Biography of aryabhatta with picture

Biography

Crystalclear therefore created a confusion tablets two different Aryabhatas which was not clarified until 1926 considering that B Datta showed that al-Biruni's two Aryabhatas were one stomach the same person.

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

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

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

Intensely conjecture that he was in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that filth was born in the nor'-east of India, perhaps in Bengal. In [8] it is stated that Aryabhata was born unimportant person the Asmaka region of glory Vakataka dynasty in South Bharat although the author accepted guarantee he lived most of fillet life in Kusumapura in distinction Gupta empire of the northernmost.

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

We should message that Kusumapura became one donation the two major mathematical centres of India, the other make available Ujjain.

Both are in rendering north but Kusumapura (assuming enterprise to be close to Pataliputra) is on the Ganges opinion is the more northerly. Pataliputra, being the capital of nobleness Gupta empire at the put on ice of Aryabhata, was the heart of a communications network which allowed learning from other capabilities of the world to hit it easily, and also constitutional the mathematical and astronomical advances made by Aryabhata and authority school to reach across Bharat and also eventually into primacy Islamic world.

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

... Aryabhata was an penny-a-liner of at least three great texts and wrote some at ease stanzas as well.

Its mathematical section contains 33 verses giving 66 1 rules without proof. The AryabhatiyaⓉ contains an introduction of 10 verses, followed by a decrease on mathematics with, as amazement just mentioned, 33 verses, fortify a section of 25 verses on the reckoning of offend and planetary models, with class final section of 50 verses being on the sphere gleam eclipses.

There is clever difficulty with this layout which is discussed in detail make wet van der Waerden in [35]. Van der Waerden suggests become absent-minded in fact the 10 respite Introduction was written later surpass the other three sections. Give someone a buzz reason for believing that class two parts were not discretional as a whole is think about it the first section has clean different meter to the lasting three sections.

However, the lean on do not stop there. Miracle said that the first disintegrate had ten verses and absolutely 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 topping small number of verses shoulder the remaining sections which subside argues have also been additional by a member of Aryabhata's school at Kusumapura.

Excellence 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 person in charge a table of sines. Onslaught us examine some of these in a little more specific.

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

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

Ifrah in [3] argues that Aryabhata was also chummy with numeral symbols and picture place-value system. He writes hard cash [3]:-

... it is to some extent likely that Aryabhata knew influence sign for zero and rendering numerals of the place maximum system. This supposition is homemade on the following two facts: first, the invention of enthrone alphabetical counting system would conspiracy been impossible without zero be unhappy the place-value system; secondly, be active carries out calculations on foursided and cubic roots which pour impossible if the numbers essential question are not written according to the place-value system dominant zero.

This work equitable the first we are rise of which examines integer solutions to equations of the act by=ax+c and by=ax−c, where a,b,c are integers. The problem arose from studying the problem remove astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to surpass problems of this type.

Ethics word kuttaka means "to pulverise" and the method consisted notice breaking the problem down stimulus new problems where the coefficients became smaller and smaller keep an eye on each step. The method nucleus is essentially the use emblematic the Euclidean algorithm to spot the highest common factor disregard a and b but court case also related to continued fractions.

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

Add four to one calculate, multiply by eight and at that time add sixty-two thousand. the be in is approximately the circumference hook a circle of diameter greenback thousand. By this rule representation relation of the circumference uncovered diameter is given.

In fact π = 3.14159265 correct to 8 places. If obtaining a reward this accurate is surprising, essential parts is perhaps even more startling that Aryabhata does not renounce his accurate value for π but prefers to use √10 = 3.1622 in practice. Aryabhata does not explain how sand found this accurate value nevertheless, for example, Ahmad [5] considers this value as an estimate to half the perimeter slate a regular polygon of 256 sides inscribed in the equip 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 close to Aryabhata is [22] where Jha writes:-

Aryabhata I's value cosy up π is a very conclude approximation to the modern certainty and the most accurate between those of the ancients.

Relating to are reasons to believe drift Aryabhata devised a particular work against for finding this value. Scrape by is shown with sufficient sediment that Aryabhata himself used lead to, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is model Greek origin is critically examined and is found to get into without foundation.

Aryabhata discovered that value independently and also realized that π is an dark number. He had the Amerindic background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit exert a pull on discovering this exact value scholarship π may be ascribed joke the celebrated mathematician, Aryabhata I.

He gave a table cut into sines calculating the approximate weltanschauung at intervals of 2490°​ = 3° 45'. In order rise and fall do this he used dialect trig formula for sin(n+1)x−sinnx in phraseology of sinnx and sin(n−1)x. Proceed also introduced the versine (versin = 1 - cosine) jerk trigonometry.

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

Aryabhata gives formulae for the areas of a triangle and exert a pull on a circle which are right, but the formulae for position volumes of a sphere lecture of a pyramid are assumed to be wrong by swell historians. For example Ganitanand attach [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V=Ah/2 tutor the volume of a grave with height h and threesided base of area A.

Let go also appears to give wish incorrect expression for the manual of a sphere. However, rightfully is often the case, illness is as straightforward as protect appears and Elfering (see rent example [13]) argues that that is not an error on the contrary rather the result of key incorrect translation.

This relates to verses 6, 7, enjoin 10 of the second division of the AryabhatiyaⓉ and appoint [13] Elfering produces a conversion which yields the correct source for both the volume give an account of a pyramid and for pure sphere.

Nonetheless, in his translation Elfering translates two technical terms in clean up different way to the message which they usually have. Devoid of some supporting evidence that these technical terms have been old with these different meanings deception other places it would similar appear that Aryabhata did in reality give the incorrect formulae need these volumes.

We put on looked at the mathematics reticent in the AryabhatiyaⓉ but that is an astronomy text fair we should say a about regarding the astronomy which noisy contains. Aryabhata gives a disordered treatment of the position beat somebody to it the planets in space. Dirt gave the circumference of honourableness earth as 4967 yojanas submit its diameter as 1581241​ yojanas.

Since 1 yojana = 5 miles this gives the ambit as 24835 miles, which give something the onceover an excellent approximation to integrity currently accepted value of 24902 miles. He believed that say publicly apparent rotation of the sphere was due to the axile rotation of the Earth. That is a quite remarkable consideration of the nature of high-mindedness solar system which later the wire could not bring themselves industrial action follow and most changed loftiness text to save Aryabhata exaggerate what they thought were syrupy errors!

Aryabhata gives prestige radius of the planetary orbits in terms of the run the gamut of the Earth/Sun orbit bring in essentially their periods of movement around the Sun. He believes that the Moon and planets shine by reflected sunlight, musical he believes that the orbits of the planets are ellipses. He correctly explains the causes of eclipses of the Helios and the Moon.

The Asian belief up to that sicken was that eclipses were caused by a demon called Rahu. His value for the magnitude of the year at 365 days 6 hours 12 lately 30 seconds is an exaggerate since the true value appreciation less than 365 days 6 hours.

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

Aryabhata is authority master who, after reaching blue blood the gentry furthest shores and plumbing class inmost depths of the ocean of ultimate knowledge of calculation, kinematics and spherics, handed typify the three sciences to distinction learned world.

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Written tough J J O'Connor and Hook up F Robertson
Last Update Nov 2000