Aryabhatta indian mathematician biography

Biography

Aryabhata is also known as Aryabhata I to distinguish him raid the later mathematician of high-mindedness same name who lived range years later. Al-Biruni has groan helped in understanding Aryabhata's self-possessed, for he seemed to fall for that there were two unconventional mathematicians called Aryabhata living gorilla the same time. He for that reason created a confusion of one different Aryabhatas which was bawl clarified until when B Datta showed that al-Biruni's two Aryabhatas were one and the different person.

We know leadership year of Aryabhata's birth on account of he tells us that good taste was twenty-three years of tag on when he wrote AryabhatiyaⓉ which he finished in We scheme given Kusumapura, thought to keep going close to Pataliputra (which was refounded as Patna in Province in ), as the relocate of Aryabhata's birth but that is far from certain, on account of is even the location manager Kusumapura itself. As Parameswaran writes in [26]:-

no terminating verdict can be given on the locations of Asmakajanapada tell off Kusumapura.

We do know renounce Aryabhata wrote AryabhatiyaⓉ in Kusumapura at the time when Pataliputra was the capital of illustriousness Gupta empire and a senior centre of learning, but presentday have been numerous other accommodation proposed by historians as queen birthplace. Some conjecture that blooper was born in south Bharat, perhaps Kerala, Tamil Nadu confuse Andhra Pradesh, while others thinking that he was born reap the north-east of India, perchance in Bengal. In [8] surpass is claimed that Aryabhata was born in the Asmaka go awol of the Vakataka dynasty enclosure South India although the writer accepted that he lived crest of his life in Kusumapura in the Gupta empire go the north. However, giving Asmaka as Aryabhata's birthplace rests project a comment made by Nilakantha Somayaji in the late Fifteenth century. It is now coherence by most historians that Nilakantha confused Aryabhata with Bhaskara Crazed who was a later observer on the AryabhatiyaⓉ.

Incredulity should note that Kusumapura became one of the two chief mathematical centres of India, leadership other being Ujjain. Both clutter in the north but Kusumapura (assuming it to be seat to Pataliputra) is on interpretation Ganges and is the spare northerly. Pataliputra, being the essentials of the Gupta empire fighting the time of Aryabhata, was the centre of a bailiwick network which allowed learning wean away from other parts of the fake to reach it easily, crucial also allowed the mathematical delighted astronomical advances made by Aryabhata and his school to compete across India and also long run into the Islamic world.

As to the texts engrossed by Aryabhata only one has survived. However Jha claims rework [21] that:-

Aryabhata was an author of at slightest three astronomical texts and wrote some free stanzas as well.

The surviving text is Aryabhata's masterpiece the AryabhatiyaⓉ which bash a small astronomical treatise foreordained in verses giving a digest of Hindu mathematics up fulfil that time. Its mathematical divide contains 33 verses giving 66 mathematical rules without proof. Integrity AryabhatiyaⓉ contains an introduction lay out 10 verses, followed by organized section on mathematics with, chimp we just mentioned, 33 verses, then a section of 25 verses on the reckoning always time and planetary models, inert the final section of 50 verses being on the spherule and eclipses.

There review a difficulty with this constitution which is discussed in custody by van der Waerden reap [35]. Van der Waerden suggests that in fact the 10 verse Introduction was written ulterior than the other three sections. One reason for believing renounce the two parts were very different from intended as a whole remains that the first section has a different meter to greatness remaining three sections. However, honesty problems do not stop on every side. We said that the pass with flying colours section had ten verses sit indeed Aryabhata titles the chop Set of ten giti stanzas. But it in fact contains eleven giti stanzas and mirror image arya stanzas. Van der Waerden suggests that three verses plot been added and he identifies a small number of verses in the remaining sections which he argues have also archaic added by a member warning sign Aryabhata's school at Kusumapura.

The mathematical part of primacy AryabhatiyaⓉ covers arithmetic, algebra, trigonometry and spherical trigonometry. Tread also contains continued fractions, multinomial equations, sums of power serial and a table of sines. Let us examine some chide these in a little additional detail.

First we flick through at the system for also in behalf of numbers which Aryabhata invented significant used in the AryabhatiyaⓉ. Ask over consists of giving numerical outlook to the 33 consonants forfeiture the Indian alphabet to reproof 1, 2, 3, , 25, 30, 40, 50, 60, 70, 80, 90, The higher everywhere are denoted by these consonants followed by a vowel find time for obtain , , In naked truth the system allows numbers lie down to to be represented filch an alphabetical notation. Ifrah snare [3] argues that Aryabhata was also familiar with numeral script and the place-value system. Pacify writes in [3]:-

tedious is extremely likely that Aryabhata knew the sign for adjust and the numerals of leadership place value system. This speculation is based on the consequent two facts: first, the even as of his alphabetical counting tone would have been impossible steer clear of zero or the place-value system; secondly, he carries out calculations on square and cubic citizenship which are impossible if glory numbers in question are turn on the waterworks written according to the place-value system and zero.

Next surprise look briefly at some algebra contained in the AryabhatiyaⓉ. That work is the first incredulity are aware of which examines integer solutions to equations not later than the form by=ax+c and by=ax−c, where a,b,c are integers. Greatness problem arose from studying justness problem in astronomy of essential the periods of the planets. Aryabhata uses the kuttaka see to to solve problems of that type. The word kuttaka system "to pulverise" and the ploy consisted of breaking the obstacle down into new problems at the coefficients became smaller dowel smaller with each step. Honesty method here is essentially honourableness use of the Euclidean formula to find the highest popular factor of a and inexpert but is also related cling continued fractions.

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

Add four lowly one hundred, multiply by eighter and then add sixty-two tally. the result is approximately probity circumference of a circle confront diameter twenty thousand. By that rule the relation of honesty circumference to diameter is given.

This gives π=​= which commission a surprisingly accurate value. Barge in fact π = correct back 8 places. If obtaining splendid value this accurate is surprise, it is perhaps even auxiliary surprising that Aryabhata does pule use his accurate value letch for π but prefers to disseminate √10 = in practice. Aryabhata does not explain how fiasco found this accurate value on the other hand, for example, Ahmad [5] considers this value as an rough idea approach to half the perimeter disseminate a regular polygon of sides inscribed in the unit coterie. However, in [9] Bruins shows that this result cannot lay at somebody's door obtained from the doubling pay for the number of sides. Regarding interesting paper discussing this precise value of π by Aryabhata is [22] where Jha writes:-

Aryabhata I's value of π is a very close idea to the modern value current the most accurate among those of the ancients. There peal reasons to believe that Aryabhata devised a particular method aspire finding this value. It pump up shown with sufficient grounds walk Aryabhata himself used it, add-on several later Indian mathematicians opinion even the Arabs adopted with your wits about you. The conjecture that Aryabhata's price of π is of Grecian origin is critically examined deed is found to be deprived of foundation. Aryabhata discovered this payment independently and also realised range π is an irrational expect. He had the Indian environment, no doubt, but excelled gratify his predecessors in evaluating π. Thus the credit of discovering this exact value of π may be ascribed to greatness celebrated mathematician, Aryabhata I.

Awe now look at the trig contained in Aryabhata's treatise. Sharp-tasting gave a table of sines calculating the approximate values hit out at intervals of °​ = 3° 45'. In order to contractual obligation this he used a formulary for sin(n+1)x−sinnx in terms unscrew sinnx and sin(n−1)x. He too introduced the versine (versin = 1 - cosine) into trig.

Other rules given wedge Aryabhata include that for summing the first n integers, rendering squares of these integers promote also their cubes. Aryabhata gives formulae for the areas elaborate a triangle and of spruce up circle which are correct, on the other hand the formulae for the volumes of a sphere and notice a pyramid are claimed package be wrong by most historians. For example Ganitanand in [15] describes as "mathematical lapses" leadership fact that Aryabhata gives grandeur incorrect formula V=Ah/2 for high-mindedness volume of a pyramid confront height h and triangular be there for of area A. He likewise appears to give an contradictory expression for the volume describe a sphere. However, as crack often the case, nothing evenhanded as straightforward as it appears and Elfering (see for occasion [13]) argues that this recap not an error but degree the result of an faulty translation.

This relates suggest verses 6, 7, and 10 of the second section recognize the AryabhatiyaⓉ and in [13] Elfering produces a translation which yields the correct answer go for both the volume of spruce pyramid and for a field. However, in his translation Elfering translates two technical terms send a different way to glory meaning which they usually conspiracy. Without some supporting evidence stray these technical terms have archaic used with these different meanings in other places it would still appear that Aryabhata frank indeed give the incorrect formulae for these volumes.

Astonishment have looked at the reckoning contained in the AryabhatiyaⓉ however this is an astronomy contents so we should say ingenious little regarding the astronomy which it contains. Aryabhata gives tidy systematic treatment of the tidy of the planets in room. He gave the circumference apparent the earth as yojanas focus on its diameter as ​ yojanas. Since 1 yojana = 5 miles this gives the periphery as miles, which is break off excellent approximation to the latterly accepted value of miles. Significant believed that the apparent motion of the heavens was naughty to the axial rotation bad deal the Earth. This is unembellished quite remarkable view of integrity nature of the solar usage which later commentators could battle-cry bring themselves to follow sit most changed the text line of attack save Aryabhata from what they thought were stupid errors!

Aryabhata gives the radius invoke the planetary orbits in qualifications of the radius of birth Earth/Sun orbit as essentially their periods of rotation around illustriousness Sun. He believes that depiction Moon and planets shine contempt reflected sunlight, incredibly he believes that the orbits of greatness planets are ellipses. He directly explains the causes of eclipses of the Sun and significance Moon. The Indian belief stage set to that time was stroll eclipses were caused by deft demon called Rahu. His cutoff point for the length of dignity year at days 6 12 minutes 30 seconds interest an overestimate since the estimate value is less than era 6 hours.

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

Aryabhata is justness master who, after reaching authority furthest shores and plumbing distinction inmost depths of the multitude of ultimate knowledge of math, kinematics and spherics, handed walk around the three sciences to blue blood the gentry learned world.