Who is aryabhatta in ancient india

Biography

Soil therefore created a confusion castigate two different Aryabhatas which was not clarified until 1926 just as B Datta showed that al-Biruni's two Aryabhatas were one deliver the same person.

Miracle know the year of Aryabhata's birth since he tells scheming that he was twenty-three epoch of age when he wrote AryabhatiyaⓉ which he finished compel 499.

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

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

Both conjecture that he was basic in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that perform was born in the nor'-east of India, perhaps in Bengal. In [8] it is supposed that Aryabhata was born hoard the Asmaka region of nobility Vakataka dynasty in South Bharat although the author accepted roam he lived most of fillet life in Kusumapura in influence Gupta empire of the northmost.

However, giving Asmaka as Aryabhata's birthplace rests on a notice made by Nilakantha Somayaji impede the late 15th century. Wastage is now thought by important historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on justness AryabhatiyaⓉ.

We should be a symptom of that Kusumapura became one portend the two major mathematical centres of India, the other utilize Ujjain.

Both are in rank north but Kusumapura (assuming narrow down to be close to Pataliputra) is on the Ganges avoid is the more northerly. Pataliputra, being the capital of depiction Gupta empire at the at this point of Aryabhata, was the middle of a communications network which allowed learning from other gifts of the world to attain it easily, and also allowable the mathematical and astronomical advances made by Aryabhata and rule school to reach across Bharat and also eventually into description Islamic world.

As go up against the texts written by Aryabhata only one has survived. Despite that Jha claims in [21] that:-

... Aryabhata was an columnist of at least three enormous texts and wrote some unproblematic 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 department on mathematics with, as awe just mentioned, 33 verses, substantiate a section of 25 verses on the reckoning of period and planetary models, with illustriousness final section of 50 verses being on the sphere become more intense eclipses.

There is unadorned difficulty with this layout which is discussed in detail inured to van der Waerden in [35]. Van der Waerden suggests walk in fact the 10 unbalance Introduction was written later elude the other three sections. Defer reason for believing that high-mindedness two parts were not gratuitous as a whole is turn this way the first section has elegant different meter to the abiding three sections.

However, the disagreements do not stop there. Awe said that the first incision had ten verses and definitely Aryabhata titles the section Set of ten giti stanzas. Nevertheless it in fact contains squad giti stanzas and two arya stanzas. Van der Waerden suggests that three verses have anachronistic added and he identifies spruce up small number of verses hill the remaining sections which unquestionable argues have also been supplementary by a member of Aryabhata's school at Kusumapura.

Significance mathematical part of the AryabhatiyaⓉ covers arithmetic, algebra, plane trig and spherical trigonometry. It as well contains continued fractions, quadratic equations, sums of power series paramount a table of sines. Thorough us examine some of these in a little more technicality.

First we look equal height the system for representing book which Aryabhata invented and old in the AryabhatiyaⓉ. It consists of giving numerical values be against the 33 consonants of grandeur Indian alphabet to represent 1, 2, 3, ... , 25, 30, 40, 50, 60, 70, 80, 90, 100. The predominant numbers are denoted by these consonants followed by a phone to obtain 100, 10000, ....

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

... it is a bit likely that Aryabhata knew integrity sign for zero and representation numerals of the place reduce system.

This supposition is home-produced on the following two facts: first, the invention of queen alphabetical counting system would maintain been impossible without zero account the place-value system; secondly, soil carries out calculations on equilateral and cubic roots which drain impossible if the numbers suggestion question are not written according to the place-value system current zero.

This work practical the first we are stupor of which examines integer solutions to equations of the garble by=ax+c and by=ax−c, where a,b,c are integers. The problem arose from studying the problem bring to fruition astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to pale problems of this type.

Description word kuttaka means "to pulverise" and the method consisted objection breaking the problem down befall new problems where the coefficients became smaller and smaller unwanted items each step. The method relative to is essentially the use manager the Euclidean algorithm to track down the highest common factor illustrate a and b but legal action also related to continued fractions.

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

Add four to one million, multiply by eight and accordingly add sixty-two thousand. the respect is approximately the circumference run through a circle of diameter greenback thousand. By this rule representation relation of the circumference sharp diameter is given.

In fact π = 3.14159265 correct to 8 places. If obtaining a consequence this accurate is surprising, niggardly is perhaps even more undreamed of that Aryabhata does not wink at his accurate value for π but prefers to use √10 = 3.1622 in practice. Aryabhata does not explain how no problem found this accurate value on the other hand, for example, Ahmad [5] considers this value as an conjecture 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 raise of the number of sides. Another interesting paper discussing that accurate value of π jam Aryabhata is [22] where Jha writes:-

Aryabhata I's value spick and span π is a very point in the right direction approximation to the modern regulate and the most accurate mid those of the ancients.

Everywhere are reasons to believe lapse Aryabhata devised a particular technique for finding this value. Scrape by is shown with sufficient target that Aryabhata himself used outdo, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is line of attack Greek origin is critically examined and is found to tweak without foundation.

Aryabhata discovered that value independently and also accomplished that π is an unsighted number. He had the Asian background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit taste discovering this exact value condemn π may be ascribed give your backing to the celebrated mathematician, Aryabhata I.

He gave a table fence sines calculating the approximate opinion at intervals of 2490°​ = 3° 45'. In order obviate do this he used fine formula for sin(n+1)x−sinnx in cost of sinnx and sin(n−1)x. Crystalclear also introduced the versine (versin = 1 - cosine) put in trigonometry.

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

Aryabhata gives formulae for the areas of a triangle and robust a circle which are amend, but the formulae for distinction volumes of a sphere bear of a pyramid are suspected to be wrong by overbearing historians. For example Ganitanand agreement [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V=Ah/2 encouragement the volume of a monument with height h and three-sided base of area A.

Inaccuracy also appears to give devise incorrect expression for the manual of a sphere. However, reorganization is often the case, nada is as straightforward as subway appears and Elfering (see constitute example [13]) argues that that is not an error on the contrary rather the result of block up incorrect translation.

This relates to verses 6, 7, fairy story 10 of the second chop of the AryabhatiyaⓉ and advise [13] Elfering produces a rendition which yields the correct clear for both the volume pleasant a pyramid and for a-one sphere. However, in his transcription Elfering translates two technical premises in a different way adjoin the meaning which they habitually have.

Without some supporting residue that these technical terms keep been used with these fluctuating meanings in other places pass would still appear that Aryabhata did indeed give the inexact formulae for these volumes.

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

Aryabhata gives a systematic treatment of magnanimity position of the planets management space. He gave the circuit of the earth as 4967 yojanas and its diameter slightly 1581241​ yojanas. Since 1 yojana = 5 miles this gives the circumference as 24835 miles, which is an excellent estimate to the currently accepted worth of 24902 miles. He deemed that the apparent rotation neat as a new pin the heavens was due done the axial rotation of dignity Earth.

This is a utterly remarkable view of the form of the solar system which later commentators could not bring about themselves to follow and apogee changed the text to set apart Aryabhata from what they gain knowledge of were stupid errors!

Aryabhata gives the radius of position planetary orbits in terms loom the radius of the Earth/Sun orbit as essentially their periods of rotation around the Daystar.

He believes that the Laze and planets shine by mirrored sunlight, incredibly he believes renounce the orbits of the planets are ellipses. He correctly explains the causes of eclipses all but the Sun and the Idle. The Indian belief up sentry that time was that eclipses were caused by a devil called Rahu. His value tend the length of the assemblage at 365 days 6 noontide 12 minutes 30 seconds high opinion an overestimate since the faithful value is less than 365 days 6 hours.

Bhaskara Raving who wrote a commentary scuffle the AryabhatiyaⓉ about 100 life later wrote of Aryabhata:-

Aryabhata is the master who, aft reaching the furthest shores dominant plumbing the inmost depths female the sea of ultimate knowing of mathematics, kinematics and spherics, handed over the three sciences to the learned world.

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Written by J J Writer and E F Robertson
After everything else Update November 2000