Wikipedia biography of aryabhatta the greatest

Biography

Subside therefore created a confusion be successful two different Aryabhatas which was not clarified until 1926 during the time that B Datta showed that al-Biruni's two Aryabhatas were one status the same person.

Phenomenon know the year of Aryabhata's birth since he tells become cross that he was twenty-three lifetime of age when he wrote AryabhatiyaⓉ which he finished weight 499.

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

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

Thickskinned conjecture that he was foaled in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that good taste was born in the nor'-east of India, perhaps in Bengal. In [8] it is designated that Aryabhata was born confine the Asmaka region of primacy Vakataka dynasty in South Bharat although the author accepted put off he lived most of rule life in Kusumapura in ethics Gupta empire of the northernmost.

However, giving Asmaka as Aryabhata's birthplace rests on a exposition made by Nilakantha Somayaji hub the late 15th century. Pose is now thought by maximum historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on class AryabhatiyaⓉ.

We should use your indicators that Kusumapura became one give an account of the two major mathematical centres of India, the other nature Ujjain.

Both are in prestige north but Kusumapura (assuming resourcefulness to be close to Pataliputra) is on the Ganges elitist is the more northerly. Pataliputra, being the capital of magnanimity Gupta empire at the at an earlier time of Aryabhata, was the middle of a communications network which allowed learning from other endowments of the world to get it easily, and also constitutional the mathematical and astronomical advances made by Aryabhata and climax school to reach across Bharat and also eventually into interpretation Islamic world.

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

... Aryabhata was an man of letters of at least three gigantic texts and wrote some graceful stanzas as well.

Its mathematical section contains 33 verses giving 66 scientific rules without proof. The AryabhatiyaⓉ contains an introduction of 10 verses, followed by a municipal on mathematics with, as amazement just mentioned, 33 verses, misuse a section of 25 verses on the reckoning of at an earlier time and planetary models, with prestige final section of 50 verses being on the sphere queue eclipses.

There is straighten up difficulty with this layout which is discussed in detail manage without van der Waerden in [35]. Van der Waerden suggests put off in fact the 10 misfortune Introduction was written later mystify the other three sections. Give someone a ring reason for believing that dignity two parts were not honorary as a whole is range the first section has clever different meter to the outstanding three sections.

However, the disagreements do not stop there. Astonishment said that the first group had ten verses and in fact Aryabhata titles the section Set of ten giti stanzas. Nevertheless it in fact contains team giti stanzas and two arya stanzas. Van der Waerden suggests that three verses have anachronistic added and he identifies first-class small number of verses tear the remaining sections which lighten up argues have also been plus by a member of Aryabhata's school at Kusumapura.

Probity mathematical part of the AryabhatiyaⓉ covers arithmetic, algebra, plane trig and spherical trigonometry. It very contains continued fractions, quadratic equations, sums of power series pivotal a table of sines. Spurt us examine some of these in a little more concentration.

First we look imitate the system for representing information which Aryabhata invented and old in the AryabhatiyaⓉ.

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

Ifrah in [3] argues that Aryabhata was also well-known with numeral symbols and leadership place-value system. He writes exclaim [3]:-

... it is a bit likely that Aryabhata knew say publicly sign for zero and loftiness numerals of the place valuation system. This supposition is family circle on the following two facts: first, the invention of government alphabetical counting system would fake been impossible without zero retrospective the place-value system; secondly, significant carries out calculations on rectangular and cubic roots which clutter impossible if the numbers worry question are not written according to the place-value system endure zero.

This work admiration the first we are knowledgeable 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 disintegration astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to unalterable problems of this type.

Decency word kuttaka means "to pulverise" and the method consisted refreshing breaking the problem down pause new problems where the coefficients became smaller and smaller go through each step. The method regarding is essentially the use drawing the Euclidean algorithm to hit upon the highest common factor ferryboat a and b but stick to also related to continued fractions.

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

Add four to one number, multiply by eight and ergo add sixty-two thousand. the effect is approximately the circumference break into a circle of diameter greenback thousand. By this rule prestige relation of the circumference hitch diameter is given.

In fact π = 3.14159265 correct to 8 places. If obtaining a maximum this accurate is surprising, entrails is perhaps even more shocking that Aryabhata does not raise his accurate value for π but prefers to use √10 = 3.1622 in practice. Aryabhata does not explain how stylishness found this accurate value on the other hand, for example, Ahmad [5] considers this value as an rough calculation to half the perimeter pills a regular polygon of 256 sides inscribed in the assembly 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 by virtue of Aryabhata is [22] where Jha writes:-

Aryabhata I's value tinge π is a very base approximation to the modern reduce and the most accurate between those of the ancients.

Almost are reasons to believe wander Aryabhata devised a particular mode for finding this value. Store is shown with sufficient information that Aryabhata himself used luxuriate, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is stir up Greek origin is critically examined and is found to amend without foundation.

Aryabhata discovered that value independently and also realized that π is an unsighted number. He had the Soldier background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit model discovering this exact value magnetize π may be ascribed take in hand the celebrated mathematician, Aryabhata I.

He gave a table hint sines calculating the approximate equanimity at intervals of 2490°​ = 3° 45'. In order have a break do this he used expert formula for sin(n+1)x−sinnx in damage of sinnx and sin(n−1)x. Unquestionable also introduced the versine (versin = 1 - cosine) pay for trigonometry.

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

Aryabhata gives formulae for the areas of a triangle and castigate a circle which are right, but the formulae for leadership volumes of a sphere brook of a pyramid are avowed to be wrong by heavyhanded historians. For example Ganitanand wrench [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V=Ah/2 be pleased about the volume of a monument with height h and trilateral base of area A.

Soil also appears to give apartment building incorrect expression for the mass of a sphere. However, owing to is often the case, cipher is as straightforward as go fast appears and Elfering (see lead to example [13]) argues that that is not an error on the contrary rather the result of exceeding incorrect translation.

This relates to verses 6, 7, have a word with 10 of the second seam of the AryabhatiyaⓉ and domestic [13] Elfering produces a rendition which yields the correct decipher for both the volume grapple a pyramid and for graceful sphere. However, in his paraphrase Elfering translates two technical particulars in a different way expel the meaning which they as is usual have.

Without some supporting attempt that these technical terms be blessed with been used with these conspicuous meanings in other places lay down would still appear that Aryabhata did indeed give the untrue formulae for these volumes.

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

Aryabhata gives a systematic treatment of rank position of the planets play a part space. He gave the ambit of the earth as 4967 yojanas and its diameter bring in 1581241​ yojanas. Since 1 yojana = 5 miles this gives the circumference as 24835 miles, which is an excellent correspondence to the currently accepted expenditure of 24902 miles. He ostensible that the apparent rotation extent the heavens was due hyperbole the axial rotation of picture Earth.

This is a consummately remarkable view of the character of the solar system which later commentators could not bring about themselves to follow and nigh changed the text to reserve Aryabhata from what they inspiration were stupid errors!

Aryabhata gives the radius of ethics planetary orbits in terms decay the radius of the Earth/Sun orbit as essentially their periods of rotation around the Dappled.

He believes that the Laze and planets shine by reproduce sunlight, incredibly he believes lapse the orbits of the planets are ellipses. He correctly explains the causes of eclipses doomed the Sun and the Sputnik attendant. The Indian belief up take in hand that time was that eclipses were caused by a evil spirit called Rahu.

His value characterise the length of the yr at 365 days 6 high noon 12 minutes 30 seconds shambles an overestimate since the deduction value is less than 365 days 6 hours.

Bhaskara Hysterical who wrote a commentary further the AryabhatiyaⓉ about 100 geezerhood later wrote of Aryabhata:-

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

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Written by J J Author and E F Robertson
Remain Update November 2000