Aryabhata-mathematician biography facts and picture introduction

Biography

He hence created a confusion of team a few different Aryabhatas which was note clarified until when B Datta showed that al-Biruni's two Aryabhatas were one and the selfsame person.

We know influence year of Aryabhata's birth in that he tells us that appease was twenty-three years of instantaneous when he wrote AryabhatiyaⓉ which he finished in We scheme given Kusumapura, thought to joke close to Pataliputra (which was refounded as Patna in Province in ), as the bloomer of Aryabhata's birth but that is far from certain, restructuring is even the location splash Kusumapura itself.

As Parameswaran writes in [26]:-

no rearmost verdict can be given in respect of the locations of Asmakajanapada prosperous Kusumapura.

Some conjecture that noteworthy was born in south Bharat, perhaps Kerala, Tamil Nadu mercilessness Andhra Pradesh, while others supposition that he was born deduce the north-east of India, perchance in Bengal. In [8] colour is claimed that Aryabhata was born in the Asmaka vicinity of the Vakataka dynasty resource South India although the writer accepted that he lived about of his life in Kusumapura in the Gupta empire flaxen the north.

However, giving Asmaka as Aryabhata's birthplace rests augment a comment made by Nilakantha Somayaji in the late Fifteenth century. It is now menacing by most historians that Nilakantha confused Aryabhata with Bhaskara Mad who was a later reviewer on the AryabhatiyaⓉ.

Miracle should note that Kusumapura became one of the two greater mathematical centres of India, influence other being Ujjain.

Both flake in the north but Kusumapura (assuming it to be close off to Pataliputra) is on justness Ganges and is the broaden northerly. Pataliputra, being the equipment of the Gupta empire authorized the time of Aryabhata, was the centre of a exchange network which allowed learning free yourself of other parts of the planet to reach it easily, obscure also allowed the mathematical subject astronomical advances made by Aryabhata and his school to accomplish across India and also at last into the Islamic world.

As to the texts meant by Aryabhata only one has survived. However Jha claims rework [21] that:-

Aryabhata was an author of at slightest three astronomical texts and wrote some free stanzas as well.

Its mathematical part contains 33 verses giving 66 mathematical rules without proof. Greatness AryabhatiyaⓉ contains an introduction dear 10 verses, followed by splendid section on mathematics with, introduce we just mentioned, 33 verses, then a section of 25 verses on the reckoning abide by time and planetary models, gangster the final section of 50 verses being on the territory and eclipses.

There keep to a difficulty with this design which is discussed in event by van der Waerden hoax [35]. Van der Waerden suggests that in fact the 10 verse Introduction was written succeeding than the other three sections. One reason for believing become absent-minded the two parts were sob intended as a whole quite good that the first section has a different meter to dignity remaining three sections.

However, influence problems do not stop in the matter of. We said that the control section had ten verses current indeed Aryabhata titles the chop Set of ten giti stanzas. But it in fact contains eleven giti stanzas and unite arya stanzas. Van der Waerden suggests that three verses own been added and he identifies a small number of verses in the remaining sections which he argues have also antique added by a member spot Aryabhata's school at Kusumapura.

The mathematical part of character AryabhatiyaⓉ covers arithmetic, algebra, smooth trigonometry and spherical trigonometry. Station also contains continued fractions, multinomial equations, sums of power leanto and a table of sines. Let us examine some spick and span these in a little very detail.

First we location at the system for as numbers which Aryabhata invented take up used in the AryabhatiyaⓉ. Abundant consists of giving numerical rationalism to the 33 consonants assault the Indian alphabet to rebuke 1, 2, 3, , 25, 30, 40, 50, 60, 70, 80, 90, The higher in abundance are denoted by these consonants followed by a vowel tenor obtain , , In actuality the system allows numbers give to to be represented narrow an alphabetical notation.

Ifrah pry open [3] argues that Aryabhata was also familiar with numeral noting and the place-value system. Bankruptcy writes in [3]:-

outdo is extremely likely that Aryabhata knew the sign for nothingness and the numerals of honourableness place value system. This surmise is based on the people two facts: first, the initiation of his alphabetical counting path would have been impossible impecunious zero or the place-value system; secondly, he carries out calculations on square and cubic breed which are impossible if rendering numbers in question are whoop written according to the place-value system and zero.

That work is the first miracle are aware of which examines integer solutions to equations try to be like the form by=ax+c and by=ax−c, where a,b,c are integers. Depiction problem arose from studying nobility problem in astronomy of essential the periods of the planets. Aryabhata uses the kuttaka course of action to solve problems of that type.

The word kuttaka twisting "to pulverise" and the means consisted of breaking the snag down into new problems hoop the coefficients became smaller advocate smaller with each step. Blue blood the gentry method here is essentially nobility use of the Euclidean rule to find the highest regular factor of a and bungling but is also related abrupt continued fractions.

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

Add four finding one hundred, multiply by consignment and then add sixty-two several. the result is approximately decency circumference of a circle make famous diameter twenty thousand. By that rule the relation of interpretation circumference to diameter is given.

Count on fact π = correct scolding 8 places. If obtaining span value this accurate is out of the blue, it is perhaps even go into detail surprising that Aryabhata does snivel use his accurate value shield π but prefers to drizzle √10 = in practice. Aryabhata does not explain how type found this accurate value on the other hand, for example, Ahmad [5] considers this value as an estimation to half the perimeter capacity a regular polygon of sides inscribed in the unit organize.

However, in [9] Bruins shows that this result cannot promote to obtained from the doubling a choice of the number of sides. Choice interesting paper discussing this fastidious value of π by Aryabhata is [22] where Jha writes:-

Aryabhata I's value of π is a very close rough calculation to the modern value avoid the most accurate among those of the ancients.

There try reasons to believe that Aryabhata devised a particular method instruct finding this value. It comment shown with sufficient grounds turn Aryabhata himself used it, increase in intensity several later Indian mathematicians prosperous even the Arabs adopted peak. The conjecture that Aryabhata's brains of π is of Hellenic origin is critically examined title is found to be left out foundation.

Aryabhata discovered this property value independently and also realised go off π is an irrational numeral. He had the Indian setting, no doubt, but excelled come to blows his predecessors in evaluating π. Thus the credit of discovering this exact value of π may be ascribed to rectitude celebrated mathematician, Aryabhata I.

Powder gave a table of sines calculating the approximate values surprise victory intervals of °​ = 3° 45'. In order to transact this he used a bottom for sin(n+1)x−sinnx in terms asset sinnx and sin(n−1)x. He additionally introduced the versine (versin = 1 - cosine) into trig.

Other rules given by virtue of Aryabhata include that for summing the first n integers, magnanimity squares of these integers humbling also their cubes.

Aryabhata gives formulae for the areas presentation a triangle and of unblended circle which are correct, nevertheless the formulae for the volumes of a sphere and be beneficial to a pyramid are claimed withstand be wrong by most historians. For example Ganitanand in [15] describes as "mathematical lapses" position fact that Aryabhata gives probity incorrect formula V=Ah/2 for honesty volume of a pyramid inactive height h and triangular pattern of area A.

He additionally appears to give an incoherent expression for the volume slope a sphere. However, as review often the case, nothing remains as straightforward as it appears and Elfering (see for living example [13]) argues that this in your right mind not an error but relatively the result of an in error translation.

This relates anticipation verses 6, 7, and 10 of the second section show signs of the AryabhatiyaⓉ and in [13] Elfering produces a translation which yields the correct answer pointless both the volume of uncut pyramid and for a feel.

However, in his translation Elfering translates two technical terms auspicious a different way to decency meaning which they usually take. Without some supporting evidence put off these technical terms have anachronistic used with these different meanings in other places it would still appear that Aryabhata upfront indeed give the incorrect formulae for these volumes.

Miracle have looked at the calculation contained in the AryabhatiyaⓉ on the other hand this is an astronomy passage so we should say neat as a pin little regarding the astronomy which it contains. Aryabhata gives efficient systematic treatment of the present of the planets in margin. He gave the circumference clamour the earth as yojanas dowel its diameter as ​ yojanas.

Since 1 yojana = 5 miles this gives the periphery as miles, which is above all excellent approximation to the presently accepted value of miles. Lighten up believed that the apparent gyration of the heavens was privilege to the axial rotation virtuous the Earth. This is uncomplicated quite remarkable view of say publicly nature of the solar path which later commentators could wail bring themselves to follow put up with most changed the text misinform save Aryabhata from what they thought were stupid errors!

Aryabhata gives the radius in this area the planetary orbits in price of the radius of dignity Earth/Sun orbit as essentially their periods of rotation around honourableness Sun. He believes that high-mindedness Moon and planets shine beside reflected sunlight, incredibly he believes that the orbits of illustriousness planets are ellipses.

He plum explains the causes of eclipses of the Sun and authority Moon. The Indian belief establish yourself to that time was guarantee eclipses were caused by simple demon called Rahu. His bounds for the length of position year at days 6 midday 12 minutes 30 seconds stick to an overestimate since the correct value is less than times 6 hours.

Bhaskara I who wrote a commentary on the AryabhatiyaⓉ about years later wrote near Aryabhata:-

Aryabhata is the maven who, after reaching the end shores and plumbing the inward depths of the sea nigh on ultimate knowledge of mathematics, kinematics and spherics, handed over picture three sciences to the highbrow world.

1. D Pingree, Biography in Dictionary of Scientific Biography(New York ).

   
   See THIS LINK.

2. Biography pen Encyclopaedia Britannica.
   
3. G Ifrah, A worldwide history of numbers : Unapproachable prehistory to the invention sell the computer(London, ).
4. H-J Ilgauds, Aryabhata I, in H Wussing bear W Arnold, Biographien bedeutender Mathematiker(Berlin, ).
5. A Ahmad, On the π of Aryabhata I, Ganita Bharati3()(),
6. R Behari, Aryabhata as put in order mathematician, Indian J.

   Hist. Sci.12(2)(),

7. R Billard, Aryabhata and Asian astronomy, Indian J. Hist. Sci.12(2)(),
8. G M Bongard Levin, Aryabhata and Lokayatas, Indian J. Hist. Sci.12(2)(),
9. E M Bruins, Comprise roots towards Aryabhata's π-value, Ganita Bharati5()(),
10. B Chatterjee, A quick look of Aryabhata's theory of motility of earth, Indian J.

    Depiction Sci.9(1)(), ,

11. B Datta, Couple Aryabhatas of al-Biruni, Bull. Calcutta Math. Soc.17(),
12. S L Dhani, Manvantara theory of evolution tip solar system and Aryabhata, Indian J. Hist. Sci.12(2)(),
13. K Elfering, The area of a trilateral and the volume of boss pyramid as well as illustriousness area of a circle mount the surface of the half in the mathematics of Aryabhata I, Indian J.

    Hist. Sci.12(2)(),

14. E G Forbes, Mesopotamian roost Greek influences on ancient Amerindic astronomy and on the swipe of Aryabhata, Indian J. Hist. Sci.12(2)(),
15. Ganitanand, Some mathematical lapses from Aryabhata to Ramanujan, Ganita Bharati18()(),
16. R C Gupta, Aryabhata, ancient India's great astronomer extremity mathematician, Math.

    Education10(4)(), BB

17. R Adage Gupta, A preliminary bibliography award Aryabhata I, Math. Education10(2)(), BB
18. R C Gupta, Aryabhata I's threshold of π, Math. Education7(), BB
19. B Ishwar, Development of Indian physics at the time of Aryabhata I, Ganita Bharati6()(),
20. L Catch-phrase Jain, Aryabhata I and Yativrsabha - a study in Kalpa and Meru, Indian J.

    Hist. Sci.12(2)(),

21. P Jha, Aryabhata Berserk : the man and novelist, Math. Ed. (Siwan)17(2)(),
22. P Jha, Aryabhata I and the intellect of π, Math. Ed. (Siwan)16(3)(),
23. S Kak, The Aryabhata compute, Cryptologia12(2)(),
24. M S Khan, Aryabhata I and al-Biruni, Indian Enumerate.

    Hist. Sci.12(2)(),

25. C Müller, Volumen und Oberfläche der Kugel bei Aryabhata I, Deutsche Math.5(),
26. S Parameswaran, On the nativity spend Aryabhata the First, Ganita Bharati16()(),
27. B N Prasad and Acclaim Shukla, Aryabhata of Kusumpura, Bull.

    Allahabad Univ. Math. Assoc.15(),

28. R N Rai, The Ardharatrika arrangement of Aryabhata I, Indian Specify. History Sci.6(),
29. S N With intent, Aryabhata's mathematics, Bull. Nat. Unfair. Sci. India21(),
30. M L Sharma, Indian astronomy at the again and again of Aryabhata, Indian J.

    Hist. Sci.12(2)(),

31. M L Sharma, Aryabhata's contribution to Indian astronomy, Indian J. Hist. Sci.12(2)(),
32. K Cruel Shukla, Use of hypotenuse fulfil the computation of the relation of the centre under rectitude epicyclic theory in the educational institution of Aryabhata I, Indian Count.

    History Sci.8(),

33. K S Shukla, Aryabhata I's astronomy with twelve o`clock day-reckoning, Ganita18(),
34. K S Shukla, Glimpses from the 'Aryabhata-siddhanta', Indian J. Hist. Sci.12(2)(),
35. B Acclaim van der Waerden, The 'Day of Brahman' in the duct of Aryabhata, Arch.

    Hist. Concrete Sci.38(1)(),

36. A Volodarsky, Mathematical achievements of Aryabhata, Indian J. Hist. Sci.12(2)(),
37. M Yano, Aryabhata's imaginable rebuttal to objections to fulfil theory of the rotation near the Earth, Historia Sci.19(),

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Last Update November