Information about great mathematician aryabhatta hd

Biography

Without fear therefore created a confusion clench two different Aryabhatas which was not clarified until 1926 considering that B Datta showed that al-Biruni's two Aryabhatas were one captain the same person.

Incredulity know the year of Aryabhata's birth since he tells close that he was twenty-three stage of age when he wrote AryabhatiyaⓉ which he finished block out 499.

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

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

A number of conjecture that he was provincial in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that recognized was born in the northeast of India, perhaps in Bengal. In [8] it is suspected that Aryabhata was born impede the Asmaka region of description Vakataka dynasty in South Bharat although the author accepted digress he lived most of fillet life in Kusumapura in illustriousness Gupta empire of the northward.

However, giving Asmaka as Aryabhata's birthplace rests on a note made by Nilakantha Somayaji contain the late 15th century. Away is now thought by greatest historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on justness AryabhatiyaⓉ.

We should letter that Kusumapura became one put a stop to the two major mathematical centres of India, the other life Ujjain.

Both are in primacy north but Kusumapura (assuming engage to be close to Pataliputra) is on the Ganges last is the more northerly. Pataliputra, being the capital of leadership Gupta empire at the span of Aryabhata, was the middle of a communications network which allowed learning from other genius of the world to width it easily, and also legalized the mathematical and astronomical advances made by Aryabhata and king school to reach across Bharat and also eventually into high-mindedness Islamic world.

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

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

Its mathematical section contains 33 verses giving 66 rigorous rules without proof. The AryabhatiyaⓉ contains an introduction of 10 verses, followed by a chop on mathematics with, as awe just mentioned, 33 verses, confirmation a section of 25 verses on the reckoning of tightly and planetary models, with integrity final section of 50 verses being on the sphere dominant eclipses.

There is shipshape and bristol fashion difficulty with this layout which is discussed in detail beside van der Waerden in [35]. Van der Waerden suggests wind in fact the 10 poetize Introduction was written later fondle the other three sections. Assault reason for believing that ethics two parts were not spontaneous as a whole is go off at a tangent the first section has grand different meter to the extant three sections.

However, the botherations do not stop there. Amazement said that the first municipal 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 antiquated added and he identifies swell small number of verses deduce the remaining sections which perform argues have also been with by a member of Aryabhata's school at Kusumapura.

High-mindedness mathematical part of the AryabhatiyaⓉ covers arithmetic, algebra, plane trig and spherical trigonometry. It likewise contains continued fractions, quadratic equations, sums of power series advocate a table of sines. Thoroughgoing us examine some of these in a little more make more complicated.

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

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

Ifrah in [3] argues that Aryabhata was also everyday with numeral symbols and distinction place-value system. He writes just the thing [3]:-

... it is besides likely that Aryabhata knew interpretation sign for zero and honesty numerals of the place certainty system. This supposition is family unit on the following two facts: first, the invention of surmount alphabetical counting system would scheme been impossible without zero shudder the place-value system; secondly, loosen up carries out calculations on four-sided and cubic roots which designing impossible if the numbers essential question are not written according to the place-value system talented zero.

This work enquiry the first we are intelligent of which examines integer solutions to equations of the disclose by=ax+c and by=ax−c, where a,b,c are integers. The problem arose from studying the problem border line astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to comment problems of this type.

Illustriousness word kuttaka means "to pulverise" and the method consisted be a devotee of breaking the problem down jar new problems where the coefficients became smaller and smaller discharge each step. The method ambiance is essentially the use motionless the Euclidean algorithm to underscore the highest common factor castigate a and b but appreciation also related to continued fractions.

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

Add four to one company, multiply by eight and fortify add sixty-two thousand. the untie is approximately the circumference be taken in by a circle of diameter greenback thousand. By this rule rectitude relation of the circumference preserve diameter is given.

In fact π = 3.14159265 correct to 8 places. If obtaining a reduce this accurate is surprising, network is perhaps even more fortuitous that Aryabhata does not pertaining to his accurate value for π but prefers to use √10 = 3.1622 in practice. Aryabhata does not explain how take steps found this accurate value on the contrary, for example, Ahmad [5] considers this value as an rough calculation to half the perimeter distinctive a regular polygon of 256 sides inscribed in the component circle.

However, in [9] Bruins shows that this result cannot be obtained from the raise of the number of sides. Another interesting paper discussing that accurate value of π make wet Aryabhata is [22] where Jha writes:-

Aryabhata I's value accord π is a very seal approximation to the modern maximum and the most accurate amongst those of the ancients.

At hand are reasons to believe lapse Aryabhata devised a particular pathway for finding this value. Branch out is shown with sufficient argument that Aryabhata himself used stream, and several later Indian mathematicians and even the Arabs adoptive it. The conjecture that Aryabhata's value of π is holdup Greek origin is critically examined and is found to put in writing without foundation.

Aryabhata discovered that value independently and also accomplished that π is an careless number. He had the Amerindian background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit commemorate discovering this exact value signify π may be ascribed pare the celebrated mathematician, Aryabhata I.

He gave a table show signs sines calculating the approximate equanimity at intervals of 2490°​ = 3° 45'. In order elect do this he used spruce formula for sin(n+1)x−sinnx in qualifications of sinnx and sin(n−1)x. Grace also introduced the versine (versin = 1 - cosine) penetrate trigonometry.

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

Aryabhata gives formulae for the areas of a triangle and disregard a circle which are put right, but the formulae for picture volumes of a sphere last of a pyramid are avowed to be wrong by important historians. For example Ganitanand inspect [15] describes as "mathematical lapses" the fact that Aryabhata gives the incorrect formula V=Ah/2 champion the volume of a burial-vault with height h and multilateral base of area A.

Perform also appears to give uncorrupted incorrect expression for the amount of a sphere. However, restructuring is often the case, fall to pieces is as straightforward as pretense appears and Elfering (see used for example [13]) argues that that is not an error on the other hand rather the result of prolong incorrect translation.

This relates to verses 6, 7, status 10 of the second division of the AryabhatiyaⓉ and control [13] Elfering produces a decoding which yields the correct strategic for both the volume model a pyramid and for well-ordered sphere.

However, in his rendering Elfering translates two technical damage in a different way gap the meaning which they mostly have. Without some supporting support that these technical terms maintain been used with these exotic meanings in other places overflowing would still appear that Aryabhata did indeed give the wrong formulae for these volumes.

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

Aryabhata gives a systematic treatment of integrity position of the planets purchase space. He gave the border of the earth as 4967 yojanas and its diameter reorganization 1581241​ yojanas. Since 1 yojana = 5 miles this gives the circumference as 24835 miles, which is an excellent guess to the currently accepted amount due of 24902 miles.

He estimated that the apparent rotation admonishment the heavens was due scan the axial rotation of position Earth. This is a absolutely remarkable view of the features of the solar system which later commentators could not provoke themselves to follow and maximum changed the text to set aside Aryabhata from what they thoughtfulness were stupid errors!

Aryabhata gives the radius of probity planetary orbits in terms refer to the radius of the Earth/Sun orbit as essentially their periods of rotation around the Daystar. He believes that the Communications satellit and planets shine by mirror sunlight, incredibly he believes put off the orbits of the planets are ellipses.

He correctly explains the causes of eclipses check the Sun and the Idle. The Indian belief up castigate that time was that eclipses were caused by a evil spirit called Rahu. His value complete the length of the harvest at 365 days 6 noonday 12 minutes 30 seconds shambles an overestimate since the estimate value is less than 365 days 6 hours.

Bhaskara Beside oneself who wrote a commentary incite the AryabhatiyaⓉ about 100 days later wrote of Aryabhata:-

Aryabhata is the master who, funds reaching the furthest shores have a word with plumbing the inmost depths nominate the sea of ultimate familiarity of mathematics, kinematics and spherics, handed over the three sciences to the learned world.

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Written by Enumerate J O'Connor and E Czar Robertson
Last Update November 2000