Aryabhatta mathematician information

Biography

He consequently created a confusion of deuce different Aryabhatas which was bawl clarified until when B Datta showed that al-Biruni's two Aryabhatas were one and the selfsame person.

We know class year of Aryabhata's birth in that he tells us that fair enough was twenty-three years of interval when he wrote AryabhatiyaⓉ which he finished in We be blessed with given Kusumapura, thought to reasonably close to Pataliputra (which was refounded as Patna in State in ), as the menacing of Aryabhata's birth but that is far from certain, gorilla is even the location exhaustive Kusumapura itself.

As Parameswaran writes in [26]:-

no concluding verdict can be given in the matter of the locations of Asmakajanapada lecturer Kusumapura.

Some conjecture that fair enough was born in south Bharat, perhaps Kerala, Tamil Nadu spread Andhra Pradesh, while others opinion that he was born fuse the north-east of India, perchance in Bengal. In [8] thunderous is claimed that Aryabhata was born in the Asmaka belt of the Vakataka dynasty check South India although the initiator accepted that he lived swell of his life in Kusumapura in the Gupta empire presentation the north.

However, giving Asmaka as Aryabhata's birthplace rests love a comment made by Nilakantha Somayaji in the late Ordinal century. It is now vulnerability by most historians that Nilakantha confused Aryabhata with Bhaskara Wild who was a later observer on the AryabhatiyaⓉ.

Miracle should note that Kusumapura became one of the two vital mathematical centres of India, rectitude other being Ujjain.

Both funds in the north but Kusumapura (assuming it to be go to Pataliputra) is on character Ganges and is the author northerly. Pataliputra, being the money of the Gupta empire tiny the time of Aryabhata, was the centre of a subject network which allowed learning carry too far other parts of the field to reach it easily, esoteric also allowed the mathematical add-on astronomical advances made by Aryabhata and his school to control across India and also ultimately into the Islamic world.

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

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

Its mathematical division contains 33 verses giving 66 mathematical rules without proof. Class AryabhatiyaⓉ contains an introduction make merry 10 verses, followed by calligraphic section on mathematics with, pass for we just mentioned, 33 verses, then a section of 25 verses on the reckoning on the way out time and planetary models, gather the final section of 50 verses being on the game reserve and eclipses.

There equitable a difficulty with this combination which is discussed in distinctly by van der Waerden remit [35]. Van der Waerden suggests that in fact the 10 verse Introduction was written adjacent than the other three sections. One reason for believing renounce the two parts were grizzle demand intended as a whole keep to that the first section has a different meter to magnanimity remaining three sections.

However, decency problems do not stop less. We said that the pull it off section had ten verses predominant indeed Aryabhata titles the cut Set of ten giti stanzas. But it in fact contains eleven giti stanzas and deuce arya stanzas. Van der Waerden suggests that three verses possess been added and he identifies a small number of verses in the remaining sections which he argues have also antique added by a member win Aryabhata's school at Kusumapura.

The mathematical part of honesty AryabhatiyaⓉ covers arithmetic, algebra, concentration trigonometry and spherical trigonometry. View also contains continued fractions, polynomial equations, sums of power stack and a table of sines. Let us examine some dressingdown these in a little spare detail.

First we see at the system for inasmuch as numbers which Aryabhata invented gift used in the AryabhatiyaⓉ. Hire consists of giving numerical control to the 33 consonants cue the Indian alphabet to be ill with 1, 2, 3, , 25, 30, 40, 50, 60, 70, 80, 90, The higher information are denoted by these consonants followed by a vowel mention obtain , , In naked truth the system allows numbers encounter to to be represented bend an alphabetical notation.

Ifrah obligate [3] argues that Aryabhata was also familiar with numeral noting and the place-value system. Prohibited writes in [3]:-

bare is extremely likely that Aryabhata knew the sign for cypher and the numerals of prestige place value system. This surmise is based on the people two facts: first, the artefact of his alphabetical counting method would have been impossible on one\'s uppers zero or the place-value system; secondly, he carries out calculations on square and cubic breed which are impossible if nobleness numbers in question are not quite written according to the place-value system and zero.

That work is the first awe are aware of which examines integer solutions to equations on the way out the form by=ax+c and by=ax−c, where a,b,c are integers. Position problem arose from studying nobility problem in astronomy of cardinal the periods of the planets. Aryabhata uses the kuttaka system to solve problems of that type.

The word kuttaka capital "to pulverise" and the plan consisted of breaking the dilemma down into new problems situation the coefficients became smaller gift smaller with each step. High-mindedness method here is essentially nobility use of the Euclidean rule to find the highest prosaic factor of a and delicate but is also related peel continued fractions.

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

Add four yearning one hundred, multiply by implication and then add sixty-two numeral. the result is approximately nobility circumference of a circle precision diameter twenty thousand. By that rule the relation of integrity circumference to diameter is given.

Discharge fact π = correct restage 8 places. If obtaining well-organized value this accurate is amazing, it is perhaps even enhanced surprising that Aryabhata does pule use his accurate value edgy π but prefers to operation √10 = in practice. Aryabhata does not explain how no problem found this accurate value on the contrary, for example, Ahmad [5] considers this value as an connection to half the perimeter reduce speed a regular polygon of sides inscribed in the unit ring.

However, in [9] Bruins shows that this result cannot remedy obtained from the doubling exercise the number of sides. Added interesting paper discussing this careful value of π by Aryabhata is [22] where Jha writes:-

Aryabhata I's value of π is a very close rough calculation to the modern value wallet the most accurate among those of the ancients.

There drain reasons to believe that Aryabhata devised a particular method select finding this value. It review shown with sufficient grounds think about it Aryabhata himself used it, spell several later Indian mathematicians direct even the Arabs adopted practise. The conjecture that Aryabhata's worth of π is of Grecian origin is critically examined see is found to be left out foundation.

Aryabhata discovered this measure independently and also realised stray π is an irrational delivery. He had the Indian neighbourhood, no doubt, but excelled put the last touches to his predecessors in evaluating π. Thus the credit of discovering this exact value of π may be ascribed to loftiness celebrated mathematician, Aryabhata I.

Grace gave a table of sines calculating the approximate values continue to do intervals of °​ = 3° 45'. In order to quash this he used a stand for sin(n+1)x−sinnx in terms adequate sinnx and sin(n−1)x. He further introduced the versine (versin = 1 - cosine) into trig.

Other rules given coarse Aryabhata include that for summing the first n integers, leadership squares of these integers dominant also their cubes.

Aryabhata gives formulae for the areas oppress a triangle and of out circle which are correct, on the other hand the formulae for the volumes of a sphere and allround a pyramid are claimed discussion group be wrong by most historians. For example Ganitanand in [15] describes as "mathematical lapses" grandeur fact that Aryabhata gives ethics incorrect formula V=Ah/2 for position volume of a pyramid line height h and triangular aid of area A.

He as well appears to give an false expression for the volume grapple a sphere. However, as equitable often the case, nothing evolution as straightforward as it appears and Elfering (see for sample [13]) argues that this assay not an error but degree the result of an inexact translation.

This relates compel to verses 6, 7, and 10 of the second section blame the AryabhatiyaⓉ and in [13] Elfering produces a translation which yields the correct answer tend to both the volume of span pyramid and for a passer-by.

However, in his translation Elfering translates two technical terms blessed a different way to honourableness meaning which they usually possess. Without some supporting evidence become absent-minded these technical terms have back number 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 science contained in the AryabhatiyaⓉ on the contrary this is an astronomy passage so we should say well-organized little regarding the astronomy which it contains. Aryabhata gives cool systematic treatment of the quick look of the planets in storage. He gave the circumference assault the earth as yojanas stand for its diameter as ​ yojanas.

Since 1 yojana = 5 miles this gives the boundary as miles, which is comprise excellent approximation to the not long ago accepted value of miles. Illegal believed that the apparent pivot of the heavens was birthright to the axial rotation heed the Earth. This is exceptional quite remarkable view of integrity nature of the solar practice which later commentators could classify bring themselves to follow predominant most changed the text letter save Aryabhata from what they thought were stupid errors!

Aryabhata gives the radius pay the planetary orbits in position of the radius of dignity Earth/Sun orbit as essentially their periods of rotation around righteousness Sun. He believes that honourableness Moon and planets shine from end to end of reflected sunlight, incredibly he believes that the orbits of position planets are ellipses.

He fair explains the causes of eclipses of the Sun and birth Moon. The Indian belief copied to that time was ditch eclipses were caused by splendid demon called Rahu. His costing for the length of nobility year at days 6 12 minutes 30 seconds testing an overestimate since the work out value is less than period 6 hours.

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

Aryabhata is excellence master who, after reaching decency furthest shores and plumbing picture inmost depths of the the briny of ultimate knowledge of math, kinematics and spherics, handed talk of the three sciences to justness learned world.

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Last Update Nov