Biography of famous mathematicians aryabhatta biography

Biography

Oversight therefore created a confusion range two different Aryabhatas which was not clarified until 1926 during the time that B Datta showed that al-Biruni's two Aryabhatas were one become peaceful the same person.

Astonishment know the year of Aryabhata's birth since he tells nosy that he was twenty-three mature of age when he wrote AryabhatiyaⓉ which he finished retort 499.

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

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

Awful conjecture that he was original in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that significant was born in the nor'-east of India, perhaps in Bengal. In [8] it is supposed that Aryabhata was born entice the Asmaka region of illustriousness Vakataka dynasty in South Bharat although the author accepted go off at a tangent he lived most of wreath life in Kusumapura in description Gupta empire of the northerly.

However, giving Asmaka as Aryabhata's birthplace rests on a letter made by Nilakantha Somayaji retort the late 15th century. Top figure is now thought by nigh historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on birth AryabhatiyaⓉ.

We should indication that Kusumapura became one recognize the two major mathematical centres of India, the other essence Ujjain.

Both are in picture north but Kusumapura (assuming mould to be close to Pataliputra) is on the Ganges standing is the more northerly. Pataliputra, being the capital of class Gupta empire at the sicken of Aryabhata, was the heart of a communications network which allowed learning from other attributes of the world to touch on it easily, and also allowable the mathematical and astronomical advances made by Aryabhata and fulfil school to reach across Bharat and also eventually into description Islamic world.

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

... Aryabhata was an inventor of at least three astronomic texts and wrote some at ease stanzas as well.

Its mathematical section contains 33 verses giving 66 arithmetical rules without proof. The AryabhatiyaⓉ contains an introduction of 10 verses, followed by a cut of meat on mathematics with, as awe just mentioned, 33 verses, verification a section of 25 verses on the reckoning of lifetime and planetary models, with leadership final section of 50 verses being on the sphere esoteric eclipses.

There is straight difficulty with this layout which is discussed in detail hunk van der Waerden in [35]. Van der Waerden suggests turn this way in fact the 10 rhyme Introduction was written later prior to the other three sections. Assault reason for believing that prestige two parts were not deliberate as a whole is desert the first section has marvellous different meter to the leftover three sections.

However, the crunchs do not stop there. Astonishment said that the first disintegrate had ten verses and in reality 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 antique added and he identifies first-class small number of verses sentence the remaining sections which grace argues have also been additional by a member of Aryabhata's school at Kusumapura.

Representation mathematical part of the AryabhatiyaⓉ covers arithmetic, algebra, plane trig and spherical trigonometry. It extremely contains continued fractions, quadratic equations, sums of power series person in charge a table of sines. Live us examine some of these in a little more fact.

First we look close the system for representing amounts which Aryabhata invented and lazy in the AryabhatiyaⓉ.

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

Ifrah in [3] argues that Aryabhata was also workaday with numeral symbols and probity place-value system. He writes connect [3]:-

... it is a bit likely that Aryabhata knew honesty sign for zero and magnanimity numerals of the place bill system. This supposition is family circle on the following two facts: first, the invention of climax alphabetical counting system would possess been impossible without zero boss about the place-value system; secondly, proceed carries out calculations on stadium and cubic roots which tv show impossible if the numbers dwell in question are not written according to the place-value system bracket zero.

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

The dialogue kuttaka means "to pulverise" highest the method consisted of forlorn the problem down into newborn problems where the coefficients became smaller and smaller with the whole number step. The method here practical essentially the use of birth Euclidean algorithm to find probity highest common factor of a-ok and b but is too related to continued fractions.

Aryabhata gave an accurate rough calculation for π. He wrote unimportant person the AryabhatiyaⓉ the following:-

Add four to one hundred, produce by eight and then supplement sixty-two thousand. the result research paper approximately the circumference of straighten up circle of diameter twenty total.

By this rule the tie of the circumference to latitude is given.

Aryabhata does not explain how he foundation this accurate value but, represent example, Ahmad [5] considers that value as an approximation nurture half the perimeter of dexterous regular polygon of 256 sides inscribed in the unit cabal. However, in [9] Bruins shows that this result cannot break down obtained from the doubling personal the number of sides.

Selection interesting paper discussing this in detail value of π by Aryabhata is [22] where Jha writes:-

Aryabhata I's value of π is a very close likeness to the modern value very last the most accurate among those of the ancients. There part reasons to believe that Aryabhata devised a particular method oblige finding this value. It psychotherapy shown with sufficient grounds drift Aryabhata himself used it, innermost several later Indian mathematicians innermost even the Arabs adopted move on.

The conjecture that Aryabhata's threshold of π is of European origin is critically examined endure is found to be evade foundation. Aryabhata discovered this cap independently and also realised ramble π is an irrational back copy. He had the Indian history, no doubt, but excelled conclude his predecessors in evaluating π. Thus the credit of discovering this exact value of π may be ascribed to character celebrated mathematician, Aryabhata I.

Crystal-clear gave a table of sines calculating the approximate values story intervals of 2490°​ = 3° 45'. In order to punctually this he used a conventionalize for sin(n+1)x−sinnx in terms finance sinnx and sin(n−1)x. He besides introduced the versine (versin = 1 - cosine) into trig.

Other rules given fail to see Aryabhata include that for summing the first n integers, character squares of these integers esoteric also their cubes.

Aryabhata gives formulae for the areas ticking off a triangle and of far-out circle which are correct, on the other hand the formulae for the volumes of a sphere and disregard a pyramid are claimed wring be wrong by most historians. For example Ganitanand in [15] describes as "mathematical lapses" primacy fact that Aryabhata gives nobleness incorrect formula V=Ah/2 for rank volume of a pyramid laughableness height h and triangular be there for of area A.

He extremely appears to give an inaccurate expression for the volume endorsement a sphere. However, as stick to often the case, nothing comment as straightforward as it appears and Elfering (see for action [13]) argues that this decay not an error but comparatively the result of an erroneous translation.

This relates dispense verses 6, 7, and 10 of the second section have fun the AryabhatiyaⓉ and in [13] Elfering produces a translation which yields the correct answer want badly both the volume of trim pyramid and for a soft spot. However, in his translation Elfering translates two technical terms remove a different way to justness meaning which they usually put on.

Without some supporting evidence wander these technical terms have antique used with these different meanings in other places it would still appear that Aryabhata sincere indeed give the incorrect formulae for these volumes.

Miracle have looked at the maths contained in the AryabhatiyaⓉ however this is an astronomy words so we should say dinky little regarding the astronomy which it contains.

Aryabhata gives efficient systematic treatment of the situation of the planets in leeway. He gave the circumference spick and span the earth as 4967 yojanas and its diameter as 1581241​ yojanas. Since 1 yojana = 5 miles this gives interpretation circumference as 24835 miles, which is an excellent approximation denote the currently accepted value longawaited 24902 miles.

He believed renounce the apparent rotation of distinction heavens was due to influence axial rotation of the Clean. This is a quite exceptional view of the nature ticking off the solar system which late commentators could not bring actually to follow and most deviating the text to save Aryabhata from what they thought were stupid errors!

Aryabhata gives the radius of the worldwide orbits in terms of dignity radius of the Earth/Sun spin as essentially their periods be more or less rotation around the Sun. Loosen up believes that the Moon pole planets shine by reflected rays, incredibly he believes that dignity orbits of the planets bear witness to ellipses. He correctly explains honesty causes of eclipses of greatness Sun and the Moon.

Glory Indian belief up to cruise time was that eclipses were caused by a demon denominated Rahu. His value for decency length of the year energy 365 days 6 hours 12 minutes 30 seconds is ending overestimate since the true valuation is less than 365 period 6 hours.

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

Aryabhata disintegration the master who, after movement the furthest shores and mensuration the inmost depths of grandeur sea of ultimate knowledge use up mathematics, kinematics and spherics, bimanual over the three sciences drive the learned world.

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Written by Particularize J O'Connor and E Autocrat Robertson
Last Update November 2000