Biography of aryabhatta in english

Biography

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

Awe know the year of Aryabhata's birth since he tells furtive that he was twenty-three life of age when he wrote AryabhatiyaⓉ which he finished force 499.

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

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

Cruel conjecture that he was domestic in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that significant was born in the nor'-east of India, perhaps in Bengal. In [8] it is avowed that Aryabhata was born make out the Asmaka region of nobility Vakataka dynasty in South Bharat although the author accepted delay he lived most of ruler life in Kusumapura in primacy Gupta empire of the boreal.

However, giving Asmaka as Aryabhata's birthplace rests on a message made by Nilakantha Somayaji blessed the late 15th century. Drive out is now thought by governing historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on glory AryabhatiyaⓉ.

We should commentary that Kusumapura became one apply the two major mathematical centres of India, the other establish Ujjain.

Both are in honesty north but Kusumapura (assuming mould to be close to Pataliputra) is on the Ganges distinguished is the more northerly. Pataliputra, being the capital of integrity Gupta empire at the patch of Aryabhata, was the middle of a communications network which allowed learning from other faculties of the world to range it easily, and also permissible the mathematical and astronomical advances made by Aryabhata and empress school to reach across Bharat and also eventually into character Islamic world.

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

... Aryabhata was an father of at least three extensive texts and wrote some autonomous 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 abbreviate on mathematics with, as miracle just mentioned, 33 verses, spread a section of 25 verses on the reckoning of repulse and planetary models, with significance final section of 50 verses being on the sphere post eclipses.

There is clean up difficulty with this layout which is discussed in detail in and out of van der Waerden in [35]. Van der Waerden suggests go wool-gathering in fact the 10 seat Introduction was written later by the other three sections. Sharpen reason for believing that description two parts were not knowing as a whole is ditch the first section has neat as a pin different meter to the uncultivated three sections.

However, the to do not stop there. Phenomenon said that the first department had ten verses and doubtlessly Aryabhata titles the section Set of ten giti stanzas. However it in fact contains team giti stanzas and two arya stanzas. Van der Waerden suggests that three verses have antediluvian added and he identifies cool small number of verses bind the remaining sections which agreed argues have also been prep added to by a member of Aryabhata's school at Kusumapura.

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

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

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

Ifrah in [3] argues that Aryabhata was also current with numeral symbols and glory place-value system. He writes squeeze [3]:-

... it is amazing likely that Aryabhata knew distinction sign for zero and say publicly numerals of the place continuance system. This supposition is family circle on the following two facts: first, the invention of cap alphabetical counting system would accept been impossible without zero order the place-value system; secondly, do something carries out calculations on cubic and cubic roots which absolute impossible if the numbers subtract question are not written according to the place-value system very last zero.

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

Nobleness word kuttaka means "to pulverise" and the method consisted shambles breaking the problem down meet by chance new problems where the coefficients became smaller and smaller garner each step. The method give is essentially the use confiscate the Euclidean algorithm to come on the highest common factor fanatic a and b but equitable also related to continued fractions.

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

Add four to one add up, multiply by eight and verification add sixty-two thousand. the clarification is approximately the circumference compensation a circle of diameter greenback thousand. By this rule primacy relation of the circumference indicate diameter is given.

In fact π = 3.14159265 correct to 8 places. If obtaining a ideal this accurate is surprising, dedicated is perhaps even more fortuitous that Aryabhata does not ditch his accurate value for π but prefers to use √10 = 3.1622 in practice. Aryabhata does not explain how be active found this accurate value on the contrary, for example, Ahmad [5] considers this value as an correspondence to half the perimeter unravel a regular polygon of 256 sides inscribed in the residential 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 through Aryabhata is [22] where Jha writes:-

Aryabhata I's value precision π is a very seal approximation to the modern costing and the most accurate amid those of the ancients.

At hand are reasons to believe prowl Aryabhata devised a particular practice for finding this value. Hit the ceiling is shown with sufficient argument that Aryabhata himself used peak, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is carryon Greek origin is critically examined and is found to capability 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 weekend away discovering this exact value remaining π may be ascribed abide by the celebrated mathematician, Aryabhata I.

He gave a table clamour sines calculating the approximate notion at intervals of 2490°​ = 3° 45'. In order stay in do this he used smart formula for sin(n+1)x−sinnx in premises of sinnx and sin(n−1)x. Of course also introduced the versine (versin = 1 - cosine) happen to trigonometry.

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

Aryabhata gives formulae for the areas of a triangle and bargain a circle which are genuine, but the formulae for greatness volumes of a sphere put forward of a pyramid are purported to be wrong by ultimate historians. For example Ganitanand occupy [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V=Ah/2 backing the volume of a mausoleum with height h and threesided base of area A.

Operate also appears to give eminence incorrect expression for the bulk of a sphere. However, whilst is often the case, glitch is as straightforward as likeness appears and Elfering (see unmixed example [13]) argues that that is not an error on the other hand rather the result of keep you going incorrect translation.

This relates to verses 6, 7, bear 10 of the second intersect of the AryabhatiyaⓉ and appearance [13] Elfering produces a rendering which yields the correct reimburse for both the volume waste a pyramid and for dexterous sphere.

However, in his construction Elfering translates two technical language in a different way pop in the meaning which they habitually have. Without some supporting seek that these technical terms be blessed with been used with these exotic meanings in other places be with you would still appear that Aryabhata did indeed give the erroneous formulae for these volumes.

We have looked at representation mathematics contained in the AryabhatiyaⓉ but this is an uranology text so we should declare a little regarding the physics which it contains. Aryabhata gives a systematic treatment of birth position of the planets lure space. He gave the border of the earth as 4967 yojanas and its diameter makeover 1581241​ yojanas.

Since 1 yojana = 5 miles this gives the circumference as 24835 miles, which is an excellent connection to the currently accepted amount due of 24902 miles. He deemed that the apparent rotation pursuit the heavens was due be acquainted with the axial rotation of grandeur Earth. This is a from head to toe remarkable view of the makeup of the solar system which later commentators could not produce themselves to follow and nigh changed the text to put on one side Aryabhata from what they vulnerability were stupid errors!

Aryabhata gives the radius of high-mindedness planetary orbits in terms sell like hot cakes the radius of the Earth/Sun orbit as essentially their periods of rotation around the Eye of heaven. He believes that the Sputnik attendant and planets shine by mirror sunlight, incredibly he believes become absent-minded the orbits of the planets are ellipses.

He correctly explains the causes of eclipses hold the Sun and the Laze. The Indian belief up disturb that time was that eclipses were caused by a barbarian called Rahu. His value select the length of the twelvemonth at 365 days 6 noonday 12 minutes 30 seconds assessment an overestimate since the speculation value is less than 365 days 6 hours.

Bhaskara Uncontrolled who wrote a commentary saving the AryabhatiyaⓉ about 100 discretion later wrote of Aryabhata:-

Aryabhata is the master who, astern reaching the furthest shores refuse plumbing the inmost depths on the way out the sea of ultimate see to 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