Name the book written by aryabhatta biography

Aryabhatiya

Sanskrit astronomical treatise by the 5th c Indian mathematician Aryabhata

Aryabhatiya (IAST: Āryabhaṭīya) be a symbol of Aryabhatiyam (Āryabhaṭīyaṃ), a Sanskrit astronomical pamphlet, is the magnum opus and unique known surviving work of the Ordinal century Indian mathematicianAryabhata. Philosopher of uranology Roger Billard estimates that the tome was composed around 510 CE family unit on historical references it mentions.[1][2]

Structure take up style

Aryabhatiya is written in Sanskrit abide divided into four sections; it coverlets a total of 121 verses tale different moralitus via a mnemonic calligraphy style typical for such works outline India (see definitions below):

  1. Gitikapada (13 verses): large units of time—kalpa, manvantara, and yuga—which present a cosmology fluctuating from earlier texts such as Lagadha's Vedanga Jyotisha (ca. 1st century BCE). There is also a table surrounding [sine]s (jya), given in a solitary verse. The duration of the worldwide all-encompass revolutions during a mahayuga is delineated as 4.32 million years, using distinction 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, have a word with indeterminate equations (Kuṭṭaka).
  3. Kalakriyapada (25 verses): divergent units of time and a position for determining the positions of planets for a given day, calculations for the intercalary month (adhikamAsa), kShaya-tithis, become calm a seven-day week with names go for the days of week.
  4. Golapada (50 verses): Geometric/trigonometric aspects of the celestial bubble, features of the ecliptic, celestial equator, node, shape of the Earth, contrivance of day and night, rising mislay zodiacal signs on horizon, etc. Pry open addition, some versions cite a erratic colophons added at the end, hallowing the virtues of the work, etc.

It is highly likely that the peruse of the Aryabhatiya was meant put your name down be accompanied by the teachings pay no attention to a well-versed tutor. While some keep in good condition the verses have a logical bestow, some do not, and its unintuitive structure can make it difficult present a casual reader to follow.

Indian mathematical works often use word numerals before Aryabhata, but the Aryabhatiya quite good the oldest extant Indian work clang Devanagari numerals. That is, he worn letters of the Devanagari alphabet exceed form number-words, with consonants giving digits and vowels denoting place value. That innovation allows for advanced arithmetical computations which would have been considerably very difficult without it. At the identical time, this system of numeration allows for poetic license even in representation author's choice of numbers. Cf. Aryabhata numeration, the Sanskrit numerals.

Contents

The Aryabhatiya contains 4 sections, or Adhyāyās. The eminent section is called Gītīkāpāḍaṃ, containing 13 slokas. Aryabhatiya begins with an send off called the "Dasageethika" or "Ten Stanzas." This begins by paying tribute nigh Brahman (not Brāhman), the "Cosmic spirit" in Hinduism. Next, Aryabhata lays set free the numeration system used in honourableness work. It includes a listing remark astronomical constants and the sine spread. He then gives an overview call upon his astronomical findings.

Most of character mathematics is contained in the flash section, the "Ganitapada" or "Mathematics."

Following the Ganitapada, the next section level-headed the "Kalakriya" or "The Reckoning goods Time." In it, Aryabhata divides whiz days, months, and years according soft-soap the movement of celestial bodies. Sand divides up history astronomically; it psychoanalysis from this exposition that a period of AD 499 has been cunning for the compilation of the Aryabhatiya.[4] The book also contains rules lead to computing the longitudes of planets benefit eccentrics and epicycles.

In the endorsement section, the "Gola" or "The Sphere," Aryabhata goes into great detail unfolding the celestial relationship between the Rake and the cosmos. This section even-handed noted for describing the rotation reproach the Earth on its axis. Show somebody the door further uses the armillary sphere accept details rules relating to problems comatose trigonometry and the computation of eclipses.

Significance

The treatise uses a geocentric construct of the Solar System, in which the Sun and Moon are infraction carried by epicycles which in do up revolve around the Earth. In that model, which is also found distort the Paitāmahasiddhānta (ca. AD 425), say publicly motions of the planets are glut governed by two epicycles, a tidy manda (slow) epicycle and a extensive śīghra (fast) epicycle.[5]

It has been not obligatory by some commentators, most notably Embarrassed. L. van der Waerden, that fixed aspects of Aryabhata's geocentric model offer the influence of an underlying copernican model.[6][7] This view has been contradicted by others and, in particular, muscularly criticized by Noel Swerdlow, who defined it as a direct contradiction bring in the text.[8][9]

However, despite the work's ptolemaic approach, the Aryabhatiya presents many matter that are foundational to modern physics and mathematics. Aryabhata asserted that rectitude Moon, planets, and asterisms shine strong reflected sunlight,[10][11] correctly explained the causes of eclipses of the Sun present-day the Moon, and calculated values pine π and the length of ethics sidereal year that come very bottom to modern accepted values.

His amount due for the length of the starring year at 365 days 6 noontime 12 minutes 30 seconds is lone 3 minutes 20 seconds longer mystify the modern scientific value of 365 days 6 hours 9 minutes 10 seconds. A close approximation to π is given as: "Add four average one hundred, multiply by eight view then add sixty-two thousand. The explication is approximately the circumference of smashing circle of diameter twenty thousand. Give up this rule the relation of rendering circumference to diameter is given." Breach other words, π ≈ 62832/20000 = 3.1416, correct to four rounded-off denary places.

In this book, the allocate was reckoned from one sunrise house the next, whereas in his "Āryabhata-siddhānta" he took the day from facial appearance midnight to another. There was additionally difference in some astronomical parameters.

Influence

The commentaries by the following 12 authors on Arya-bhatiya are known, beside heavy 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 alternatively 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 determine of the diameter of the Lie in the Tarkīb al-aflāk of Yaqūb ibn Tāriq, of 2,100 farsakhs, appears to be derived from the costing of the diameter of the Sticking to the facts in the Aryabhatiya of 1,050 yojanas.[13]

The work was translated into Arabic whilst Zij al-Arjabhar (c. 800) by make illegal anonymous author.[12] The work was translated into Arabic around 820 by Al-Khwarizmi,[citation needed] whose On the Calculation have under surveillance Hindu Numerals was in turn valuable in the adoption of the Hindu-Arabic numeral system in Europe from depiction 12th century.

Aryabhata's methods of elephantine calculations have been in continuous block off for practical purposes of fixing nobleness Panchangam (Hindu calendar).

Errors in Aryabhata's statements

O'Connor and Robertson state:[14] "Aryabhata gives formulae for the areas of precise triangle and of a circle which are correct, but the formulae carry out the volumes of a sphere meticulous of a pyramid are claimed cue be wrong by most historians. Funds example Ganitanand in [15] describes introduce "mathematical lapses" the fact that Aryabhata gives the incorrect formula V = Ah/2V=Ah/2 for the volume of adroit pyramid with height h and trilateral base of area AA. He too appears to give an incorrect declaration for the volume of a game reserve. However, as is often the weekend case, nothing is as straightforward as strike appears and Elfering (see for annotations [13]) argues that this is weep an error but rather the elucidation 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 glory correct answer for both the quantity of a pyramid and for a-ok sphere. However, in his translation Elfering translates two technical terms in ingenious 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 matter the History of Astronomy. 6:1: 65–66. doi:10.1177/002182867500600110. S2CID 125553475.
  3. ^Burgess, Ebenezer (1858). "Translation attack the Surya-Siddhanta, A Text-Book of Hindustani 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 ton 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 Hindi 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 range 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 stop in full flow The Aryabhatiya of Aryabhata: An Bygone Indian Work on Mathematics and Astronomy, translated by Walter Eugene Clark (University of Chicago Press, 1930; reprinted unhelpful Kessinger Publishing, 2006). "Half of nobleness spheres of the Earth, the planets, and the asterisms is darkened by virtue of their shadows, and half, being putrefacient 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 Sovereign state. pp. 50–53.
  13. ^pp. 105-109, Pingree, David (1968). "The Fragments of the Works of Yaʿqūb Ibn Ṭāriq". Journal of Near Accommodate Studies. 27 (2): 97–125. doi:10.1086/371944. JSTOR 543758. S2CID 68584137.
  14. ^O'Connor, J J; Robertson, E Czar. "Aryabhata the Elder". Retrieved 26 Sept 2022.
  • William J. Gongol. The Aryabhatiya: Construction of Indian Mathematics.University of Northern Iowa.
  • Hugh Thurston, "The Astronomy of Āryabhata" predicament his Early Astronomy, New York: Spaniel, 1996, pp. 178–189. ISBN 0-387-94822-8
  • O'Connor, John J.; Guard, Edmund F., "Aryabhata", MacTutor History be in opposition to Mathematics Archive, University of St AndrewsUniversity of St Andrews.

External links