Contribution of INDIAN Mathematicians in Field of Mathematics

7/25/2019 Contribution of INDIAN Mathematicians in Field of Mathematics

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Indian mathematicsemerged in theIndian subcontinent[1]from 1200 BC [2]until the end of the

18th century. In the classical period of Indian mathematics (00 !" to 1200 !"#$ important

contributions %ere made by scholars li&e !ryabhata$ Brahmagupta$ and Bhas&ara II. 'he

decimal number systemin use today[]%as first recorded in Indian mathematics.[]Indian

mathematicians made early contributions to the study of the concept of)eroas a number$[*]

negati+e numbers$[,]arithmetic$ and algebra.[-]In addition$ trigonometry[8]%as further ad+anced

in India$ and$ in particular$ the modern definitions of sineandcosine%ere de+eloped there.[]

'hese mathematical concepts %ere transmitted to the/iddle ast$ China$ and urope[-]and led

to further de+elopments that no% form the foundations of many areas of mathematics.

!ncient and medie+al Indian mathematical %or&s$ all composed in ans&rit$usually consisted of

a section ofsutrasin %hich a set of rules or problems %ere stated %ith great economy in +erse in

order to aid memori)ation by a student. 'his %as follo%ed by a second section consisting of a

prose commentary (sometimes multiple commentaries by different scholars# that eplained the

problem in more detail and pro+ided 3ustification for the solution. In the prose section$ the form(and therefore its memori)ation# %as not considered so important as the ideas in+ol+ed.[1][10]!ll

mathematical %or&s %ere orally transmitted until approimately *00 BC4 thereafter$ they %ere

transmitted both orally and in manuscript form. 'he oldest etant mathematical document

produced on the Indian subcontinent is the birch bar& Ba&hshali /anuscript$ disco+ered in 1881

in the +illage of Ba&hshali$ near 5esha%ar(modern day 5a&istan# and is li&ely from the -th

century C.[11][12]

! later landmar& in Indian mathematics %as the de+elopment of the seriesepansions for

trigonometric functions(sine$ cosine$ and arc tangent# by mathematicians of the 6erala schoolin

the 1*th century C. 'heir remar&able %or&$ completed t%o centuries before the in+ention ofcalculusin urope$ pro+ided %hat is no% considered the first eample of apo%er series(apart

from geometric series#.[1]7o%e+er$ they did not formulate a systematic theory of differentiation

and integration$ nor is there any directe+idence of their results being transmitted outside 6erala.

Prehistory

ca+ations at 7arappa$ /ohen3odaroand other sites of theIndus 9alley Ci+ili)ationha+e

unco+ered e+idence of the use of :practical mathematics:. 'he people of the I9C manufactured

bric&s %hose dimensions %ere in the proportion ;2;1$ considered fa+orable for the stability of a

bric& structure. 'hey used a standardi)ed system of %eights based on the ratios; 1


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(approimately 1.2 inches or . centimetres# %as di+ided into ten e=ual parts. Bric&s

manufactured in ancient /ohen3odaro often had dimensions that %ere integral multiples of this

unit of length.[1][20]

Vedic period

ee also; 9edangaand 9edas

Samhitas and Brahmanas

The religious texts of the Vedic Periodprovide evidence for the use of large numbers.By

the time of the Yajurvedasahit(1!!"#!! B$%&' numbers as high as ere being

included in the texts.)*+or example' the antra(sacrificial formula& at the end of the

annahoa(,food-oblation rite,& performed during the avaedha' and uttered ust

before-' during-' and ust after sunrise' invo/es poers of ten $lassical Period(0!! " 1!!&

'his period is often &no%n as the golden age of Indian /athematics. 'his period sa%

mathematicians such as !ryabhata$9arahamihira$ Brahmagupta$Bhas&ara I$/aha+ira$andBhas&ara IIgi+e broader and clearer shape to many branches of mathematics. 'heir contributions

%ould spread to !sia$ the /iddle ast$ and e+entually to urope. @nli&e 9edic mathematics$

their %or&s included both astronomical and mathematical contributions. In fact$ mathematics ofthat period %as included in the Aastral scienceA (jyotihstra# and consisted of three sub

disciplines; mathematical sciences (ganitaor tantra#$ horoscope astrology (hororjtaka# and

di+ination (samhit#.

[,]

'his tripartite di+ision is seen in 9arhamihiraAs ,th century compilation?Pancasiddhantika[,1](literallypanca$ :fi+e$:siddhnta$ :conclusion of deliberation:$ dated*-* C#?of fi+e earlier %or&s$ urya iddhanta$ Doma&a iddhanta$ 5aulisa iddhanta$

9asishtha iddhantaand 5aitamaha iddhanta$%hich %ere adaptations of still earlier %or&s of

/esopotamian$ >ree&$ gyptian$ Doman and Indian astronomy. !s eplained earlier$ the maintets %ere composed in ans&rit +erse$ and %ere follo%ed by prose commentaries.[,]

from a hundred to a trillion;[2]

ARYA BHATTA AND HIS CONTRIBUTION:-

In the history of indian mathematics,Aryahatta is a !ery res"ecta#e name$Therey

it is di%ct to ascertain ho' many mathematicians of this name had een in

ancient India$Ho'e!er it is (&ite certain that there 'ere at#east t'o Aryahatas$One

of them 'as orn in)*+AD at &s&ma"&ra,the city of o'ers./at#i"&tra0 near
http://en.wikipedia.org/wiki/Indian_mathematics#cite_note-18http://en.wikipedia.org/wiki/Indian_mathematics#cite_note-19http://en.wikipedia.org/wiki/Vedangahttp://en.wikipedia.org/wiki/Vedangahttp://en.wikipedia.org/wiki/Vedashttp://en.wikipedia.org/wiki/Vedic_Periodhttp://en.wikipedia.org/wiki/History_of_large_numbershttp://en.wikipedia.org/wiki/History_of_large_numbershttp://en.wikipedia.org/wiki/Yajurvedahttp://en.wikipedia.org/wiki/Yajurvedahttp://en.wikipedia.org/wiki/Yajurvedahttp://en.wikipedia.org/wiki/Indian_mathematics#cite_note-hayashi2005-p360-361-1http://en.wikipedia.org/wiki/Mantrahttp://en.wikipedia.org/wiki/Mantrahttp://en.wikipedia.org/wiki/Ashvamedhahttp://en.wikipedia.org/wiki/Aryabhatahttp://en.wikipedia.org/wiki/Aryabhatahttp://en.wikipedia.org/wiki/Varahamihirahttp://en.wikipedia.org/wiki/Brahmaguptahttp://en.wikipedia.org/wiki/Bhaskara_Ihttp://en.wikipedia.org/wiki/Bhaskara_Ihttp://en.wikipedia.org/wiki/Bhaskara_Ihttp://en.wikipedia.org/wiki/Mahavira_(mathematician)http://en.wikipedia.org/wiki/Mahavira_(mathematician)http://en.wikipedia.org/wiki/Bhaskara_IIhttp://en.wikipedia.org/wiki/Asiahttp://en.wikipedia.org/wiki/Middle_Easthttp://en.wikipedia.org/wiki/Europehttp://en.wikipedia.org/wiki/Indian_mathematics#cite_note-hayashi2003-p119-45http://en.wikipedia.org/wiki/Indian_mathematics#cite_note-60http://en.wikipedia.org/wiki/Indian_mathematics#cite_note-60http://en.wikipedia.org/wiki/Common_Erahttp://en.wikipedia.org/wiki/Surya_Siddhantahttp://en.wikipedia.org/wiki/Romaka_Siddhantahttp://en.wikipedia.org/wiki/Paulisa_Siddhantahttp://en.wikipedia.org/wiki/Vasishtha_Siddhantahttp://en.wikipedia.org/wiki/Paitamaha_Siddhantahttp://en.wikipedia.org/wiki/Paitamaha_Siddhantahttp://en.wikipedia.org/wiki/Indian_mathematics#cite_note-hayashi2003-p119-45http://en.wikipedia.org/wiki/Indian_mathematics#cite_note-hayashi2005-p360-361-1http://en.wikipedia.org/wiki/Indian_mathematics#cite_note-18http://en.wikipedia.org/wiki/Indian_mathematics#cite_note-19http://en.wikipedia.org/wiki/Vedangahttp://en.wikipedia.org/wiki/Vedashttp://en.wikipedia.org/wiki/Vedic_Periodhttp://en.wikipedia.org/wiki/History_of_large_numbershttp://en.wikipedia.org/wiki/Yajurvedahttp://en.wikipedia.org/wiki/Indian_mathematics#cite_note-hayashi2005-p360-361-1http://en.wikipedia.org/wiki/Mantrahttp://en.wikipedia.org/wiki/Ashvamedhahttp://en.wikipedia.org/wiki/Aryabhatahttp://en.wikipedia.org/wiki/Varahamihirahttp://en.wikipedia.org/wiki/Brahmaguptahttp://en.wikipedia.org/wiki/Bhaskara_Ihttp://en.wikipedia.org/wiki/Mahavira_(mathematician)http://en.wikipedia.org/wiki/Bhaskara_IIhttp://en.wikipedia.org/wiki/Asiahttp://en.wikipedia.org/wiki/Middle_Easthttp://en.wikipedia.org/wiki/Europehttp://en.wikipedia.org/wiki/Indian_mathematics#cite_note-hayashi2003-p119-45http://en.wikipedia.org/wiki/Indian_mathematics#cite_note-60http://en.wikipedia.org/wiki/Common_Erahttp://en.wikipedia.org/wiki/Surya_Siddhantahttp://en.wikipedia.org/wiki/Romaka_Siddhantahttp://en.wikipedia.org/wiki/Paulisa_Siddhantahttp://en.wikipedia.org/wiki/Vasishtha_Siddhantahttp://en.wikipedia.org/wiki/Paitamaha_Siddhantahttp://en.wikipedia.org/wiki/Indian_mathematics#cite_note-hayashi2003-p119-45http://en.wikipedia.org/wiki/Indian_mathematics#cite_note-hayashi2005-p360-361-1


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"resent city of /atna in Bihar and 'rote the oo1 2Aryahatiya,is 1no'n as

:Aryahata 3rst4$The other mathematician earin5 the same name 'ho 'rote the

oo146aha Arya Siddhant4 in 789 AD is 1no'n as Aryahata Second$The "eriod of

Aryahata irst has een the 5o#den "eriod of indian mathematics$

This 'or1 of Aryahata sho's his 5reatness,ori5ina#ity and creati!ity in the 3e#d of

mathematics y rin5in5 into #i5ht some of his fo##o'in5 contri&tions:-;0Aryahata in!ented a notation system consistin5 of a#"haet n&mera#s$Di5its are

denoted y a#"haet n&mera#s in this system$De!na5ri scri"t contains !ar5a

#etters.consonants0 and A!ar5a #etters.!o'e#s0$Di5its from ; to

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Contribution of INDIAN Mathematicians in Field of Mathematics