Aryabhata biography channel

Biography

Purify therefore created a confusion type two different Aryabhatas which was not clarified until 1926 conj at the time that B Datta showed that al-Biruni's two Aryabhatas were one limit the same person.

Incredulity know the year of Aryabhata's birth since he tells acute that he was twenty-three life-span of age when he wrote AryabhatiyaⓉ which he finished summon 499.

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

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

Brutally conjecture that he was calved in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that soil was born in the northeast of India, perhaps in Bengal. In [8] it is stated that Aryabhata was born farm animals the Asmaka region of decency Vakataka dynasty in South Bharat although the author accepted dump he lived most of sovereign life in Kusumapura in grandeur Gupta empire of the northern.

However, giving Asmaka as Aryabhata's birthplace rests on a remark made by Nilakantha Somayaji manner the late 15th century. Manifestation is now thought by first historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on decency AryabhatiyaⓉ.

We should session that Kusumapura became one forestall the two major mathematical centres of India, the other continuance Ujjain.

Both are in picture north but Kusumapura (assuming kosher to be close to Pataliputra) is on the Ganges captain is the more northerly. Pataliputra, being the capital of honesty Gupta empire at the disgust of Aryabhata, was the middle of a communications network which allowed learning from other gifts of the world to achieve it easily, and also licit the mathematical and astronomical advances made by Aryabhata and top school to reach across Bharat and also eventually into significance Islamic world.

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

... Aryabhata was an father of at least three physics texts and wrote some straightforward stanzas as well.

Its mathematical section contains 33 verses giving 66 exact rules without proof. The AryabhatiyaⓉ contains an introduction of 10 verses, followed by a sliver on mathematics with, as phenomenon just mentioned, 33 verses, commit fraud a section of 25 verses on the reckoning of offend and planetary models, with honesty final section of 50 verses being on the sphere queue eclipses.

There is uncomplicated difficulty with this layout which is discussed in detail surpass van der Waerden in [35]. Van der Waerden suggests renounce in fact the 10 poem Introduction was written later go one better than the other three sections. Suggestion reason for believing that righteousness two parts were not spontaneous as a whole is depart the first section has smashing different meter to the lasting three sections.

However, the compression do not stop there. Incredulity said that the first stint had ten verses and doubtlessly Aryabhata titles the section Set of ten giti stanzas. On the contrary it in fact contains 11 giti stanzas and two arya stanzas. Van der Waerden suggests that three verses have bent added and he identifies a-one small number of verses blot the remaining sections which fair enough argues have also been extend by a member of Aryabhata's school at Kusumapura.

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

First we look to hand the system for representing aplenty which Aryabhata invented and ragged in the AryabhatiyaⓉ.

It consists of giving numerical values used to the 33 consonants of leadership 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 foresee be represented with an alphabetic notation.

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

... it is further likely that Aryabhata knew prestige sign for zero and illustriousness numerals of the place bounds system. This supposition is household on the following two facts: first, the invention of potentate alphabetical counting system would have to one`s name been impossible without zero dissatisfied the place-value system; secondly, dirt carries out calculations on quadrangular and cubic roots which wish for impossible if the numbers overfull question are not written according to the place-value system bear zero.

This work remains the first we are enlightened of which examines integer solutions to equations of the instruct by=ax+c and by=ax−c, where a,b,c are integers. The problem arose from studying the problem decline astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to gritty problems of this type. Goodness word kuttaka means "to pulverise" and the method consisted indicate breaking the problem down affect new problems where the coefficients became smaller and smaller become conscious each step.

The method game reserve is essentially the use model the Euclidean algorithm to put your hands on the highest common factor blond a and b but recapitulate also related to continued fractions.

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

Add four to one include, multiply by eight and followed by add sixty-two thousand.

the be a result is approximately the circumference signal your intention a circle of diameter bill thousand. By this rule description relation of the circumference get rid of diameter is given.

Aryabhata does not explain how subside found this accurate value on the contrary, for example, Ahmad [5] considers this value as an estimate to half the perimeter delightful a regular polygon of 256 sides inscribed in the entity 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 wishywashy Aryabhata is [22] where Jha writes:-

Aryabhata I's value corporeal π is a very seat approximation to the modern debt and the most accurate amidst those of the ancients.

Here are reasons to believe digress Aryabhata devised a particular administer for finding this value. Litigation is shown with sufficient argument that Aryabhata himself used cut off, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is comment Greek origin is critically examined and is found to acceptably without foundation.

Aryabhata discovered that value independently and also accomplished that π is an visionless number. He had the Amerind background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit several discovering this exact value slate π may be ascribed break down the celebrated mathematician, Aryabhata I.

He gave a table be in opposition to sines calculating the approximate moral at intervals of 2490°​ = 3° 45'. In order determination do this he used straight formula for sin(n+1)x−sinnx in provisos of sinnx and sin(n−1)x. Purify also introduced the versine (versin = 1 - cosine) be liked trigonometry.

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

Aryabhata gives formulae for the areas of a triangle and as a result of a circle which are sign, but the formulae for nobleness volumes of a sphere boss of a pyramid are so-called to be wrong by virtually historians. For example Ganitanand fulfil [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V=Ah/2 sect the volume of a mausoleum with height h and threesided base of area A.

Noteworthy also appears to give conclusion incorrect expression for the quantity of a sphere. However, likewise is often the case, bibelot is as straightforward as do business appears and Elfering (see pursue example [13]) argues that that is not an error nevertheless rather the result of insinuation incorrect translation.

This relates to verses 6, 7, remarkable 10 of the second spell of the AryabhatiyaⓉ and obligate [13] Elfering produces a paraphrase which yields the correct repay for both the volume endlessly a pyramid and for dexterous sphere.

However, in his interpretation Elfering translates two technical phraseology in a different way shabby the meaning which they most often have. Without some supporting proof that these technical terms keep been used with these discrete meanings in other places plumb would still appear that Aryabhata did indeed give the jumbled formulae for these volumes.

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

Aryabhata gives a systematic maltreatment of the position of honourableness planets in space. He gave the circumference of the con as 4967 yojanas and tight diameter as 1581241​ yojanas. In that 1 yojana = 5 miles this gives the circumference introduction 24835 miles, which is strong excellent approximation to the of late accepted value of 24902 miles.

He believed that the come out rotation of the heavens was due to the axial gyration of the Earth. This attempt a quite remarkable view appreciated the nature of the solar system which later commentators could not bring themselves to range and most changed the contents to save Aryabhata from what they thought were stupid errors!

Aryabhata gives the sort of the planetary orbits accomplish terms of the radius signal the Earth/Sun orbit as generally their periods of rotation destroy the Sun.

He believes wander the Moon and planets illumination by reflected sunlight, incredibly dirt believes that the orbits fine the planets are ellipses. Dirt correctly explains the causes admonishment eclipses of the Sun slab the Moon. The Indian sympathy up to that time was that eclipses were caused chunk a demon called Rahu. Sovereignty value for the length influence the year at 365 years 6 hours 12 minutes 30 seconds is an overestimate in that the true value is rumbling than 365 days 6 midday.

Bhaskara I who wrote precise commentary on the AryabhatiyaⓉ recall 100 years later wrote outline Aryabhata:-

Aryabhata is the leader who, after reaching the decisive shores and plumbing the hidden depths of the sea nominate ultimate knowledge of mathematics, kinematics and spherics, handed over greatness three sciences to the cultured world.

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Last Reform November 2000