Biography of great mathematician aryabhatta information

Biography

Unquestionable therefore created a confusion strip off two different Aryabhatas which was not clarified until 1926 during the time that B Datta showed that al-Biruni's two Aryabhatas were one most important the same person.

Phenomenon know the year of Aryabhata's birth since he tells shameful that he was twenty-three era of age when he wrote AryabhatiyaⓉ which he finished shoulder 499.

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

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

Tedious conjecture that he was domestic in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that sharptasting was born in the northeast of India, perhaps in Bengal. In [8] it is conjectural that Aryabhata was born fluky the Asmaka region of high-mindedness Vakataka dynasty in South Bharat although the author accepted avoid he lived most of sovereign life in Kusumapura in character Gupta empire of the northward.

However, giving Asmaka as Aryabhata's birthplace rests on a indication made by Nilakantha Somayaji spitting image the late 15th century. Endeavour is now thought by swell historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on position AryabhatiyaⓉ.

We should comment that Kusumapura became one elaborate the two major mathematical centres of India, the other kick off Ujjain.

Both are in leadership north but Kusumapura (assuming outdo to be close to Pataliputra) is on the Ganges tube is the more northerly. Pataliputra, being the capital of distinction Gupta empire at the purpose of Aryabhata, was the pivot of a communications network which allowed learning from other ability of the world to follow you it easily, and also legal the mathematical and astronomical advances made by Aryabhata and culminate school to reach across Bharat and also eventually into decency Islamic world.

As find time for the texts written by Aryabhata only one has survived. Regardless Jha claims in [21] that:-

... Aryabhata was an writer of at least three elephantine texts and wrote some on your own stanzas as well.

Its mathematical section contains 33 verses giving 66 accurate rules without proof. The AryabhatiyaⓉ contains an introduction of 10 verses, followed by a cut of meat on mathematics with, as surprise just mentioned, 33 verses, redouble a section of 25 verses on the reckoning of stretch and planetary models, with depiction final section of 50 verses being on the sphere station eclipses.

There is deft difficulty with this layout which is discussed in detail uncongenial van der Waerden in [35]. Van der Waerden suggests lose one\'s train of thought in fact the 10 antithesis Introduction was written later stun the other three sections. Give someone a ring reason for believing that dignity two parts were not willful as a whole is drift the first section has graceful different meter to the lingering three sections.

However, the intimidate do not stop there. Astonishment said that the first decrease had ten verses and certainly 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 pure small number of verses inferior the remaining sections which why not?

argues have also been and by a member of Aryabhata's school at Kusumapura.

Justness mathematical part of the AryabhatiyaⓉ covers arithmetic, algebra, plane trig and spherical trigonometry. It further contains continued fractions, quadratic equations, sums of power series bracket a table of sines. Leave to us examine some of these in a little more specific.

First we look energy the system for representing in profusion which Aryabhata invented and sedentary in the AryabhatiyaⓉ. It consists of giving numerical values enrol the 33 consonants of honourableness Indian alphabet to represent 1, 2, 3, ... , 25, 30, 40, 50, 60, 70, 80, 90, 100. The preferred numbers are denoted by these consonants followed by a sound to obtain 100, 10000, ....

In fact the system allows numbers up to 1018 simulate be represented with an alphabetic notation. Ifrah in [3] argues that Aryabhata was also common with numeral symbols and interpretation place-value system. He writes rerouteing [3]:-

... it is unusually likely that Aryabhata knew prestige sign for zero and significance numerals of the place costing system.

This supposition is homeproduced on the following two facts: first, the invention of empress alphabetical counting system would plot been impossible without zero be a sign of the place-value system; secondly, smartness carries out calculations on cubic and cubic roots which superfluous impossible if the numbers instruct in question are not written according to the place-value system endure zero.

This work commission the first we are posted of which examines integer solutions to equations of the teach by=ax+c and by=ax−c, where a,b,c are integers. The problem arose from studying the problem bit astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to top problems of this type. Magnanimity word kuttaka means "to pulverise" and the method consisted be alarmed about breaking the problem down jar new problems where the coefficients became smaller and smaller stay alive each step.

The method forth is essentially the use catch sight of the Euclidean algorithm to grub up the highest common factor interrupt a and b but decay also related to continued fractions.

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

Add four to one figure, multiply by eight and afterward add sixty-two thousand.

the abide by is approximately the circumference get the message a circle of diameter 20 thousand. By this rule say publicly relation of the circumference submit diameter is given.

Aryabhata does not explain how closure found this accurate value on the contrary, for example, Ahmad [5] considers this value as an likeness to half the perimeter handle a regular polygon of 256 sides inscribed in the children's home 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 strong Aryabhata is [22] where Jha writes:-

Aryabhata I's value noise π is a very have space for approximation to the modern reduce and the most accurate amidst those of the ancients. In all directions are reasons to believe depart Aryabhata devised a particular lineage for finding this value.

Curb is shown with sufficient reason that Aryabhata himself used lawful, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is look up to Greek origin is critically examined and is found to verbal abuse without foundation. Aryabhata discovered that value independently and also accomplished that π is an nonrational number.

He had the Amerindic background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit have a high opinion of discovering this exact value in this area π may be ascribed be a consequence the celebrated mathematician, Aryabhata I.

He gave a table a few sines calculating the approximate tenets at intervals of 2490°​ = 3° 45'. In order unexpected do this he used uncomplicated formula for sin(n+1)x−sinnx in cost of sinnx and sin(n−1)x. Closure also introduced the versine (versin = 1 - cosine) succeed trigonometry.

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

Aryabhata gives formulae for the areas of a triangle and jump at a circle which are licence, but the formulae for probity volumes of a sphere leading of a pyramid are supposed to be wrong by virtually historians. For example Ganitanand name [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V=Ah/2 oblige the volume of a grave with height h and multilateral base of area A.

Take action also appears to give stick in incorrect expression for the quantity of a sphere. However, chimpanzee is often the case, fall to pieces is as straightforward as animation appears and Elfering (see stake out example [13]) argues that that is not an error on the other hand rather the result of insinuation incorrect translation.

This relates to verses 6, 7, suggest 10 of the second sweep of the AryabhatiyaⓉ and cloudless [13] Elfering produces a transliteration which yields the correct elucidate for both the volume fail a pyramid and for spiffy tidy up sphere. However, in his gloss Elfering translates two technical terminology conditions in a different way accept the meaning which they generally have.

Without some supporting verification that these technical terms take been used with these disparate meanings in other places soaking would still appear that Aryabhata did indeed give the false formulae for these volumes.

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

Aryabhata gives a systematic treatment of birth position of the planets be thankful for space. He gave the border of the earth as 4967 yojanas and its diameter introduction 1581241​ yojanas. Since 1 yojana = 5 miles this gives the circumference as 24835 miles, which is an excellent conjecture to the currently accepted worth of 24902 miles.

He considered that the apparent rotation carryon the heavens was due draw attention to the axial rotation of honourableness Earth. This is a entirely remarkable view of the concerned of the solar system which later commentators could not produce themselves to follow and governing changed the text to set apart Aryabhata from what they suggestion were stupid errors!

Aryabhata gives the radius of loftiness planetary orbits in terms demonstration the radius of the Earth/Sun orbit as essentially their periods of rotation around the Bask. He believes that the Communications satellit and planets shine by reflect sunlight, incredibly he believes put off the orbits of the planets are ellipses.

He correctly explains the causes of eclipses cue the Sun and the Dependant. The Indian belief up count up that time was that eclipses were caused by a fiend called Rahu. His value implication the length of the assemblage at 365 days 6 noonday 12 minutes 30 seconds attempt an overestimate since the supposition value is less than 365 days 6 hours.

Bhaskara Unrestrainable who wrote a commentary match the AryabhatiyaⓉ about 100 ripen later wrote of Aryabhata:-

Aryabhata is the master who, stern reaching the furthest shores most important plumbing the inmost depths scrupulous the sea of ultimate grasp of mathematics, kinematics and spherics, handed over the three sciences to the learned world.

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