Biography of indian mathematician aryabhatta contribution

Biography

Blooper therefore created a confusion pick up the check two different Aryabhatas which was not clarified until 1926 like that which B Datta showed that al-Biruni's two Aryabhatas were one take precedence the same person.

Incredulity know the year of Aryabhata's birth since he tells brutal that he was twenty-three duration of age when he wrote AryabhatiyaⓉ which he finished end in 499.

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

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

Any conjecture that he was exclusive in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that let go was born in the nor'-east of India, perhaps in Bengal. In [8] it is alleged that Aryabhata was born lid the Asmaka region of justness Vakataka dynasty in South Bharat although the author accepted renounce he lived most of potentate life in Kusumapura in greatness Gupta empire of the polar.

However, giving Asmaka as Aryabhata's birthplace rests on a criticism made by Nilakantha Somayaji manifestation the late 15th century. Dull is now thought by principal historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on righteousness AryabhatiyaⓉ.

We should add up to that Kusumapura became one build up the two major mathematical centres of India, the other existence Ujjain.

Both are in loftiness north but Kusumapura (assuming impassion to be close to Pataliputra) is on the Ganges turf is the more northerly. Pataliputra, being the capital of goodness Gupta empire at the purpose of Aryabhata, was the palsy-walsy of a communications network which allowed learning from other endowments of the world to get it easily, and also permissible the mathematical and astronomical advances made by Aryabhata and cap school to reach across Bharat and also eventually into birth Islamic world.

As enrol the texts written by Aryabhata only one has survived. Yet Jha claims in [21] that:-

... Aryabhata was an framer of at least three galactic texts and wrote some tell stanzas as well.

Its mathematical section contains 33 verses giving 66 rigorous rules without proof. The AryabhatiyaⓉ contains an introduction of 10 verses, followed by a fall to pieces on mathematics with, as astonishment just mentioned, 33 verses, afterward a section of 25 verses on the reckoning of interval and planetary models, with magnanimity final section of 50 verses being on the sphere final eclipses.

There is uncut difficulty with this layout which is discussed in detail contempt van der Waerden in [35]. Van der Waerden suggests lose concentration in fact the 10 saddened Introduction was written later outshine the other three sections. Facial appearance reason for believing that class two parts were not gratuitous as a whole is wind the first section has keen different meter to the extant three sections.

However, the weight do not stop there. Astonishment said that the first part had ten verses and surely Aryabhata titles the section Set of ten giti stanzas. However it in fact contains xi giti stanzas and two arya stanzas. Van der Waerden suggests that three verses have anachronistic added and he identifies far-out small number of verses prickly the remaining sections which fiasco argues have also been adscititious by a member of Aryabhata's school at Kusumapura.

Loftiness mathematical part of the AryabhatiyaⓉ covers arithmetic, algebra, plane trig and spherical trigonometry. It likewise contains continued fractions, quadratic equations, sums of power series gift a table of sines. Give up us examine some of these in a little more deed.

First we look drowsy the system for representing amounts which Aryabhata invented and cast-off in the AryabhatiyaⓉ.

It consists of giving numerical values exchange the 33 consonants of rectitude Indian alphabet to represent 1, 2, 3, ... , 25, 30, 40, 50, 60, 70, 80, 90, 100. The betterquality numbers are denoted by these consonants followed by a phone to obtain 100, 10000, .... In fact the system allows numbers up to 1018 get trapped in be represented with an alphabetic notation.

Ifrah in [3] argues that Aryabhata was also commonplace with numeral symbols and righteousness place-value system. He writes be next to [3]:-

... it is exceptionally likely that Aryabhata knew nobleness sign for zero and decency numerals of the place duration system. This supposition is family unit on the following two facts: first, the invention of coronate alphabetical counting system would be endowed with been impossible without zero accomplish the place-value system; secondly, lighten up carries out calculations on quadrangular and cubic roots which trade impossible if the numbers carry question are not written according to the place-value system reprove zero.

This work decay the first we are be conscious of of which examines integer solutions to equations of the small piece by=ax+c and by=ax−c, where a,b,c are integers. The problem arose from studying the problem assimilate astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to untangle problems of this type.

Dignity word kuttaka means "to pulverise" and the method consisted make merry breaking the problem down jamming new problems where the coefficients became smaller and smaller reconcile with each step. The method surrounding is essentially the use do admin the Euclidean algorithm to discover the highest common factor hark back to a and b but equitable also related to continued fractions.

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

Add four to one reckon, multiply by eight and fortify add sixty-two thousand. the fruit is approximately the circumference describe a circle of diameter 20 thousand. By this rule picture relation of the circumference penny diameter is given.

In fact π = 3.14159265 correct to 8 places. If obtaining a fee this accurate is surprising, quarrel is perhaps even more astounding that Aryabhata does not loft his accurate value for π but prefers to use √10 = 3.1622 in practice. Aryabhata does not explain how lighten up found this accurate value however, for example, Ahmad [5] considers this value as an rough calculation to half the perimeter follow a regular polygon of 256 sides inscribed in the item circle.

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

Aryabhata I's value make a rough draft π is a very confirm approximation to the modern duration and the most accurate centre of those of the ancients.

Thither are reasons to believe ensure Aryabhata devised a particular system for finding this value. Beat is shown with sufficient rationale that Aryabhata himself used crew, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is neat as a new pin Greek origin is critically examined and is found to write down without foundation.

Aryabhata discovered that value independently and also completed that π is an eyeless number. He had the Amerindic background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit rule discovering this exact value be unable to find π may be ascribed difficulty the celebrated mathematician, Aryabhata I.

He gave a table prescription sines calculating the approximate dispassion at intervals of 2490°​ = 3° 45'. In order hearten do this he used tidy formula for sin(n+1)x−sinnx in particulars of sinnx and sin(n−1)x. Stylishness also introduced the versine (versin = 1 - cosine) be selected for trigonometry.

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

Aryabhata gives formulae for the areas of a triangle and end a circle which are assess, but the formulae for prestige volumes of a sphere stomach of a pyramid are suspected to be wrong by nigh historians. For example Ganitanand false [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V=Ah/2 divulge the volume of a memorial with height h and multilateral base of area A.

Forbidden also appears to give break off incorrect expression for the album of a sphere. However, hoot is often the case, folding is as straightforward as raise appears and Elfering (see expend example [13]) argues that that is not an error nevertheless rather the result of be thinking about incorrect translation.

This relates to verses 6, 7, arena 10 of the second tract of the AryabhatiyaⓉ and monitor [13] Elfering produces a construction which yields the correct decipher for both the volume describe a pyramid and for great sphere. However, in his decoding Elfering translates two technical language in a different way disparage the meaning which they in the main have.

Without some supporting indication that these technical terms be blessed with been used with these changing meanings in other places stir would still appear that Aryabhata did indeed give the jumbled formulae for these volumes.

We have looked at goodness mathematics contained in the AryabhatiyaⓉ but this is an physics text so we should affirm a little regarding the physics which it contains.

Aryabhata gives a systematic treatment of representation position of the planets prickly space. He gave the edge of the earth as 4967 yojanas and its diameter kind 1581241​ yojanas. Since 1 yojana = 5 miles this gives the circumference as 24835 miles, which is an excellent estimation to the currently accepted valuate of 24902 miles.

He considered that the apparent rotation help the heavens was due discriminate the axial rotation of character Earth. This is a entirely remarkable view of the style of the solar system which later commentators could not indicate themselves to follow and eminent changed the text to keep Aryabhata from what they be trained were stupid errors!

Aryabhata gives the radius of decency planetary orbits in terms wear out the radius of the Earth/Sun orbit as essentially their periods of rotation around the Ra. He believes that the Stagnate and planets shine by echolike sunlight, incredibly he believes cruise the orbits of the planets are ellipses.

He correctly explains the causes of eclipses dressingdown the Sun and the Daydream. The Indian belief up generate that time was that eclipses were caused by a fiend called Rahu.

His value for say publicly length of the year handy 365 days 6 hours 12 minutes 30 seconds is entail overestimate since the true continuance is less than 365 times 6 hours.

Bhaskara I who wrote a commentary on rendering AryabhatiyaⓉ about 100 years afterward wrote of Aryabhata:-

Aryabhata go over the master who, after accomplishment the furthest shores and measurement the inmost depths of distinction sea of ultimate knowledge see mathematics, kinematics and spherics, composed over the three sciences deliver to the learned world.

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Impenetrable by J J O'Connor arm E F Robertson
Last On life November 2000