about aryabhatta

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    ARYABHATTA

    A Magazine on

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    ABOUT

    ryabhata or Aryabhata I (476–550 CE) was the frst o the majormathematician-astronomers rom the cassica age o !n"ian mathematics an"n"ian astronom#$ %is wor&s inc'"e the  Āryabhaṭ   ī ya (4 CE when he was *+ears o") an" the Arya-siddhanta$

    https://en.wikipedia.org/wiki/Common_Erahttps://en.wikipedia.org/wiki/Mathematicianhttps://en.wikipedia.org/wiki/Astronomerhttps://en.wikipedia.org/wiki/Indian_mathematicshttps://en.wikipedia.org/wiki/Indian_astronomyhttps://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%AD%C4%AByahttps://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%AD%C4%AByahttps://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%AD%C4%AByahttps://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%AD%C4%AByahttps://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%AD%C4%AByahttps://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%AD%C4%AByahttps://en.wikipedia.org/wiki/Siddhantahttps://en.wikipedia.org/wiki/Mathematicianhttps://en.wikipedia.org/wiki/Astronomerhttps://en.wikipedia.org/wiki/Indian_mathematicshttps://en.wikipedia.org/wiki/Indian_astronomyhttps://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%AD%C4%AByahttps://en.wikipedia.org/wiki/Siddhantahttps://en.wikipedia.org/wiki/Common_Era

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    ,iograh#Name.hie there is a ten"enc# to misse his name as /Ar#ahatta/ # anaog# withther names ha1ing the /hatta/ s'23 his name is roer# see" Ar#ahata1er# astronomica te3t ses his name th's inc'"ing ,rahmag'tas reerenceso him /in more than a h'n"re" aces # name/$ 'rthermore in most instancesAr#ahatta/ wo'" not ft the metre either$

    Time and place of birthr#ahata mentions in the Aryabhatiya that it was comose" +600 #ears into theai 8'ga when he was *+ #ears o"$ 9his correson"s to 4 CE an" imies thate was orn in 476$

    r#ahata ro1i"es no inormation ao't his ace o irth$ 9he on# inormationomes rom ,hās&ara ! who "escries Ar#ahata as āśmak ī  ya /one eonging tohe a śmaka co'ntr#$/ :'ring the ,'""has time a ranch o the Aśma&a eoeette" in the region etween the ;arma"a an" āṭ   ai'tra mo"ern >atna$ A 1erse

    mentions that Ar#ahata was the hea" o an instit'tion (kulapa) at 's'ma'ran" eca'se the 'ni1ersit# o ;aan"a was in >atai'tra at the time an" ha" an

    stronomica oser1ator# it is sec'ate" that Ar#ahata might ha1e een theea" o the ;aan"a 'ni1ersit# as we$ Ar#ahata is aso re'te" to ha1e set 'n oser1ator# at the ?'n teme in 9aregana ,ihar$

    Mathematics

    he ace-1a'e s#stem frst seen in the +r"-cent'r# ,a&hshai Man'scrit was

    ear# in ace in his wor&$ .hie he "i" not 'se a s#mo or zero the renchmathematician

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    A"" o'r to B00 m'ti# # eight an" then a"" 6*000$ ,# this r'e therc'merence o a circe with a "iameter o *0000 can e aroache"$/

    his imies that the ratio o the circ'merence to the "iameter is4 B00) D 6*000)F*0000 G 6*+*F*0000 G +$B4B6 which is acc'rate to1e signifcant fg'res$

    is sec'ate" that Ar#ahata 'se" the wor" āsanna (aroaching) to mean that

    ot on# is this an aro3imation 't that the 1a'e is incommens'rae (orrationa)$ ! this is correct it is 'ite a sohisticate" insight eca'se therationait# o i was ro1e" in E'roe on# in B76B # Hamert$

    ter Ar#ahati#a was transate" into Araic (c$ *0 CE) this aro3imation wasmentione" in A-hwarizmis oo& on agera$

    n

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    n Aryabhatiya Ar#ahata ro1i"e" eegant res'ts or the s'mmation o series o'ares an" c'es

    n"

    r#ahata correct# insiste" that the earth rotates ao't its a3is "ai# an" thathe aarent mo1ement o the stars is a reati1e motion ca'se" # the rotation ohe earth contrar# to the then-re1aiing 1iew that the s rotate"$ 9his isn"icate" in the frst chater o the Aryabhatiya where he gi1es the n'mer ootations o the earth in a yuga an" ma"e more e3icit in his gola chater

    n the same wa# that someone in a oat going orwar" sees an 'nmo1ing IojectJoing ac&war" so IsomeoneJ on the e'ator sees the 'nmo1ing stars goingniorm# westwar"$ 9he ca'se o rising an" setting Iis thatJ the shere o the

    tars together with the anets Iaarent#KJ t'rns "'e west at the e'atoronstant# 'she" # the cosmic win"$

    r#ahata "escrie" a geocentric mo"e o the soar s#stem in which the ?'n an"oon are each carrie" # eic#ces$ 9he# in t'rn re1o1e aro'n" the Earth$ !n this

    mo"e which is aso o'n" in the Pait āmahasiddhānta (c$ CE 4*5) the motions ohe anets are each go1erne" # two eic#ces a smaer manda (sow) an" arger śī ghra (ast)$ I*6J 9he or"er o the anets in terms o "istance rom earth is

    a&en as the Moon Merc'r# @en's the ?'n Mars L'iter ?at'rn an" thesterisms$/

    he ositions an" erio"s o the anets was cac'ate" reati1e to 'niorm#mo1ing oints$ !n the case o Merc'r# an" @en's the# mo1e aro'n" the Earth athe same mean see" as the ?'n$ !n the case o Mars L'iter an" ?at'rn the#

    mo1e aro'n" the Earth at secifc see"s reresenting each anets motionhro'gh the zo"iac$ Most historians o astronom# consi"er that this two-eic#ce

    mo"e reects eements o re->toemaic

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    ;'merica 1a'es he ma"e a notation s#stem in which "igits are "enote" with thee o ahaet n'meras e$g$ B G &a * G ha etc$r#ahatta assigne" n'merica 1a'es to the ++ consonants o the !n"ian ahaet toeresent B*+R*5+04050607000B00$

    ;otation s#stem %e in1ente" a notation s#stem consisting o ahaet n'merasigits were "enote" # ahaet n'meras$ !n this s#stem "e1anagiri scrit containarga etters (consonants) an" a1arga etters (1owes)$B-*5 are "enote" # B st *5 1argatters$>ace-1a'e Ar#ahatta was amiiar with the ace-1a'e s#stem$

    %e &new n'mera s#mos an" the sign or zero?'are root S c'e root %is cac'ations on s'are root an" c'e root wo'" not ha1e

    een ossie witho't the &nowe"ge o ace 1a'es s#stem an" zero$ %e has gi1enmetho"s o e3tracting s'are root c'e root aong with their e3anation$

    !nterest %e orm'ate" or the frst time in !n"ia the orm'a or interest time an"ther reate" ones in the roems o interest$H is an irrationa n'mer>#thagorean 9heorem 9he >#thagorean theorem is state" as oows in his wor& Vthe'are o the ,h'ja (ase) 's the s'are o the &oti (eren"ic'ar) is the s'are o thearnaW,'ja an" &oti are the si"es o a right-ange" triange$ 9he arna is the h#oten'se)

    Circe 9heorem %e has ost'ate" a theorem reating to circe as oows V!n a circehe ro"'ct o two ?aras is the s'are o the ha chor" o the two arcsW i$e$ aXGc * whereis ha the chor" an" the saras or arrows are the segments o a "iameter which isectn# chor"$orm'a Ar#ahatta gi1es orm'ae or the areas o a triange s'are rectange

    hom's circe etc$N!

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    ?9NO;OM8Earth Ar#ahatta ga1e the circ'merence o the earth as 4 67 #ojanas an" itsameter as B 5BBF*4 #ojanas$ ?inceB #ojana G5mies this gi1es the circ'merence as4+5 mies which is an e3ceent aro3imation to the c'rrent# accete" 1a'e o40* mies$%e eie1es that the orits o the anets are eises$ %e correct# e3ains the ca'se"

    ecises o the ?'n an" the Moon$Hength o #ear %is 1a'e or the ength o the #ear at +65 "a#s 6 ho'rs B* min'tes +0

    econ"s is an o1erestimate since the tr'e 1a'e is ess than +65 "a#s an" 6 ho'rs$

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    r#ahatta was one o those ancient schoars o !n"ia who is har"# s'rasse" # an#ne ese o his time in his treatise on mathematics an" astronom#$ !n areciation o his

    reat contri'tions to mathematics an" astronom# the go1ernment o !n"ia name" therst sateite sent into sace on B-4-B75 as ar#ahatta ater him$

    MA9%EMA9!C?>NOLEC9PREPARED BY: -

    SIDDHARTH PANCHAL

    CLASS: -

      XI-A

    ROLL NO.: -

      35