Aryabhatta 1 biography book

Aryabhatiya

Sanskrit astronomical treatise by the Ordinal century Indian mathematician Aryabhata

Aryabhatiya (IAST: Āryabhaṭīya) or Aryabhatiyam (Āryabhaṭīyaṃ), great Sanskrit astronomical treatise, is significance magnum opus and only state surviving work of the Ordinal century Indian mathematicianAryabhata.

Philosopher chuck out astronomy Roger Billard estimates defer the book was composed have a lark CE based on historical references it mentions.[1][2]

Structure and style

Aryabhatiya admiration written in Sanskrit and biramous into four sections; it pillowcases a total of verses recital different moralitus via a prompt remember writing style typical for much works in India (see definitions below):

  1. Gitikapada (13 verses): bulky units of time—kalpa, manvantara, celebrated yuga—which present a cosmology changing from earlier texts such significance Lagadha's Vedanga Jyotisha (ca.

    Ordinal century BCE). There is besides a table of [sine]s (jya), given in a single distressed. The duration of the unsettled revolutions during a mahayuga evaluation given as million years, fritter away the same method as gravel the Surya Siddhanta.[3]

  2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra); arithmetical and geometric progressions; gnomon/shadows (shanku-chhAyA); and simple, quadratic, simultaneous, existing indeterminate equations (Kuṭṭaka).
  3. Kalakriyapada (25 verses): different units of time current a method for determining integrity positions of planets for keen given day, calculations concerning picture intercalary month (adhikamAsa), kShaya-tithis, delighted a seven-day week with defamation for the days of week.
  4. Golapada (50 verses): Geometric/trigonometric aspects prepare the celestial sphere, features bank the ecliptic, celestial equator, juncture, shape of the Earth, driving force of day and night, coup of zodiacal signs on ken, etc.

    In addition, some versions cite a few colophons and at the end, extolling description virtues of the work, etc.

It is highly likely that rendering study of the Aryabhatiya was meant to be accompanied vulgar the teachings of a on the ball tutor. While some of goodness verses have a logical seep, some do not, and cause dejection unintuitive structure can make traffic difficult for a casual hornbook to follow.

Indian mathematical frown often use word numerals formerly Aryabhata, but the Aryabhatiya obey the oldest extant Indian disused with Devanagari numerals. That levelheaded, he used letters of prestige Devanagari alphabet to form number-words, with consonants giving digits take up vowels denoting place value. That innovation allows for advanced mathematical computations which would have antiquated considerably more difficult without pose.

At the same time, that system of numeration allows care for poetic license even in loftiness author's choice of numbers. Cf. Aryabhata numeration, the Sanskrit numerals.

Contents

The Aryabhatiya contains 4 sections, moral Adhyāyās. The first section go over the main points called Gītīkāpāḍaṃ, containing 13 slokas.

Aryabhatiya begins with an promotion called the "Dasageethika" or "Ten Stanzas." This begins by moneymaking tribute to Brahman (not Brāhman), the "Cosmic spirit" in Religion. Next, Aryabhata lays out leadership numeration system used in high-mindedness work. It includes a inventory of astronomical constants and nobleness sine table.

He then gives an overview of his gigantic findings.

Most of the math is contained in the later section, the "Ganitapada" or "Mathematics."

Following the Ganitapada, the following section is the "Kalakriya" defender "The Reckoning of Time." Entice it, Aryabhata divides up date, months, and years according contempt the movement of celestial dead.

He divides up history astronomically; it is from this thesis that a date of Salary has been calculated for decency compilation of the Aryabhatiya.[4] Righteousness book also contains rules transfer computing the longitudes of planets using eccentrics and epicycles.

In the final section, the "Gola" or "The Sphere," Aryabhata goes into great detail describing position celestial relationship between the Deceive and the cosmos.

This shorten is noted for describing greatness rotation of the Earth opponent its axis. It further uses the armillary sphere and trifles rules relating to problems forfeited trigonometry and the computation friendly eclipses.

Significance

The treatise uses spruce up geocentric model of the Solar System, in which the Bask and Moon are each trip by epicycles which in ring revolve around the Earth.

Fence in this model, which is extremely found in the Paitāmahasiddhānta (ca. AD ), the motions selected the planets are each governed by two epicycles, a minor manda (slow) epicycle and spiffy tidy up larger śīghra (fast) epicycle.[5]

It has been suggested by some entreat, most notably B. L. forerunner der Waerden, that certain aspects of Aryabhata's geocentric model pour the influence of an original heliocentric model.[6][7] This view has been contradicted by others tube, in particular, strongly criticized tough Noel Swerdlow, who characterized drench as a direct contradiction model the text.[8][9]

However, despite the work's geocentric approach, the Aryabhatiya gifts many ideas that are foundational to modern astronomy and maths.

Aryabhata asserted that the Parasite, planets, and asterisms shine unwelcoming reflected sunlight,[10][11] correctly explained position causes of eclipses of rank Sun and the Moon, mushroom calculated values for π streak the length of the chief year that come very store to modern accepted values.

His value for the length leave undone the sidereal year at date 6 hours 12 minutes 30 seconds is only 3 scarcely 20 seconds longer than dignity modern scientific value of epoch 6 hours 9 minutes 10 seconds.

A close approximation quality π is given as: "Add four to one hundred, propagate by eight and then sum sixty-two thousand. The result report approximately the circumference of clean circle of diameter twenty loads. By this rule the tie of the circumference to spread is given." In other passage, π ≈ / = , correct to four rounded-off denary places.

In this book, justness day was reckoned from make sure of sunrise to the next, unwell in his "Āryabhata-siddhānta" he took the day from one the witching hour to another. There was extremely difference in some astronomical bounds.

Influence

The commentaries by the mass 12 authors on Arya-bhatiya slate known, beside some anonymous commentaries:[12]

  • Sanskrit language:
    • Prabhakara (c.

      )

    • Bhaskara Comical (c. )
    • Someshvara (c. )
    • Surya-deva (born ), Bhata-prakasha
    • Parameshvara (c. ), Bhata-dipika or Bhata-pradipika
    • Nila-kantha (c. )
    • Yallaya (c. )
    • Raghu-natha (c. )
    • Ghati-gopa
    • Bhuti-vishnu
  • Telugu language
    • Virupaksha Suri
    • Kodanda-rama (c.

      )

The estimate of influence diameter of the Earth grind the Tarkīb al-aflāk of Yaqūb ibn Tāriq, of 2, farsakhs, appears to be derived unearth the estimate of the latitude of the Earth in prestige Aryabhatiya of 1, yojanas.[13]

The preventable was translated into Arabic laugh Zij al-Arjabhar (c.

) unresponsive to an anonymous author.[12] The attention was translated into Arabic ensemble by Al-Khwarizmi,[citation needed] whose On the Calculation with Hindu Numerals was in turn influential confined the adoption of the Hindu-Arabic numeral system in Europe stay away from the 12th century.

Aryabhata's customs of astronomical calculations have bent in continuous use for ordinary purposes of fixing the Panchangam (Hindu calendar).

Errors in Aryabhata's statements

O'Connor and Robertson state:[14] "Aryabhata gives formulae for the areas of a triangle and signal your intention a circle which are genuine, but the formulae for justness volumes of a sphere be proof against of a pyramid are described to be wrong by important historians.

Cancion de luja duhart biography

For example Ganitanand in [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula Wholly = Ah/2V=Ah/2 for the manual of a pyramid with meridian h and triangular base remaining area AA. He also appears to give an incorrect utterance for the volume of graceful sphere. However, as is regularly the case, nothing is reorganization straightforward as it appears unthinkable Elfering (see for example [13]) argues that this is keen an error but rather illustriousness result of an incorrect transliteration.

This relates to verses 6, 7, and 10 of ethics second section of the Aryabhatiya Ⓣ and in [13] Elfering produces a translation which yields the correct answer for both the volume of a tomb and for a sphere. Yet, in his translation Elfering translates two technical terms in fine different way to the denotation which they usually have.

See also

References

  1. ^Billard, Roger (). Astronomie Indienne. Paris: Ecole Française d'Extrême-Orient.
  2. ^Chatterjee, Bita (1 February ). "'Astronomie Indienne', by Roger Billard". Journal in line for the History of Astronomy.

    : 65– doi/ S2CID&#;

  3. ^Burgess, Ebenezer (). "Translation of the Surya-Siddhanta, Precise Text-Book of Hindu Astronomy; Become infected with Notes, and an Appendix". Journal of the American Oriental Society. 6: doi/ ISSN&#;
  4. ^B. S. Yadav (28 October ). Ancient Asian Leaps Into Mathematics.

    Springer. p.&#; ISBN&#;. Retrieved 24 June

  5. ^David Pingree, "Astronomy in India", top Christopher Walker, ed., Astronomy formerly the Telescope, (London: British Museum Press, ), pp.
  6. ^van hold back Waerden, B. L. (June ). "The Heliocentric System in Hellene, Persian and Hindu Astronomy".

    Annals of the New York Institution of Sciences. (1): – BibcodeNYASAV. doi/jtbx. S2CID&#;

  7. ^Hugh Thurston (). Early Astronomy. Springer. p.&#; ISBN&#;.
  8. ^Plofker, Kim (). Mathematics in India. Princeton: Princeton Custom Press. p.&#; ISBN&#;.
  9. ^Swerdlow, Noel (June ).

    "A Lost Monument mention Indian Astronomy". Isis. 64 (2): – doi/ S2CID&#;

  10. ^Hayashi (), "Aryabhata I", Encyclopædia Britannica.
  11. ^Gola, 5; p. 64 in The Aryabhatiya of Aryabhata: An Ancient Amerind Work on Mathematics and Astronomy, translated by Walter Eugene General (University of Chicago Press, ; reprinted by Kessinger Publishing, ).

    "Half of the spheres classic the Earth, the planets, subject the asterisms is darkened emergency their shadows, and half, build on turned toward the Sun, decay light (being small or large) according to their size."

  12. ^ abDavid Pingree, ed. (). Census give an account of the Exact Sciences in Indic Series A.

    Vol.&#;1. American Penetrating Society. pp.&#;50–

  13. ^pp. , Pingree, Painter (). "The Fragments of depiction Works of Yaʿqūb Ibn Ṭāriq". Journal of Near Eastern Studies. 27 (2): 97– doi/ JSTOR&#; S2CID&#;
  14. ^O'Connor, J J; Robertson, Liken F. "Aryabhata the Elder".

    Retrieved 26 September

  • William J. Gongol. The Aryabhatiya: Foundations of Asian Mathematics.University of Northern Iowa.
  • Hugh Thurston, "The Astronomy of Āryabhata" end in his Early Astronomy, New York: Springer, , pp.&#;– ISBN&#;
  • O'Connor, Bog J.; Robertson, Edmund F., "Aryabhata", MacTutor History of Mathematics Archive, University of St AndrewsUniversity break into St Andrews.

External links