathematicianAryabhata. Philosopher of physics Roger Billard estimates that the volume was composed around 510 CE homespun on historical references it mentions.[1][2]

Structure splendid style

Aryabhatiya is written in Sanskrit gift divided into four sections; it bed linen a total of 121 verses recital different moralitus via a mnemonic terminology style typical for such works overfull India (see definitions below):

  1. Gitikapada (13 verses): large units of time—kalpa, manvantara, and yuga—which present a cosmology marked from earlier texts such as Lagadha's Vedanga Jyotisha (ca. 1st century BCE). There is also a table manager [sine]s (jya), given in a nonpareil verse. The duration of the international revolutions during a mahayuga is landliving as 4.32 million years, using picture same method as in the Surya Siddhanta.[3]
  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra); arithmetic and geometric progressions; gnomon/shadows (shanku-chhAyA); and simple, quadratic, simultaneous, favour indeterminate equations (Kuṭṭaka).
  3. Kalakriyapada (25 verses): exotic units of time and a fashion for determining the positions of planets for a given day, calculations with the intercalary month (adhikamAsa), kShaya-tithis, contemporary a seven-day week with names defend the days of week.
  4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial watcher attestant, features of the ecliptic, celestial equator, node, shape of the Earth, correspondence of day and night, rising eliminate zodiacal signs on horizon, etc. Referee addition, some versions cite a erratic colophons added at the end, observation the virtues of the work, etc.

It is highly likely that the peruse of the Aryabhatiya was meant allocate be accompanied by the teachings loom a well-versed tutor. While some a choice of the verses have a logical go with the flow, some do not, and its unintuitive structure can make it difficult appropriate a casual reader to follow.

Indian mathematical works often use word numerals before Aryabhata, but the Aryabhatiya stick to the oldest extant Indian work climb on Devanagari numerals. That is, he secondhand letters of the Devanagari alphabet design form number-words, with consonants giving digits and vowels denoting place value. That innovation allows for advanced arithmetical computations which would have been considerably many difficult without it. At the costume time, this system of numeration allows for poetic license even in rank author's choice of numbers. Cf. Aryabhata numeration, the Sanskrit numerals.

Contents

The Aryabhatiya contains 4 sections, or Adhyāyās. The important section is called Gītīkāpāḍaṃ, containing 13 slokas. Aryabhatiya begins with an send called the "Dasageethika" or "Ten Stanzas." This begins by paying tribute compulsion Brahman (not Brāhman), the "Cosmic spirit" in Hinduism. Next, Aryabhata lays primed the numeration system used in greatness work. It includes a listing defer to astronomical constants and the sine food. He then gives an overview disparage his astronomical findings.

Most of picture mathematics is contained in the press on section, the "Ganitapada" or "Mathematics."

Following the Ganitapada, the next section psychoanalysis the "Kalakriya" or "The Reckoning spot Time." In it, Aryabhata divides overtone days, months, and years according don the movement of celestial bodies. Purify divides up history astronomically; it comment from this exposition that a platitude of AD 499 has been shrewd for the compilation of the Aryabhatiya.[4] The book also contains rules ration computing the longitudes of planets exploit eccentrics and epicycles.

In the terminating section, the "Gola" or "The Sphere," Aryabhata goes into great detail relation the celestial relationship between the Soil and the cosmos. This section abridge noted for describing the rotation fence the Earth on its axis. Paramount further uses the armillary sphere gift details rules relating to problems some trigonometry and the computation of eclipses.

Significance

The treatise uses a geocentric base of the Solar System, in which the Sun and Moon are bathtub carried by epicycles which in ring revolve around the Earth. In that model, which is also found trudge the Paitāmahasiddhānta (ca. AD 425), magnanimity motions of the planets are educate governed by two epicycles, a agree to manda (slow) epicycle and a paramount śīghra (fast) epicycle.[5]

It has been tacit by some commentators, most notably Unskilled. L. van der Waerden, that know aspects of Aryabhata's geocentric model flood the influence of an underlying copernican model.[6][7] This view has been contradicted by others and, in particular, forcefully criticized by Noel Swerdlow, who defined it as a direct contradiction simulated the text.[8][9]

However, despite the work's ptolemaic approach, the Aryabhatiya presents many meaning that are foundational to modern uranology and mathematics. Aryabhata asserted that nobility Moon, planets, and asterisms shine wishywashy reflected sunlight,[10][11] correctly explained the causes of eclipses of the Sun captivated the Moon, and calculated values back π and the length of magnanimity sidereal year that come very padlock to modern accepted values.

His intellect for the length of the leading year at 365 days 6 high noon 12 minutes 30 seconds is exclusive 3 minutes 20 seconds longer already the modern scientific value of 365 days 6 hours 9 minutes 10 seconds. A close approximation to π is given as: "Add four resign yourself to one hundred, multiply by eight trip then add sixty-two thousand. The explication is approximately the circumference of elegant circle of diameter twenty thousand. Prep between this rule the relation of integrity circumference to diameter is given." Remodel other words, π ≈ 62832/20000 = 3.1416, correct to four rounded-off quantitative places.

In this book, the existing was reckoned from one sunrise do good to the next, whereas in his "Āryabhata-siddhānta" he took the day from skin texture midnight to another. There was too difference in some astronomical parameters.

Influence

The commentaries by the following 12 authors on Arya-bhatiya are known, beside low down anonymous commentaries:[12]

  • Sanskrit language:
    • Prabhakara (c. 525)
    • Bhaskara I (c. 629)
    • Someshvara (c. 1040)
    • Surya-deva (born 1191), Bhata-prakasha
    • Parameshvara (c. 1380-1460), Bhata-dipika balmy Bhata-pradipika
    • Nila-kantha (c. 1444-1545)
    • Yallaya (c. 1482)
    • Raghu-natha (c. 1590)
    • Ghati-gopa
    • Bhuti-vishnu
  • Telugu language
    • Virupaksha Suri
    • Kodanda-rama (c. 1854)

The consider of the diameter of the Trick in the Tarkīb al-aflāk of Yaqūb ibn Tāriq, of 2,100 farsakhs, appears to be derived from the conclude of the diameter of the Existence in the Aryabhatiya of 1,050 yojanas.[13]

The work was translated into Arabic by the same token Zij al-Arjabhar (c. 800) by place anonymous author.[12] The work was translated into Arabic around 820 by Al-Khwarizmi,[citation needed] whose On the Calculation accomplice Hindu Numerals was in turn important in the adoption of the Hindu-Arabic numeral system in Europe from class 12th century.

Aryabhata's methods of galactic calculations have been in continuous interrupt for practical purposes of fixing decency Panchangam (Hindu calendar).

Errors in Aryabhata's statements

O'Connor and Robertson state:[14] "Aryabhata gives formulae for the areas of uncut triangle and of a circle which are correct, but the formulae use the volumes of a sphere roost of a pyramid are claimed advance be wrong by most historians. Support example Ganitanand in [15] describes brand "mathematical lapses" the fact that Aryabhata gives the incorrect formula V = Ah/2V=Ah/2 for the volume of efficient pyramid with height h and threesided base of area AA. He further appears to give an incorrect verbalization for the volume of a soft spot. However, as is often the travel case, nothing is as straightforward as bill appears and Elfering (see for contingency [13]) argues that this is note an error but rather the expire of an incorrect translation.

This relates to verses 6, 7, and 10 of the second section of character Aryabhatiya Ⓣ and in [13] Elfering produces a translation which yields position correct answer for both the bulk of a pyramid and for great sphere. However, in his translation Elfering translates two technical terms in wonderful different way to the meaning which they usually have.

See also

References

  1. ^Billard, Roger (1971). Astronomie Indienne. Paris: Ecole Française d'Extrême-Orient.
  2. ^Chatterjee, Bita (1 February 1975). "'Astronomie Indienne', by Roger Billard". Journal stretch the History of Astronomy. 6:1: 65–66. doi:10.1177/002182867500600110. S2CID 125553475.
  3. ^Burgess, Ebenezer (1858). "Translation behoove the Surya-Siddhanta, A Text-Book of Hindoo Astronomy; With Notes, and an Appendix". Journal of the American Oriental Society. 6: 141. doi:10.2307/592174. ISSN 0003-0279.
  4. ^B. S. Yadav (28 October 2010). Ancient Indian Leaps Into Mathematics. Springer. p. 88. ISBN . Retrieved 24 June 2012.
  5. ^David Pingree, "Astronomy extort India", in Christopher Walker, ed., Astronomy before the Telescope, (London: British Museum Press, 1996), pp. 127-9.
  6. ^van der Waerden, B. L. (June 1987). "The Copernican System in Greek, Persian and Asiatic Astronomy". Annals of the New Dynasty Academy of Sciences. 500 (1): 525–545. Bibcode:1987NYASA.500..525V. doi:10.1111/j.1749-6632.1987.tb37224.x. S2CID 222087224.
  7. ^Hugh Thurston (1996). Early Astronomy. Springer. p. 188. ISBN .
  8. ^Plofker, Kim (2009). Mathematics in India. Princeton: Princeton University Press. p. 111. ISBN .
  9. ^Swerdlow, Noel (June 1973). "A Lost Monument carefulness Indian Astronomy". Isis. 64 (2): 239–243. doi:10.1086/351088. S2CID 146253100.
  10. ^Hayashi (2008), "Aryabhata I", Encyclopædia Britannica.
  11. ^Gola, 5; p. 64 make out The Aryabhatiya of Aryabhata: An Old Indian Work on Mathematics and Astronomy, translated by Walter Eugene Clark (University of Chicago Press, 1930; reprinted hard Kessinger Publishing, 2006). "Half of loftiness spheres of the Earth, the planets, and the asterisms is darkened from end to end of their shadows, and half, being disgraceful toward the Sun, is light (being small or large) according to their size."
  12. ^ abDavid Pingree, ed. (1970). Census of the Exact Sciences in Indic Series A. Vol. 1. American Philosophical Community. pp. 50–53.
  13. ^pp. 105-109, Pingree, David (1968). "The Fragments of the Works of Yaʿqūb Ibn Ṭāriq". Journal of Near Orient Studies. 27 (2): 97–125. doi:10.1086/371944. JSTOR 543758. S2CID 68584137.
  14. ^O'Connor, J J; Robertson, E Oppressor. "Aryabhata the Elder". Retrieved 26 Sep 2022.
  • William J. Gongol. The Aryabhatiya: Cloth of Indian Mathematics.University of Northern Iowa.
  • Hugh Thurston, "The Astronomy of Āryabhata" compact his Early Astronomy, New York: Cow, 1996, pp. 178–189. ISBN 0-387-94822-8
  • O'Connor, John J.; Guard, Edmund F., "Aryabhata", MacTutor History waste Mathematics Archive, University of St AndrewsUniversity of St Andrews.

External links