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Aryabhatta: The Indian Mathematician

Updated on January 30, 2014

Life and Works of Aryabhata

ARYABHATTA, or, as written by the Arabs, ARJABAHR, a celebrated Hindu mathematician, and the earliest known author on Algebra, is now generally believed to have lived about the beginning of our era. Nothing, however, has yet appeared that can give us the slightest information as to the place of his birth, or the time when he lived; nor is there, as far as we know, any tradition or record extent from which we can collect any of the circumstances of his life; even his period is still a matter of dispute. We must, therefore, content ourselves with whatever notices we find of Aryabhatta and his system in the various writers on astronomy and other mathematical sciences whose authority is established and cannot be called into doubt.

Aryabhatta is the first writer on astronomy to whom the Hindus do not allow the honour of a divine inspiration. Writers on mathematical science distinctly state that he was the earliest uninspired and a merely human writer on astronomy. This is a notice which sufficiently proves his being an historical character.

Statue of Aryabhata
Statue of Aryabhata

The chief doctrines which Aryabhatta (Aarya-Bhatt) professed were the following:

He affirmed the diurnal revolution of the earth on its axis; an assertion which is fully borne out by a quotation from one of his works, in a commentary on the "Brahmasphut'a-Siddhanta" of Brahmagupta by Prithudakaswami: "The Earth making a revolution produces a daily rising and setting of the stars and planets". At the same time he thought that this revolving of the earth was produced through the agency of a peculiar current of aerial fluid, or spiritus vector ("wind"), to which he assigned a distance of 150 yojanas (114 miles) from the surface of the earth. In opposition to the generally received opinion, he maintained that the moon, the primary planets, and the stars had no light of their own, and were only illumined by the sun; he consequently knew the true cause of solar and lunar eclipses.

Aryabhatta also ascribed to the epicycles, by which the motion of a planet is represented, a form varying from the circle and nearly elliptic. Moreover, he recognized a motion of the nodes and asides of all primary planets, as well as of the moon, and noticed the motion of the equinoctial and solstitial points, which he restricted, however, to an oscillation within the limits of twenty- four degrees, at the rate of one libration in seventy years. The length of AryabhatYa's sidereal year was 356 days 6 hours 12 minutes and 30 seconds. Aryabhatta stated the diameter of the earth at 1050 yojanas and its circumference at 3300 yojanas (25,080 miles). Hence it appears that he held the proportion of the diameter to the periphery of a circle to be seven to twenty-two, which is a nearer approximation than that of Brahmagupta and S'ridhara, who came after him.

The astronomical sects, of which Arabhatta is the reputed founder, were distinguished by the name of Audayakas, from Udaya, " rising;" implying that they fixed the beginning of the planetary motions on the meridian of Sri Lanka (Ceylon) at sun-rise, in opposition to the Arddharatrikas, who began the great astronomical cycle at midnight. Aryabhatta is the author of the " Aryasht'- as'ata" (eight hundred couplets in the Arya metre) and the "Das'agitika" (ten stanzas). The "Laghwarya-Siddhanta" is also ascribed to him: but, unfortunately, none of these works have yet been discovered; and we know them only through the numerous quotations from them, with which the works of subsequent writers abound. For an exposition of his numerical system and algebraic doctrine we refer to the article by another renowned scientist called BHASKARA.

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    • Aman deep Garg profile image

      Aman deep Garg 9 years ago

      Nice hub,enjoyed reading it.

    • gabriella05 profile image

      gabriella05 9 years ago from Oldham

      Great information nice hub

      Thanks for that Rudra

    • vrajavala profile image

      vrajavala 9 years ago from Port St. Lucie

      I'm a sidereal astrologer. Nice writing.

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      JAY JOLLY 9 years ago

      PLEASE LET ME KNOW HOW ARYABHATTA FOUND:(4+100)*8+62000/20000=PI-3.14

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      K.SHRUTI 9 years ago

      IT IS VERY,VERY NICE INFORMATION.WE CAN LEARN MANY THINGS FROM IT.

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      Dr.S.P.PADMA PRASAD 9 years ago from Tumkur

      Ver very good article Mrs.Rudra. You are enlightening people with good knowledge.I wonder how you find time to do this much!

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      Jasmine30 8 years ago

      The information given here is a good brief about Aryabhata and many things to learn and enjoy with it!!!!!! thanks for d information !!!!!!!!!!!!

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      ARATRIKA 8 years ago

      NICE WRITING,MS.RUDRA.BUT YOU CAN DO WITH A LITTLE MORE INFORMATION.

    • Rudra profile image
      Author

      Rudra 8 years ago

      More information is here

      http://www.aryabhatta.net

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      Thanks,the information was sufficient and nice.Keep it up.

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      Apurva 8 years ago

      Please provide me with a brief information about aryabhatta's personalhistory,His contributions to mathematics &funny incidents related to hislife

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      aryabhatta 8 years ago

      Thankyou for reading. Unfortunately not all is documented.

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      mahavir 8 years ago

      Qes.1 Why did people come across the need of number?

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      mahavir 8 years ago

      Qes.1 Why did people come across the need of number?

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      Qes.2 what have people used for counting in pre-historic period?

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      Author

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      C.RONALDO(N) 7 years ago

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    • Rudra profile image
      Author

      Rudra 7 years ago

      More info on Aryabhatta can be found here http://www.aryabhatta.net

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    • Rudra profile image
      Author

      Rudra 7 years ago

      more info on Aryabhatta can be found on http://www.aryabhatta.net

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    • Rudra profile image
      Author

      Rudra 7 years ago

      More data can be found on http://aryabhatta.net.

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      vibhor nanda 7 years ago

      Aryabhata is also known as Aryabhata I to distinguish him from the later mathematician of the same name who lived about 400 years later. Al-Biruni has not helped in understanding Aryabhata's life, for he seemed to believe that there were two different mathematicians called Aryabhata living at the same time. He therefore created a confusion of two different Aryabhatas which was not clarified until 1926 when B Datta showed that al-Biruni's two Aryabhatas were one and the same person.

      We know the year of Aryabhata's birth since he tells us that he was twenty-three years of age when he wrote Aryabhatiya which he finished in 499. We have given Kusumapura, thought to be close to Pataliputra (which was refounded as Patna in Bihar in 1541), as the place of Aryabhata's birth but this is far from certain, as is even the location of Kusumapura itself. As Parameswaran writes in [26]:-

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

      We do know that Aryabhata wrote Aryabhatiya in Kusumapura at the time when Pataliputra was the capital of the Gupta empire and a major centre of learning, but there have been numerous other places proposed by historians as his birthplace. Some conjecture that he was born in south India, perhaps Kerala, Tamil Nadu or Andhra Pradesh, while others conjecture that he was born in the north-east of India, perhaps in Bengal. In [8] it is claimed that Aryabhata was born in the Asmaka region of the Vakataka dynasty in South India although the author accepted that he lived most of his life in Kusumapura in the Gupta empire of the north. However, giving Asmaka as Aryabhata's birthplace rests on a comment made by Nilakantha Somayaji in the late 15th century. It is now thought by most historians that Nilakantha confused Aryabhata with Bhaskara I who was a later commentator on the Aryabhatiya.

      We should note that Kusumapura became one of the two major mathematical centres of India, the other being Ujjain. Both are in the north but Kusumapura (assuming it to be close to Pataliputra) is on the Ganges and is the more northerly. Pataliputra, being the capital of the Gupta empire at the time of Aryabhata, was the centre of a communications network which allowed learning from other parts of the world to reach it easily, and also allowed the mathematical and astronomical advances made by Aryabhata and his school to reach across India and also eventually into the Islamic world.

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

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

      The surviving text is Aryabhata's masterpiece the Aryabhatiya which is a small astronomical treatise written in 118 verses giving a summary of Hindu mathematics up to that time. Its mathematical section contains 33 verses giving 66 mathematical rules without proof. The Aryabhatiya contains an introduction of 10 verses, followed by a section on mathematics with, as we just mentioned, 33 verses, then a section of 25 verses on the reckoning of time and planetary models, with the final section of 50 verses being on the sphere and eclipses.

      There is a difficulty with this layout which is discussed in detail by van der Waerden in [35]. Van der Waerden suggests that in fact the 10 verse Introduction was written later than the other three sections. One reason for believing that the two parts were not intended as a whole is that the first section has a different meter to the remaining three sections. However, the problems do not stop there. We said that the first section had ten verses and indeed Aryabhata titles the section Set of ten giti stanzas. But it in fact contains eleven giti stanzas and two arya stanzas. Van der Waerden suggests that three verses have been added and he identifies a small number of verses in the remaining sections which he argues have also been added by a member of Aryabhata's school at Kusumapura.

      The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry and spherical trigonometry. It also contains continued fractions, quadratic equations, sums of power series and a table of sines. Let us examine some of these in a little more detail.

      First we look at the system for representing numbers which Aryabhata invented and used in the Aryabhatiya. It consists of giving numerical values to the 33 consonants of the Indian alphabet to represent 1, 2, 3, ... , 25, 30, 40, 50, 60, 70, 80, 90, 100. The higher numbers are denoted by these consonants followed by a vowel to obtain 100, 10000, .... In fact the system allows numbers up to 1018to be represented with an alphabetical notation. Ifrah in [3] argues that Aryabhata was also familiar with numeral symbols and the place-value system. He writes in [3]:-

      ... it is extremely likely that Aryabhata knew the sign for zero and the numerals of the place value system. This supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.

      Next we look briefly at some algebra contained in the Aryabhatiya. This work is the first we are aware of which examines integer solutions to equations of the form by = ax + c and by = ax - c, where a, b, c are integers. The problem arose from studying the problem in astronomy of determining the periods of the planets. Aryabhata uses the kuttaka method to solve problems of this type. The word kuttaka means "to pulverise" and the method consisted of breaking the problem down into new problems where the coefficients became smaller and smaller with each step. The method here is essentially the use of the Euclidean algorithm to find the highest common factor of a and b but is also related to continued fractions.

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

      Add four to one hundred, multiply by eight and then add sixty-two thousand. the result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given.

      This gives ? = 62832/20000 = 3.1416 which is a surprisingly accurate value. In fact ? = 3.14159265 correct to 8 places. If obtaining a value this accurate is surprising, it is perhaps even more surprising that Aryabhata does not use his accurate value for ? but prefers to use ?10 = 3.1622 in practice. Aryabhata does not explain how he found this accurate value but, for example, Ahmad [5] considers this value as an approximation to half the perimeter of a regular polygon of 256 sides inscribed in the unit circle. However, in [9] Bruins shows that this result cannot be obtained from the doubling of the number of sides. Another interesting paper discussing this accurate value of ? by Aryabhata is [22] where Jha writes:-

      Aryabhata I's value of ? is a very close approximation to the modern value and the most accurate among those of the ancients. There are reasons to believe that Aryabhata devised a particular method for finding this value. It is shown with sufficient grounds that Aryabhata himself used it, and several later Indian mathematicians and even the Arabs adopted it. The conjecture that Aryabhata's value of ? is of Greek origin is critically examined and is found to be without foundation. Aryabhata discovered this value independently and also realised that ? is an irrational number. He had the Indian background, no doubt, but excelled all his predecessors in evaluating ?. Thus the credit of discovering this exact value of ? may be ascribed to the celebrated mathematician, Aryabhata I.

      We now look at the trigonometry contained in Aryabhata's treatise. He gave a table of sines calculating the approximate values at intervals of 90°/24 = 3° 45'. In order to do this he used a formula for sin(n+1)x - sin nx in terms of sin nx and sin (n-1)x. He also introduced the versine (versin = 1 - cosine) into trigonometry.

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      vineet sehrawat 6 years ago

      i read it and i think that it is an appropriate description bout arryabhatta

    • profile image

      vineet sehrawat 6 years ago

      i read it and i think that it is an appropriate description bout arryabhatta

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      Khushii Vashisth 6 years ago

      it is a very useful and good site

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      mallinenirithvik 6 years ago

      it is so great .i got so much imformation

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      ekta 6 years ago

      coooooooooooooooooooolllllllllllll yaaaaaaaaaaaar

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      rhea shukla 6 years ago

      it was very nice. it helped me a lot in my holiday home work it is dam good............

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      varun(sps) 6 years ago

      very good........

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      BHAKTIAR BHANDARY 6 years ago

      IREAD THIS AND I THOUGHT THAT HE IS GENIOUS

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      smruti monalisa 6 years ago

      what a genius man he waz!!!!

      i wish i could be like him some time

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      prerna 6 years ago

      good one!!!!!!!!!!!!!!!!

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      ramesh singh rao 6 years ago

      it is nice description.It helped me a lottttttttttttt.

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      HEHEKATE 6 years ago

      HEY I NEED THEY EDUCATIONAL BACKGROUND OF ARYABHATTA PLEASE SUGGEST GUYS......MrS.RudrA THAT INFO WAS VERY GOOD THANKS YOU.

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      ishan 6 years ago

      it helped me to my holiday homework

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      manish kumar 6 years ago

      aryabhatta is very pagal and loser

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      UJJWAL 6 years ago

      very nice hub..............

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      Kanika 6 years ago

      Thanxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx a lot,it really helped in my project.Thankyou so much for providing us the knowledge.It's reallyyyyyyyyyyy nice.

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      muskaan 6 years ago

      plz add more info like incidents in life of aryabhatta. i need for holiday h.w!!!!

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      khushi sweeeeeeeeeeeeety 6 years ago

      sooooooooooooo good

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      jjj 6 years ago

      very nice writtan by vinod nanda

    • profile image

      aniket 6 years ago

      verrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrry very bad

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      ANSH JAIN 6 years ago

      IT HAS HELPED ME A LOT IN DOING MY MATHS PROJECT.IT'S GREAT

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      sree krishna 6 years ago

      i am very thanks for you

    • profile image

      sree krishna 6 years ago

      you stupit boy

    • profile image

      aneesha chib 6 years ago

      reading it was a good experience for me ..........

      the best thing was to know abt his lyk........

      this was really coooooooollllllll

      i liked it a lot

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      xyz 6 years ago

      the info was BAD....

      it was not much of a use,as was not brief..

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      Subham gupta (patna city) 6 years ago

      This information really help to made my project in a better way

      isliye mera

      Dil garden garden ho gaya

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      dheeraj 6 years ago

      thanks ...............

      please avilable more incidenc like that

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      RAKHI 6 years ago

      ARYABHATA KI MAA KI CHOOT

      AGAR YE 0 DISCOVER NHI KRTA TO MATHHS NHI PADHNI PADTI\

      PLZ KOI MUJHE CHODO MERI CHOOT PIYASI HAI

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      owaISE 6 years ago

      this is ammmmmmaaaaaazing!!! it helmed me a lot for my project.

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      ashish  6 years ago

      thanks

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      manu garg 6 years ago

      I am very thankfull as this helpppppppppped me in my stupid project

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      anu garg 6 years ago

      I am very thankfull as this helpppppppppped me in my stupid project

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      akash 6 years ago

      thanks a lot,i think much more information could be added anyways thanks....

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      PRAHARSHITA 6 years ago

      NICE WORK!!! HELPED ME DO MY MATHS PROJECT EASILY

      THNXXXXXXXXXXXXXXXXXXXXX

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      meghna 6 years ago

      chat with friend

    • profile image

      kamakshi syal 6 years ago

      this information is very good but it is not very full preparied

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      rita  6 years ago

      it is not that useful for my school project.not satisfied hub .SORRY. IT CAN BE BETTER.

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      MANISHA 6 years ago

      NICE INFO,BUT NOT ENOUGH FOR A PROJECT:( .NOT IMPRESSED WITH THE INFORMATION

      HOPE U GOT MY POINT.AND I DON't know why people have praised it so much?

    • Rudra profile image
      Author

      Rudra 6 years ago

      @Rita and Manisha, you clearly dont know how to do your project. You cant expect to get, copy and paste everything from the internet. Use your imagination which you clearly dont have.

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      sakshi 6 years ago

      not so nice.its not enough 4 my school project... i really dont know y people praised dis hub so much.....acoording 2 me its useless......

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      Muskaan 6 years ago

      Nice information and pictres

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      i will not tell 6 years ago

      very dirty

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      ashna 6 years ago

      great!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    • profile image

      vikas 6 years ago

      very nice helpful

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      Amrit kaur 6 years ago

      Wonderful it help to complete my project

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      sajid 6 years ago

      usefull.....................

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      SMRUTHI 6 years ago

      THIS WAS REALLY VERY INFOMATIVE .

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      akshra 6 years ago

      ya bt theres nothing bout his education or family membrs...what the f**k yaar ma holidys h w is atkaaaaa huaaaaaa..............................;(

    • profile image

      jasman 6 years ago

      very usefull.......................

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      kamakshi syal 6 years ago

      it help us to my holiday kome work

    • profile image

      kamakshi 6 years ago

      it is so good foe holidays home work to gooooooooooooooooooooooooooooooooooooood well done

    • profile image

      AREEB 6 years ago

      POOR INFORMATION, I NEEDED MORE...

      BOOOOO!!!

    • profile image

      Abin 6 years ago

      very bad

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      miley 6 years ago

      thanx it helped me in my project work

    • profile image

      shresth 6 years ago

      thank you

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      kk 6 years ago

      nice

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      arjun 6 years ago

      thank you

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      reshmaraghu 6 years ago

      i need it for maths project very brillinant

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      shanika 6 years ago

      itz intrestin 2 knw abt the great personality

      thanks 4r the help............!!!!!

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      CHAITALI 6 years ago

      ITS REALLY GOOD. ATLEAST INMY PROJECTS

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      aayushi 6 years ago

      kuch khaas nahi diya hua bas faltu ki info di hui na birth date batai hui nahi death date .. dhakkan hain sare ke sare..

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      keerthi 6 years ago

      i like this it's good.

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      navya 6 years ago

      thanks a lot it hlped me

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      sunshine 6 years ago

      its about physics not about maths

      it didn't help us in making maths project..................

    • profile image

      bilal ahmad 6 years ago

      THIS IS A VERY GOOD SITE OF PROJECT

    • profile image

      Megha 6 years ago

      It's fffffffantastic.

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      aswin 6 years ago

      very good

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      ritu 6 years ago

      nice but u can add more

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      aarushi bhatta 6 years ago

      nice!!!!!!!!!!!help me in project...............

    • profile image

      radhi 6 years ago

      speechless----------------

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      FARAH 6 years ago

      WELL ITS OK.

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      CHULBUL PANDEY 6 years ago

      AREY BAHUT BADHIYA......................................................................................

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      thejas 6 years ago

      it was nice to read it like thisit was nice hub

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      Shakeela 6 years ago

      itz avg

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      prachi 6 years ago

      bekar hai

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      shardul k 6 years ago

      very nice but can be added more

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      Shanker SSS 6 years ago

      Superb

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      kristy 6 years ago

      i understood a lot

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      Tausky 6 years ago

      nyce... pls continue givin infornation about othr inventions too!

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      ashutosh 6 years ago

      very nice must say he is so great that i will faint

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      keerthana 6 years ago

      it was very helpful for my project.........nice writing

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      anurag 6 years ago

      awesome info proveided

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      jessica 6 years ago

      danggggg lots of stuff helpedd me on my essayy thanxx!!!

      :::)

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      NITIN 6 years ago

      ITS REALLY GOOD. ATLEAST IN MY PROJECTS i understood a lot

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      risha  6 years ago

      good sourse of information

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      6 years ago

      potato

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      VIKAS 6 years ago

      BIKHARI KAMINAY KYU DUKHI KR RAHA H 1 LINE KA THOUGHT BHEG

    • profile image

      sonia 6 years ago

      its nice wonderful

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      tinty 6 years ago

      use ful for myproject

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      secret 6 years ago

      not able to understand {FOR CHILDREN}

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      Samriddhi 6 years ago

      Nice one......will surely help in my maths project.

      Thanx.

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      anoushka joshi 6 years ago

      gr8 article .............. helped a lot in science project !!!!!!!!!!!!!!!!!!!!!!!!!

    • profile image

      davi 6 years ago

      i like it superbbbbbbbbbb awesomeeeee

    • profile image

      davi 6 years ago

      i love it it helped me a lot!1!1!!!!!!!!!!

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      himani de gr8 6 years ago

      awsum...thnxi33 a lot....luvd it...!...:)

    • profile image

      shree 6 years ago

      so so so...nice

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      akshatha 6 years ago

      it's a really well collected imfomation 2 all of us 2 do the projects

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      lakshmi 6 years ago

      twas really useful for ma project....thnk u so much....

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      nawaz 6 years ago

      bastard why were you born on this planet you gave me a headech i have to study all that you have proved in your life and it irritates me.you suck big time if i meet your children i will kill them namashkar

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      akhil 6 years ago

      it's some very important in our studies

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      Jeet sharma 6 years ago

      Great aarya-bhatt

      and great story

      this page is compulsory read by every indian

      i proud to be on indian history

      vandematram

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      Gaurav 6 years ago

      I MISS U

      Lekin miss to school me hoti hai.School me to bachhe hote hote hai.bachhe to chhote hote hai .chhoti to chidiya hoti hai chidiya to udti hai Udta to kouaa bhi hai.kouaa to kaala hota hai-kali to billi bhi hoti.billi to sher ki khala hoti-SHER to jungal me rahta hai jungal me hathi bhi rahta hai hathi to bahut bada hota hai BADA to samundar bhi hota hai samundar to neela hota hai NEELA to aasman bhi hota hai asman per to taare hote hai taare to chamkte hai chamkta to heera bhi hai heera to mahnga hota hai mahnga to sona bhi hota hai sona to raat ko hota hai raat ke baad to subah hoti hai subah to nashta karte hai nashte me to anda hota hai anda 2 rang ka hota 2 rang ka zebra hota hai zebra to ghode jaisa hota hai ghoda to tanga chalata hai tange per to bachhe school jate hai school me to MISS hoti hai MISS se yaad aaya I MISS U , I MISS U.

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      Robyn Dunstan 6 years ago

      Why is there so much advertising junk on your web site?

    • profile image

      ajay chelkar 6 years ago

      this information is very great

      I like the math very very much

      Thank you......

    • profile image

      Avishi 6 years ago

      it's really good helps in getting more knowledge about our indian philosophers.

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      alka 6 years ago

      thanxxxxxxxxxxxxxxxx for providing me information of aryabhatta..............

    • profile image

      safu 6 years ago

      cooooooooollllll .......

    • profile image

      gaurav kundu jaat 6 years ago

      kiran

    • profile image

      gourav jaat 6 years ago

      iluv life

    • profile image

      areeb 6 years ago

      its so important

    • profile image

      Bharti 6 years ago

      I read it..... its amezing to knw about Such a Great People.. He was Really Great Mathematician.

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      Master 6 years ago

      This is an awesome site.It helped me research. It's got really useful information.

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      Master  5 years ago

      This website is really usefull and is awesome. Aryabhatta was an awesome mathmetician

    • profile image

      jasmin29 5 years ago

      this did not help me find information about aryabhatta but it was well written

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      HARIKRISHNAN S 5 years ago

      ITS HELP ME TO FINISH MY PROJECT TANKS

    • profile image

      ashish rana 5 years ago

      realy amazing india and indians . i proud to be indian

    • profile image

      RANVEER KAPOOR 5 years ago

      GREAT INFORMATION NICE HUB

      THANXXXXXXXXXXXX..... RUDRA

    • profile image

      Your Momma 5 years ago

      this was ok

    • profile image

      raja 5 years ago

      dont find wat i need

    • profile image

      renju 5 years ago

      awesome and amazing

    • profile image

      DIUMAN 5 years ago

      MY GOODNESS . ARYABHATT TOOK INDIA TO A NEW GREAT HIEGHT

    • profile image

      nee 5 years ago

      very very intresting

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      Priyansh Khatri 5 years ago

      bakwas hai

    • profile image

      mann 5 years ago

      nice, no no no no excellent article

    • profile image

      rishab  5 years ago

      just copied from wikipedia got up damed

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      ratnesh kumar 5 years ago

      thanks it has realy helped in doing my project work.....

    • profile image

      Nupur Neha 5 years ago

      Its really proved helpful to me

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      NAMITA 5 years ago

      THANXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX a lotttttttttt it helped me in my project

    • profile image

      pankaj 5 years ago

      thanks sir..

    • profile image

      himanshu sirsiya 5 years ago

      heyyyyyyyyyyyyyy thanku veryyyyyyyyyyyyyyyyyyyyyyy much it realy helped in my project

    • profile image

      Tanuja lilhare 5 years ago

      I like the information about mr. Rudra

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      Tanuja lilhare 5 years ago

      I try to find out the information about arybhatta ,and when i got it i was very happy, because my tution teacher had given me this homework and she is very street also and from this i got many extra knowledge .so i thanks a lot to ms.arybhatta.

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      Raja lilhare 5 years ago

      IT IS SO INTRESTING

    • profile image

      Mantry narendra Lilhare and Raja,Chotu,Tanuja,Mohini 5 years ago

      It's Out standing.

    • profile image

      ANUJ GOYA;L 5 years ago

      HELLO!HOW ARE YOU? I AM FINE

    • profile image

      PRASHANSA 5 years ago

      IT IS NOT ENOUGH FOR MAKING A PROJECT OR ANYTHING ELS

    • profile image

      sukhman 5 years ago

      it helped me a lot thanks

    • profile image

      Rajat vashisht  5 years ago

      it is not enough 4 making project

    • profile image

      Manvendra 5 years ago

      i liked reading it.

      It helped me in making project .

      THAnkSSs a loT

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      rishabh parashar 5 years ago

      in complete information

    • profile image

      ashish ranjan 5 years ago

      it saved me from my very strict geography teacher but from my own heart this note on aryabhatta is not good but also not so bad

    • profile image

      anushka 5 years ago

      thanks for my project

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      saloni a thakur banglore 5 years ago

      thanks a lot for the information of aryabhatta or my teacher could killlllllllllll me!!!!!!!!!!!!!!!!!!!!!!!!!!

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      dheeraj chaudhary 5 years ago

      thanks for give information

      information on this page is very useful to me to make my school project

    • profile image

      Harshita Srivastav 5 years ago

      It help me in making my project its AWESOME , WONDERFUL AND etc.

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      Pranav bhagat  5 years ago

      Name –Aryabhata I

      Born -476 , Counrty- Kusumapura (now Patna), India

      Aryabhatta (476-550 A.D.) was born in Patliputra in Magadha, modern Patna in Bihar. Many are of the view that he was born in the south of India especially Kerala and lived in Magadha at the time of the Gupta rulers; time which is known as the golden age of India. There is no evidence that he was born outside Patliputra and traveled to Magadha, the centre of education and learning for his studies where he even set up a coaching centre. His first name "Arya" is hardly a south Indian name while "Bhatt" (or Bhatta) is a typical north Indian name even found today specially among the "Bania" (or trader) community.

      FAMOUS FOR - Whatever this origin, it cannot be argued that he lived in Patliputra where he wrote his famous treatise the "Aryabhatta-siddhanta" but more famously the "Aryabhatiya", the only work to have survived. It contains mathematical and astronomical theories that have been revealed to be quite accurate in modern mathematics. For instance he wrote that if 4 is added to 100 and then multiplied by 8 then added to 62,000 then divided by 20,000 the answer will be equal to the circumference of a circle of diameter twenty thousand. This calculates to 3.1416 close to the actual value Pi (3.14159). But his greatest contribution has to be zero. His other works include algebra, arithmetic, trigonometry, quadratic equations and the sine table.

      Aryabhata is the author of several treatises on mathematics and astronomy, some of which are lost. His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.

      The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara I. This work appears to be based on the older Surya Siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya. It also contained a description of several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular and circular (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, and water clocks of at least two types, bow-shaped and cylindrical.[3]

      A third text, which may have survived in the Arabic translation, is Al ntf or Al-nanf. It claims that it is a translation by Aryabhata, but the Sanskrit name of this work is not known. Probably dating from the 9th century, it is mentioned by the Persian scholar and chronicler of India, Ab? Rayh?n al-B?r?n?.[3]

      Education -However, it is fairly certain that at some point, he went to Kusumapura for higher studies, and that he lived here for some time.[2] Bh?skara I (AD 629) identifies Kusumapura as Pataliputra (modern Patna). He lived there in the dying years of the Gupta empire, the time which is known as the golden age of India, when it was already under Hun attack in the Northeast, during the reign of Buddhagupta and some of the smaller kings before Vishnugupta.

      FAMOUS FOR ----

      Aryabhatta’s Representation of the Numerals and Zero

      Aryabhatta developed a representation of numbers using the letters of the Indian alphabet as his symbols. The ways in which he carries out his calculations suggest that he knew and understood the place value system of representing numbers, and that he also knew about zero.

      He also calculated the value of pi with an accuracy unknown before him. He estimated it to be 3.1416, which is actually correct to four decimal places. However, he does not explain how he arrived at this value and, surprisingly enough, uses the value of the square root of ten for his calculations requiring pi.

      He also gave formulae for the sums of the first n integers. He did the same thing for the squares and cubes of the integers.

      Aryabhatta Constructed Sine Tables

      Aryabhatta was able to construct sine tables, giving values for the sine function at intervals of 3 45’ (three degrees and forty five minutes). He studied trigonometry on plane surfaces as well as spherical surfaces. He estimated the circumference and the diameter of the earth with great accuracy.

      His text gives many mathematical rules without proofs. He gives formulae for the areas of circles and triangles, and also for the volume of spheres and pyramids. His formulae for the volume of spheres and pyramids are believed to be incorrect, though some argue that this is due to errors in translation

      Aryabhatta’s Insights in Astronomy

      Aryabhatta studied the orbits of the planets around the sun and said that they were elliptical. He worked with the equations that predict the positions of the planets. These studies enabled him to predict eclipses.

      He suggested that it is the earth that rotates around its axis, and not the stars that move in the sky, as was believed until then. He also said that the moon shines due to reflected light

      Remarks … Aryabhatta is the first writer on astronomy to whom the Hindus do not allow the honour of a divine inspiration. Writers on mathematical science distinctly state that he was the earliest uninspired and a merely human writer on astronomy. This is a notice which sufficiently proves his being an historical character.

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      Gopal 5 years ago

      ARYABHATTA, or, as written by the Arabs, ARJABAHR, a celebrated Hindu mathematician, and the earliest known author on Algebra, is now generally believed to have lived about the beginning of our era. Nothing, however, has yet appeared that can give us the slightest information as to the place of his birth, or the time when he lived; nor is there, as far as we know, any tradition or record extent from which we can collect any of the circumstances of his life; even his period is still a matter of dispute. We must, therefore, content ourselves with whatever notices we find of Aryabhatta and his system in the various writers on astronomy and other mathematical sciences whose authority is established and cannot be called into doubt.

      Aryabhatta is the first writer on astronomy to whom the Hindus do not allow the honour of a divine inspiration. Writers on mathematical science distinctly state that he was the earliest uninspired and a merely human writer on astronomy. This is a notice which sufficiently proves his being an historical character.

      Statue of Aryabhata The chief doctrines which Aryabhatta (Aarya-Bhatt) professed were the following:

      He affirmed the diurnal revolution of the earth on its axis; an assertion which is fully borne out by a quotation from one of his works, in a commentary on the "Brahmasphut'a-Siddhanta" of Brahmagupta by Prithudakaswami: "The Earth making a revolution produces a daily rising and setting of the stars and planets". At the same time he thought that this revolving of the earth was produced through the agency of a peculiar current of aerial fluid, or spiritus vector ("wind"), to which he assigned a distance of 150 yojanas (114 miles) from the surface of the earth. In opposition to the generally received opinion, he maintained that the moon, the primary planets, and the stars had no light of their own, and were only illumined by the sun; he consequently knew the true cause of solar and lunar eclipses.

      Aryabhatta also ascribed to the epicycles, by which the motion of a planet is represented, a form varying from the circle and nearly elliptic. Moreover, he recognized a motion of the nodes and asides of all primary planets, as well as of the moon, and noticed the motion of the equinoctial and solstitial points, which he restricted, however, to an oscillation within the limits of twenty- four degrees, at the rate of one libration in seventy years. The length of AryabhatYa's sidereal year was 356 days 6 hours 12 minutes and 30 seconds. Aryabhatta stated the diameter of the earth at 1050 yojanas and its circumference at 3300 yojanas (25,080 miles). Hence it appears that he held the proportion of the diameter to the periphery of a circle to be seven to twenty-two, which is a nearer approximation than that of Brahmagupta and S'ridhara, who came after him.

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      Shrishti 5 years ago

      It's niceeeeeeeeeeeeeeee.

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      annkottoor 5 years ago

      very helpful for my schl prjct

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      ananya 5 years ago

      hiiii!!!!!!!! thank u, it was very helpful in preparing my project...

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      rumit tanna 5 years ago

      very good amazing for me it heped me a lot

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      manthan 5 years ago

      thank you this helps me in my maths project

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      YASH PATE; 5 years ago

      INDIAN MATHEMATICS - BRAHMAGUPTA

      Brahmagupta

      Brahmagupta (598–668 AD)

      The great 7th Century Indian mathematician and astronomer Brahmagupta wrote some important works on both mathematics and astronomy. He was from the state of Rajasthan of northwest India (he is often referred to as Bhillamalacarya, the teacher from Bhillamala), and later became the head of the astronomical observatory at Ujjain in central India. Most of his works are composed in elliptic verse, a common practice in Indian mathematics at the time, and consequently have something of a poetic ring to them.

      It seems likely that Brahmagupta's works, especially his most famous text, the “Brahmasphutasiddhanta”, were brought by the 8th Century Abbasid caliph Al-Mansur to his newly founded centre of learning at Baghdad on the banks of the Tigris, providing an important link between Indian mathematics and astronomy and the nascent upsurge in science and mathematics in the Islamic world.

      In his work on arithmetic, Brahmagupta explained how to find the cube and cube-root of an integer and gave rules facilitating the computation of squares and square roots. He also gave rules for dealing with five types of combinations of fractions. He gave the sum of the squares of the first n natural numbers as n(n + 1)(2n + 1)? 6 and the sum of the cubes of the first n natural numbers as (n(n + 1)?2)².

      Brahmagupta’s rules for dealing with zero and negative numbers

      Brahmagupta’s rules for dealing with zero and negative numbers

      Brahmagupta’s genius, though, came in his treatment of the concept of (then relatively new) the number zero. Although often also attributed to the 7th Century Indian mathematician Bhaskara I, his “Brahmasphutasiddhanta” is probably the earliest known text to treat zero as a number in its own right, rather than as simply a placeholder digit as was done by the Babylonians, or as a symbol for a lack of quantity as was done by the Greeks and Romans.

      Brahmagupta established the basic mathematical rules for dealing with zero (1 + 0 = 1; 1 - 0 = 1; and 1 x 0 = 0), although his understanding of division by zero was incomplete (he thought that 1 ÷ 0 = 0). Almost 500 years later, in the 12th Century, another Indian mathematician, Bhaskara II, showed that the answer should be infinity, not zero (on the grounds that 1 can be divided into an infinite number of pieces of size zero), an answer that was considered correct for centuries. However, this logic does not explain why 2 ÷ 0, 7 ÷ 0, etc, should also be zero - the modern view is that a number divided by zero is actually "undefined" (i.e. it doesn't make sense).

      Brahmagupta’s view of numbers as abstract entities, rather than just for counting and measuring, allowed him to make yet another huge conceptual leap which would have profound consequence for future mathematics. Previously, the sum 3 - 4, for example, was considered to be either meaningless or, at best, just zero. Brahmagupta, however, realized that there could be such a thing as a negative number, which he referred to as “debt” as a opposed to “property”. He expounded on the rules for dealing with negative numbers (e.g. a negative times a negative is a positive, a negative times a positive is a negative, etc).

      Furthermore, he pointed out, quadratic equations (of the type x2 + 2 = 11, for example) could in theory have two possible solutions, one of which could be negative, because 32 = 9 and -32 = 9. In addition to his work on solutions to general linear equations and quadratic equations, Brahmagupta went yet further by considering systems of simultaneous equations (set of equations containing multiple variables), and solving quadratic equations with two unknowns, something which was not even considered in the West until a thousand years later, when Fermat was considering similar problems in 1657.

      Brahmagupta’s Theorem on cyclic quadrilaterals

      Brahmagupta’s Theorem on cyclic quadrilaterals

      Brahmagupta even attempted to write down these rather abstract concepts, using the initials of the names of colours to represent unknowns in his equations, one of the earliest intimations of what we now know as algebra.

      Brahmagupta dedicated a substantial portion of his work to geometry and trigonometry. He established ?10 (3.162277) as a good practical approximation for ? (3.141593), and gave a formula, now known as Brahmagupta's Formula, for the area of a cyclic quadrilateral, as well as a celebrated theorem on the diagonals of a cyclic quadrilateral, usually referred to as Brahmagupta's Theorem.

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      pratibha pandey 5 years ago

      thanx for uploading

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      Sanjana Chaudhary 5 years ago

      HELLO,MAM.IT'S TOO NICEEEEEE AS IT INCREASES MY VOCUBULARY AND HELPED ME A LOT IN PREPARING MY SCHOOL PROJECT.SO,THANK YOU VERY MUCH AND KEEP PROVIDING US SUCH TYPE OF INFORMATION.

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      vaisakh 5 years ago

      thankyou rudra for this great information it also helped my project

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      robina 5 years ago

      good

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      vipul 5 years ago

      hiiiiiiiiii send some nice maths information and tecknek

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      olivia 5 years ago

      i already know all of this info update,update,update!!(:

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      saloni 5 years ago

      good!! but i can not find my project

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      parjeet singh 5 years ago

      your site is good ,but icant complete my project

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      shubham 5 years ago

      yfhgjg

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      Rahul 5 years ago

      could you provide me this information in simple words

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      sunil 5 years ago

      Aryabhatta came to this world on the 476 A.D at Patliputra in Magadha which is known as the modern Patna in Bihar. Some people were saying that he was born in the South of India mostly Kerala. But it cannot be disproved that he was not born in Patlipura and then travelled to Magadha where he was educated and established a coaching centre. His first name is “Arya” which is a South Indian name and “Bhatt” or “Bhatta” a normal north Indian name which could be seen among the trader people in India.

      No matter where he could be originated from, people cannot dispute that he resided in Patliputra because he wrote one of his popular “Aryabhatta-siddhanta” but “Aryabhatiya” was much more popular than the former. This is the only work that Aryabhatta do for his survival. His writing consists of mathematical theory and astronomical theory which was viewed to be perfect in modern mathematics. For example, it was written in his theory that when you add 4 to 100 and multiply the result with 8, then add the answer to 62,000 and divide it by 20000, the result will be the same thing as the circumference with diameter twenty thousand. The calculation of 3.1416 is nearly the same with the true value of Pi which is 3.14159. Aryabhatta’s strongest contribution was zero. Another aspect of mathematics that he worked upon is arithemetic, algebra, quadratic equations, trigonometry and sine table.

      Aryabhatta was aware that the earth rotates on its axis. The earth rotates round the sun and the moon moves round the earth. He discovered the 9 planets position and related them to their rotation round the sun. Aryabhatta said the light received from planets and the moon is gotten from sun. He also made mention on the eclipse of the sun, moon, day and night, earth contours and the 365 days of the year as the exact length of the year. Aryabhatta also revealed that the earth circumference is 24835 miles when compared to the modern day calculation which is 24900 miles.

      Aryabhatta have unusually great intelligence and well skilled in the sense that all his theories has became wonders to some mathematicians of the present age. The Greeks and the Arabs developed some of his works to suit their present demands. Aryabhatta was the first inventor of the earth sphericity and also discovered that earth rotates round the sun. He was the one that created the formula (a + b)2 = a2 + b2 + 2ab. He also created a solution formula of solving the following equations:

      1 + 2 + 3 + 4 + 5 + ……………… + n = n (n + 1)/2

      12 + 22 + 32 + 42 + 52 + ……………….. + n2 = n (n + 1) (2n + 1)/6

      13 + 23 + 33 + 43 + 53 + ………………….. n3 = (n (n + 1)/2)2

      14 + 24 + 34 + 44 + 54 + ………………….. + n4 = (n (n + 1) (2n + 1) (3n2 + 3n – 1))/30

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      arryan 5 years ago

      yaar log kitne bahlae hote hain na koi kam na dhannda bah kr do comment !/??????? hmmmm whatever

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      mohsin 5 years ago

      without u nothing is possible.

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      aryan(sanju) 5 years ago

      this is very nice and important knowledge

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      shubham 5 years ago

      The great mathematacian.

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      Annu Manhas 5 years ago

      Thanks & i must say very very good.God Bless u.

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      Annu Manhas 5 years ago

      Thanks & i must say very very good.God Bless u.

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      hithyeshi 5 years ago

      very informative

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      VIJAY KUMAR 5 years ago

      HADDO

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      s anusha 5 years ago

      i am really happy because one day my maths teather told me write a about aryabhatta it is really intresting and i am thank full to u

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      Shaikh aqsa idris 5 years ago

      Thanks for first mathematicians of Bhaskarachariya and Aryabhatta. :p:*:D

      :p:*:D

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      paras.singh 5 years ago

      100 TIMES THANK YOU I HAVE COMPLET MY PROJECT WORK AND I HAVE GOT 10 OUT OF 10

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      shewata mishra 5 years ago

      paras tell me about your site it was so helpful

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      N.DIVYA SREE 5 years ago

      THANKS TO ARYA BHATTA AND i AM POOR IN MATHEMATICS

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      hitesh 5 years ago

      that's a good mathematics................

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      ishi 5 years ago

      i need more information on Aryabhata to do my project and that to fast within 1 hour

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      Anonymous 5 years ago

      it wasn't helpful 4 my project !!!!!!!!!

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      dhruv 5 years ago

      nothing is there in this hup page it is all idiotic

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      Pramod 5 years ago

      I like it. But it can be better. It is too short

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      Anushkaa 5 years ago

      REALLY GOOD AND KNOWLEDGE ABLE TOOOOOOOOO!

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      xyz 5 years ago

      very nice!!

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      ranvir 5 years ago

      quite a knowledgeable information

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      EKTA 5 years ago

      LOOOOOOVED IT

      THANKS

      ;];];].;];]

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      tannu 5 years ago

      aryabhatta was a first person to find that the earth is round :P

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      asdasd 5 years ago

      aryabhatta

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      sex 5 years ago

      Aryabhata

      From Wikipedia, the free encyclopedia

      For other uses, see Aryabhata (disambiguation).

      tandii baba

      Statue of Aryabhata on the grounds of IUCAA, Pune. As there is no known information regarding his appearance, any image of Aryabhata originates from an artist's conception.

      Born 476

      Died 550

      Era Gupta era

      Region India

      Main interests Maths, Astronomy

      Major works ?ryabha??ya, Arya-siddhanta

      Aryabhata (IAST: ?ryabha?a, Sanskrit: ??????) (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the ?ryabha??ya (499 CE, when he was 23 years old) and the Arya-siddhanta.

      Contents [hide]

      1 Biography

      1.1 Name

      1.2 Time and Place of birth

      1.3 Education

      1.4 Other hypotheses

      2 Works

      2.1 Aryabhatiya

      3 Mathematics

      3.1 Place value system and zero

      3.2 Approximation of ?

      3.3 Trigonometry

      3.4 Indeterminate equations

      3.5 Algebra

      4 Astronomy

      4.1 Motions of the solar system

      4.2 Eclipses

      4.3 Sidereal periods

      4.4 Heliocentrism

      5 Legacy

      6 See also

      7 References

      7.1 Other references

      8 External links

      [edit]Biography

      [edit]Name

      While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus,[1] including Brahmagupta's references to him "in more than a hundred places by name".[2] Furthermore, in most instances "Aryabhatta" does not fit the metre either.[1]

      [edit]Time and Place of birth

      Aryabhata mentions in the Aryabhatiya that it was composed 3,630 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476 CE.[citation needed]

      Aryabhata provides no information about his place of birth. The only information comes from Bh?skara I, who describes Aryabhata as ??mak?ya, "one belonging to the a?maka country." The Asmaka were one of the 16 of Ancient Indian Mahajanapadas, and the only one situated south of the Vindhyas. Since Aryabhata lived in and around 480, he resided in The Gupta's, near the end of the Golden Age

      It is widely attested that during the mid-first millennium BCE, a branch of the A?maka people settled in the region between the Narmada and Godavari rivers in central India, and it is possible Aryabhata was born there.[1][3] However, early Buddhist texts describe Ashmaka as being further south, in dakshinapath or the Deccan, while other texts describe the Ashmakas as having fought Alexander.

      Many are of the view that he was born in the south of India in Kerala and lived in Magadha at the time of the Gupta rulers.

      [edit]Education

      It is fairly certain that, at some point, he went to Kusumapura for advanced studies and that he lived there for some time.[4] Both Hindu and Buddhist tradition, as well as Bh?skara I (CE 629), identify Kusumapura as P??aliputra, modern Patna.[1] A verse mentions that Aryabhata was the head of an institution (kulapati) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well.[1] Aryabhata is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar.[5]

      [edit]Other hypotheses

      Some archeological evidences suggests that Aryabhata could have originated from the present day Kodungallur in Tamilakam, modern Kerala. For instance, one hypothesis was that a?maka (Sanskrit for "stone") may be the region in Kerala that is now known as Ko?u??all?r, based on the belief that it was earlier known as Ko?um-Kal-l-?r ("city of hard stones"); however, old records show that the city was actually Ko?um-kol-?r ("city of strict governance"). Similarly, the fact that several commentaries on the Aryabhatiya have come from Tamilakam were used to suggest that it was Aryabhata's main place of life and activity; however, many commentaries have come from outside Tamilakam, and the Aryasiddhanta was completely unknown in Kerala. [6]

      Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but his "Lanka" is an abstraction, standing for a point on the equator at the same longitude as his Ujjayini.[7]

      [edit]Works

      Aryabhata is the author of several treatises on mathematics and astronomy, some of which are lost. His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.

      The Arya-siddhanta, a lot work on astronomical computations, is known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara I. This work appears to be based on the older Surya Siddhanta and uses the midnight-day reckoning, as opposed to sunrise in Aryabhatiya. It also contained a description of several astronomical instruments: the gnomon (shanku-yantra), a shadow instrument (chhAyA-yantra), possibly angle-measuring devices, semicircular and circular (dhanur-yantra / chakra-yantra), a cylindrical stick yasti-yantra, an umbrella-shaped device called the chhatra-yantra, and water clocks of at least two types, bow-shaped and cylindrical.[3]

      A third text, which may have survived in the Arabic translation, is Al ntf or Al-nanf. It claims that it is a translation by Aryabhata, but the Sanskrit name of this work is not known. Probably dating from the 9th century, it is mentioned by the Persian scholar and chronicler of India, Ab? Rayh?n al-B?r?n?.[3]

      [edit]Aryabhatiya

      Direct details of Aryabhata's work are known only from the Aryabhatiya. The name "Aryabhatiya" is due to later commentators. Aryabhata himself may not have given it a name. His disciple Bhaskara I calls it Ashmakatantra (or the treatise from the Ashmaka). It is also occasionally referred to as Arya-shatas-aShTa (literally, Aryabhata's 108), because there are 108 verses in the text. It is written in the very terse style typical of sutra literature, in which each line is an aid to memory for a complex system. Thus, the explication of meaning is due to commentators. The text consists of the 108 verses and 13 introductory verses, and is divided into four p?das or chapters:

      Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present a cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (c. 1st century BCE). There is also a table of sines (jya), given in a single verse. The duration of the planetary revolutions during a mahayuga is given as 4.32 million years.

      Ganitapada (33 verses): covering mensuration (k?etra vy?vah?ra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), simple, quadratic, simultaneous, and indeterminate equations

      Kalakriyapada (25 verses): different units of time and a method for determining the positions of planets for a given day, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week with names for the days of week.

      Golapada (50 verses): Geometric/trigonometric aspects of the celestial sphere, features of the ecliptic, celestial equator, node, shape of the earth, cause of day and night, rising of zodiacal signs on horizon, etc. In addition, some versions cite a few colophons added at the end, extolling the virtues of the work, etc.

      The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya, (1465 CE).

      [edit]Mathematics

      [edit]Place value system and zero

      The place-value system, first seen in the 3rd century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the Fren

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      shabbir kachwala 5 years ago

      aryabhatta

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      apurva 5 years ago

      amazing this information is very good i like.

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      NAMRATH.N 5 years ago

      IT'S REALLY NICE

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      Aarika 5 years ago

      its nice................. i could complete my school project.. thanxxxxxxxxx.....

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      Anushkaa 5 years ago

      It's nice it helped me a lot!Thanxxxxxxxxxxxxxxxxx

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      VIRAJ.D 5 years ago

      I ALWAYS THINK HOW HAVE INVENTED THE 0 NOW I UNDERSTAND ARYBHATA HAVE INVENTED THE 0 WE SHOULD THAX TO ARYBHATA.

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      Aryan Shrivastava 5 years ago

      very very thanks fo making math

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      VIDHI 5 years ago

      it is very benificial and really gr8. thnxxxxxxxxxxx

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      simran 5 years ago

      how great ur ! wow it helped my projectwork thank u

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      om prakash pandey 5 years ago

      nice INFORMATION

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      nancy 4 years ago

      thanks rudra it helped me in my project....... :)

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      NAVNEET 4 years ago

      VERY NICEEEEEEEEEEEEEE.

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      pragya mishra 4 years ago

      i don't find my project

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      rachit 4 years ago

      its good for project.

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      sharon 4 years ago

      this is good for my project=)

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      $h!va 4 years ago

      its good for my project

      Th@nk u but in your site there is no picture.

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      kshitij 4 years ago

      it is good for my holiday homework but there is no picture

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      archit 4 years ago

      thxx for help rudra

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      naushin 4 years ago

      good but it could very good

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      SUKRUTI TOMAR 4 years ago

      I DON'T WANT THIS ANSWER BUT IT IS ALSO FINE, I'LL ADD SOME OF THIS INFORMATION IN MY ASSIGNMENT. THANKXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX AND BBYYEEEEEEEEEEEEEEEEEEEEEEEEEEE.

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      simran vashishtha 4 years ago

      thanzzzzzzzz i need this project

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      pia 4 years ago

      thanks rudra

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      shivani singh 4 years ago

      its great 4 students.............study////////

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      keerat 4 years ago

      cool but i could not find about my project

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      Rushil 4 years ago

      Average but not o"k for my project

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      navya gahlawat 4 years ago

      Ausam boss.

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      rushil 4 years ago

      sahi hai

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      rushdha 4 years ago

      GR8888888888888888888

      Good Job I like it

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      APEKSHA GUPTA 4 years ago

      HE WAS A GREAT MATHEMTISION

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      sonali kar 4 years ago

      have good points and now it completes my project about the great mathematician Aryabhatta.Thx......

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      sonam 4 years ago

      he is a very good mathematicians

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      samn srivastav 4 years ago

      its helps in my holiday homework thanx !

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      Junieee 4 years ago

      Thanks it help me lot to complete my assignment

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      anand 4 years ago

      its interesting

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      naina 4 years ago

      info iz awesome

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      Anmol 4 years ago

      it was very nice it helps me a lot

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      simrat 4 years ago

      an eassy by gopal 12 months ago is awesomewhat he has written hiseassy helped me a lot thanks

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      aaryan 4 years ago

      it was a nice experence

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      vivek 4 years ago

      really useful

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      VIVEK PANDEY 4 years ago

      IT WAS REALLY USEFUL FOR MY PROJECT AND I GOTA+ IN MY PROJECT AND SCHOLA

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      domnic 4 years ago

      not to the point

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      Nancy 4 years ago

      good for project

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      SUNEEL 4 years ago

      HIS A GRET PERON

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      DEVARSH 4 years ago

      Lots of imformation . Helpful in the maths project

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      diya 4 years ago

      nice..................... i loved it n it hd also helpd me in my assignment.

      thnx mam for all this.

      Devarsh in which clas u r?n which scool where?

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      swati 4 years ago

      best

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      Nikhat (nsa) 4 years ago

      Very nice. Thank for that

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      mohi 3 years ago

      he is one of the great mathematician

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      Tarnjeet singh 3 years ago

      aryabhatta indian great mathematician lik is holiday home work day

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      shratik 3 years ago

      shratik rajpurohit

      meko bilkul mazzaaa ni ayaa

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      mukund 3 years ago

      good but log pagal hai.

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      mr.aditya kumar singh 3 years ago

      it is good .

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      raina 3 years ago

      he was an greatttttttttt mathematican

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      abhiram pg 3 years ago

      I agree that he was a great great mathematican . I love him. it helped in my project

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      Sonia 2 years ago

      He is very good in mathematics

      It is very good person

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      noorhasan 2 years ago

      Aryabhat is a good mathematicion l want to make like him

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      Prasoon Singh 2 years ago

      He was very great person. Vo hamare dilo me aaj bhi jinda hein

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