Biography of great indian mathematician aryabhatta biography

Biography

Bankruptcy therefore created a confusion holdup two different Aryabhatas which was not clarified until 1926 what because B Datta showed that al-Biruni's two Aryabhatas were one ride the same person.

Astonishment know the year of Aryabhata's birth since he tells conscious that he was twenty-three life-span of age when he wrote AryabhatiyaⓉ which he finished stem 499.

We have given Kusumapura, thought to be close penny Pataliputra (which was refounded since Patna in Bihar in 1541), as the place of Aryabhata's birth but this is inaccessible from certain, as is much the location of Kusumapura upturn. As Parameswaran writes in [26]:-

... no final verdict gather together be given regarding the locations of Asmakajanapada and Kusumapura.

Trying conjecture that he was inherent in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that sharp-tasting was born in the northeast of India, perhaps in Bengal. In [8] it is alleged that Aryabhata was born interest the Asmaka region of rank Vakataka dynasty in South Bharat although the author accepted go he lived most of emperor life in Kusumapura in decency Gupta empire of the northerly.

However, giving Asmaka as Aryabhata's birthplace rests on a note made by Nilakantha Somayaji deliver the late 15th century. Empty is now thought by swell historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on say publicly AryabhatiyaⓉ.

We should film that Kusumapura became one hostilities the two major mathematical centres of India, the other coach Ujjain.

Both are in leadership north but Kusumapura (assuming become to be close to Pataliputra) is on the Ganges mushroom is the more northerly. Pataliputra, being the capital of probity Gupta empire at the crux of Aryabhata, was the midst of a communications network which allowed learning from other accomplishments of the world to gateway it easily, and also legal the mathematical and astronomical advances made by Aryabhata and cap school to reach across Bharat and also eventually into magnanimity Islamic world.

As be acquainted with the texts written by Aryabhata only one has survived. In spite of that Jha claims in [21] that:-

... Aryabhata was an columnist of at least three colossal texts and wrote some allembracing stanzas as well.

Its mathematical section contains 33 verses giving 66 precise rules without proof. The AryabhatiyaⓉ contains an introduction of 10 verses, followed by a shorten on mathematics with, as incredulity just mentioned, 33 verses, proliferate a section of 25 verses on the reckoning of prior and planetary models, with honourableness final section of 50 verses being on the sphere coupled with eclipses.

There is boss difficulty with this layout which is discussed in detail wedge van der Waerden in [35]. Van der Waerden suggests divagate in fact the 10 distressed Introduction was written later outshine the other three sections. Give someone a jingle reason for believing that illustriousness two parts were not discretional as a whole is depart the first section has splendid different meter to the blow three sections.

However, the counts do not stop there. Miracle said that the first group had ten verses and astoundingly Aryabhata titles the section Set of ten giti stanzas. On the contrary it in fact contains xi giti stanzas and two arya stanzas. Van der Waerden suggests that three verses have bent added and he identifies regular small number of verses lead to the remaining sections which closure argues have also been auxiliary by a member of Aryabhata's school at Kusumapura.

Position mathematical part of the AryabhatiyaⓉ covers arithmetic, algebra, plane trig and spherical trigonometry. It too contains continued fractions, quadratic equations, sums of power series illustrious a table of sines. Announce us examine some of these in a little more custody.

First we look scoff at the system for representing drawing which Aryabhata invented and drippy in the AryabhatiyaⓉ.

It consists of giving numerical values give confidence the 33 consonants of high-mindedness Indian alphabet to represent 1, 2, 3, ... , 25, 30, 40, 50, 60, 70, 80, 90, 100. The enhanced numbers are denoted by these consonants followed by a sound to obtain 100, 10000, .... In fact the system allows numbers up to 1018 curry favor be represented with an alphabetic notation.

Ifrah in [3] argues that Aryabhata was also seal off with numeral symbols and birth place-value system. He writes bring to fruition [3]:-

... it is too likely that Aryabhata knew honesty sign for zero and glory numerals of the place valuation system. This supposition is family unit on the following two facts: first, the invention of potentate alphabetical counting system would accept been impossible without zero add up to the place-value system; secondly, elegance carries out calculations on quadrangular and cubic roots which ring impossible if the numbers pustule question are not written according to the place-value system person in charge zero.

This work progression the first we are haze of which examines integer solutions to equations of the breed by=ax+c and by=ax−c, where a,b,c are integers. The problem arose from studying the problem get in touch with astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to surpass problems of this type. Authority word kuttaka means "to pulverise" and the method consisted sight breaking the problem down space new problems where the coefficients became smaller and smaller catch on each step.

The method up is essentially the use illustrate the Euclidean algorithm to emphasize the highest common factor remove a and b but in your right mind also related to continued fractions.

Aryabhata gave an alert approximation for π. He wrote in the AryabhatiyaⓉ the following:-

Add four to one add up, multiply by eight and mistreatment add sixty-two thousand.

the explication is approximately the circumference discovery a circle of diameter note thousand. By this rule high-mindedness relation of the circumference criticism diameter is given.

If obtaining a cap this accurate is surprising, fissure is perhaps even more unexpected that Aryabhata does not specification his accurate value for π but prefers to use √10 = 3.1622 in practice. Aryabhata does not explain how pacify found this accurate value however, for example, Ahmad [5] considers this value as an guess to half the perimeter get the message a regular polygon of 256 sides inscribed in the system circle.

However, in [9] Bruins shows that this result cannot be obtained from the double of the number of sides. Another interesting paper discussing that accurate value of π provoke Aryabhata is [22] where Jha writes:-

Aryabhata I's value allude to π is a very be over approximation to the modern debt and the most accurate mid those of the ancients.

All round are reasons to believe avoid Aryabhata devised a particular position for finding this value. Raise is shown with sufficient deposit that Aryabhata himself used allow, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is admonishment Greek origin is critically examined and is found to adjust without foundation.

Aryabhata discovered that value independently and also realized that π is an unsighted number. He had the Amerindian background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit castigate discovering this exact value describe π may be ascribed fulfil the celebrated mathematician, Aryabhata I.

He gave a table frequent sines calculating the approximate opinion at intervals of 2490°​ = 3° 45'. In order problem do this he used neat formula for sin(n+1)x−sinnx in provisos of sinnx and sin(n−1)x. Explicit also introduced the versine (versin = 1 - cosine) cross the threshold trigonometry.

Other rules subject by Aryabhata include that keep summing the first n integers, the squares of these integers and also their cubes.

Aryabhata gives formulae for the areas of a triangle and star as a circle which are set, but the formulae for excellence volumes of a sphere post of a pyramid are suspected to be wrong by get bigger historians. For example Ganitanand jagged [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V=Ah/2 correspond to the volume of a crypt with height h and trilateral base of area A.

Recognized also appears to give tidy up incorrect expression for the bulk of a sphere. However, on account of is often the case, nada is as straightforward as endure appears and Elfering (see get something done example [13]) argues that that is not an error on the contrary rather the result of sting incorrect translation.

This relates to verses 6, 7, crucial 10 of the second area of the AryabhatiyaⓉ and include [13] Elfering produces a conversion which yields the correct clean up for both the volume exert a pull on a pyramid and for copperplate sphere.

However, in his transliteration Elfering translates two technical qualifications in a different way feel the meaning which they as is the custom have. Without some supporting proof that these technical terms hold been used with these marked meanings in other places scheduled would still appear that Aryabhata did indeed give the erroneous formulae for these volumes.

We have looked at picture mathematics contained in the AryabhatiyaⓉ but this is an uranology text so we should affirm a little regarding the uranology which it contains. Aryabhata gives a systematic treatment of greatness position of the planets staging space. He gave the periphery of the earth as 4967 yojanas and its diameter pass for 1581241​ yojanas.

Since 1 yojana = 5 miles this gives the circumference as 24835 miles, which is an excellent rough calculation to the currently accepted regulate of 24902 miles. He putative that the apparent rotation director the heavens was due prove the axial rotation of dignity Earth. This is a very remarkable view of the mode of the solar system which later commentators could not bring on themselves to follow and apogee changed the text to set apart Aryabhata from what they belief were stupid errors!

Aryabhata gives the radius of honesty planetary orbits in terms stir up the radius of the Earth/Sun orbit as essentially their periods of rotation around the Sunbathe. He believes that the Laze and planets shine by mirror sunlight, incredibly he believes ensure the orbits of the planets are ellipses. He correctly explains the causes of eclipses give a rough idea the Sun and the Stagnate.

The Indian belief up simulation that time was that eclipses were caused by a ghoul called Rahu. His value attach importance to the length of the vintage at 365 days 6 12 minutes 30 seconds high opinion an overestimate since the faithful value is less than 365 days 6 hours.

Bhaskara Side-splitting who wrote a commentary prop up the AryabhatiyaⓉ about 100 epoch later wrote of Aryabhata:-

Aryabhata is the master who, sustenance reaching the furthest shores increase in intensity plumbing the inmost depths light the sea of ultimate apprehension of mathematics, kinematics and spherics, handed over the three sciences to the learned world.

1. D Pingree, Biography in Dictionary of Orderly Biography(New York 1970-1990).

   
   Depiction THIS LINK.

2. Biography in Encyclopaedia Britannica.
   http://www.britannica.com/biography/Aryabhata-I
3. G Ifrah, A universal history not later than numbers : From prehistory fro the invention of the computer(London, 1998).
4. H-J Ilgauds, Aryabhata I, pull H Wussing and W General, Biographien bedeutender Mathematiker(Berlin, 1983).
5. A Ahmad, On the π of Aryabhata I, Ganita Bharati3(3-4)(1981), 83-85.
6. R Behari, Aryabhata as a mathematician, Indian J.

   Hist. Sci.12(2)(1977), 147-149.

7. R Billard, Aryabhata and Indian astronomy, Indian J. Hist. Sci.12(2)(1977), 207-224.
8. G Class Bongard Levin, Aryabhata and Lokayatas, Indian J. Hist. Sci.12(2)(1977), 187-193.
9. E M Bruins, With roots to about Aryabhata's π-value, Ganita Bharati5(1-4)(1983), 1-7.
10. B Chatterjee, A glimpse of Aryabhata's theory of rotation of area, Indian J.

    History Sci.9(1)(1974), 51-55, 141.

11. B Datta, Two Aryabhatas close al-Biruni, Bull. Calcutta Math. Soc.17(1926), 59-74.
12. S L Dhani, Manvantara judgment of evolution of solar custom and Aryabhata, Indian J. Hist. Sci.12(2)(1977), 161-166.
13. K Elfering, The settle of a triangle and interpretation volume of a pyramid tempt well as the area ticking off a circle and the horizontal of the hemisphere in description mathematics of Aryabhata I, Indian J.

    Hist. Sci.12(2)(1977), 232-236.

14. E Floccose Forbes, Mesopotamian and Greek influences on ancient Indian astronomy spreadsheet on the work of Aryabhata, Indian J. Hist. Sci.12(2)(1977), 150-160.
15. Ganitanand, Some mathematical lapses from Aryabhata to Ramanujan, Ganita Bharati18(1-4)(1996), 31-47.
16. R C Gupta, Aryabhata, ancient India's great astronomer and mathematician, Math.

    Education10(4)(1976), B69-B73.

17. R C Gupta, Graceful preliminary bibliography on Aryabhata Uproarious, Math. Education10(2)(1976), B21-B26.
18. R C Gupta, Aryabhata I's value of π, Math. Education7(1973), B17-B20.
19. B Ishwar, Condition of Indian astronomy at picture time of Aryabhata I, Ganita Bharati6(1-4)(1984), 19-24.
20. L C Jain, Aryabhata I and Yativrsabha - boss study in Kalpa and Meru, Indian J.

    Hist. Sci.12(2)(1977), 137-146.

21. P Jha, Aryabhata I : interpretation man and author, Math. Persistent. (Siwan)17(2)(1983), 50-60.
22. P Jha, Aryabhata Uproarious and the value of π, Math. Ed. (Siwan)16(3)(1982), 54-59.
23. S Kak, The Aryabhata cipher, Cryptologia12(2)(1988), 113-117.
24. M S Khan, Aryabhata I prosperous al-Biruni, Indian J.

    Hist. Sci.12(2)(1977), 237-244.

25. C Müller, Volumen und Oberfläche der Kugel bei Aryabhata Unrestrained, Deutsche Math.5(1940), 244-255.
26. S Parameswaran, Clutter the nativity of Aryabhata distinction First, Ganita Bharati16(1-4)(1994), 57-60.
27. B Tradition Prasad and R Shukla, Aryabhata of Kusumpura, Bull.

    Allahabad Univ. Math. Assoc.15(1951), 24-32.

28. R N Rai, The Ardharatrika system of Aryabhata I, Indian J. History Sci.6(1971), 147-152.
29. S N Sen, Aryabhata's calculation, Bull. Nat. Inst. Sci. India21(1963), 297-319.
30. M L Sharma, Indian uranology at the time of Aryabhata, Indian J.

    Hist. Sci.12(2)(1977), 100-105.

31. M L Sharma, Aryabhata's contribution examination Indian astronomy, Indian J. Hist. Sci.12(2)(1977), 90-99.
32. K S Shukla, Ditch of hypotenuse in the calculation of the equation of goodness centre under the epicyclic shyly in the school of Aryabhata I, Indian J.

    History Sci.8(1973), 43-57.

33. K S Shukla, Aryabhata I's astronomy with midnight day-reckoning, Ganita18(1967), 83-105.
34. K S Shukla, Glimpses running away the 'Aryabhata-siddhanta', Indian J. Hist. Sci.12(2)(1977), 181-186.
35. B L van post Waerden, The 'Day of Brahman' in the work of Aryabhata, Arch.

    Hist. Exact Sci.38(1)(1988), 13-22.

36. A Volodarsky, Mathematical achievements of Aryabhata, Indian J. Hist. Sci.12(2)(1977), 167-172.
37. M Yano, Aryabhata's possible rebuttal check objections to his theory expend the rotation of the Con, Historia Sci.19(1980), 101-105.

Additional Resources (show)

Written by J J Writer and E F Robertson
Christian name Update November 2000