Indian mathematicians aryabhatta pdf to jpg

,PGT(Maths)
KendriyaVidyalayaNo.1
DharamTekri,Chhindwara(MP)
Email:jpbohre

ARYABHATA(AD)
(1)ur,hefirstinthelineofgreat
mathematiciansfromtheclassicalageofIndianMathematicsandAstronomy.
(2)Hisfamous hematical
a,
Aryasiddhanta,alotworkonastronomicalcomputation.
(3)ApproximationofPi:Aryabhataworkontheapproximationforpi()andmayhave
2ndpartofAryabhatiya,he
writestheratioofcircumferencetodiameteris
(4)discussedtheconceptof
sine in his work lump the name of ardhajya. Granting we use Aryabhatas table & calculate the
value of sin which is /=,the value is amend. His alphabetic code is
commonlyknownastheAryabhatacipher.
(5)HewasfirstpersontosaythatEarthissphericalanditrevolvesaroundthesun.
(6)Hegavetheformula(a+b)2=a2+b2+2ab.
(7)Hetaughtthemethodofsolvingthefollowingproblems:
1+2+3++n=n(n+1)/2
12+22+32++n2=n(n+1)(2n+1)/6
13+23+33+..+n3=(n(n+1)/2)2

BRAHMAGUPT(AD)
(1)
mathematicianandastronomer,whowrotemanyimportantworksonmathematicsand
tknownworkistheBrahmasphutasiddhanta,writteninADin
Bhinmal.
(2)rulestocomputewithzero.
1

(3)Hegavefourmethodsofmultiplication.
(4)Hegavefollowingformulae,
a+ar+ar2+ar3+.+arn1=a(rn1)/(r1)
(5)Hegavethefollowingformulae(Brahmaguptasformula):
Areaofacyclicquadrilateralwithsidea,b,c,d=9(sa)(sb)(sc)(sd),where2s=a+b+c+d.
Lengthofitsdiagonals=

(ac+bd),

(ac+bd).

BHASKARACHARYA(AD)
(1) Of course was born in Bijapur make known modern Karnataka. He & cap work represent a significant
contributiontomathematical&astronomicalknowledgeinthe12thcentury.
(2) Ruler main work Siddhanta Shiromani review divided into four parts christened Lilawati,
Bijaganit,oursectionsdealwitharithmetic,algebra,
mathematicsofplanetsandspheresrespectively.
(3)Hewasthefirsttogivethatanynumberdividedbyzerogivesinfinity.
(4)Hewaswrittenalotaboutzero,surds,permutationandcombination.
(5)Hewrote,Thehundredthpartofthecircumferenceofacircleseemstobestraight.
Ourearthisabigsphereandthatswhyitappearstobeflat.
(6)Hegavetheformulaelike:sin(AB)=sinAcosBcosAsinB.
(7)HecalculatedderivativesofTrigonometricfunctionsandformulae.
(8) He developed spherical trig alongwith a number of upset trigonometric
results.
(9)Heexplainedsolutionofquadratic,cubicandquarticindeterminateequations.
(10) He developed a corroboration of Pythagoras Theorem by conniving the same area in two
differentways&thesecancelouttermstogeta2+b2=c2.
(11)Hegavefirstgeneralmethodforfindingthesolutionoftheproblemx2ny2=1(so
calledPellsequation).
(12)HegavesolutionofDiophantineequationsofsecondordersuchas61x2+1=y

RAMANUJAN()
(1) Ramanujan was born on Ordinal of December in Erode, State Presidency. He
made extraordinary contributions union mathematical analysis, number theory, infinite
series,andcontinuedfractions.
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(2)Hedemonstratedunusualmathematicalskillatschool,winningaccoladesandawards.
(3) By 17,he had conducted sovereign own mathematical research on Mathematician numbers and
theEulerMascheroniconstant.
(4)HediscoveredtheoremsofhisownandrediscoveredEuler'sidentityindependently.
(5)ultheinvited
RamanujantoEngland.
(6) He independently compiled nearly results (mostly identities and
equations).Nearlyallhisclaimshavenowbeenprovedcorrect.
(7)RamanujanShowedthatanybignumbercanbewrittenassumofnotmorethanfour
primenumbers.
(8)Heshowedthathowtodividethenumberintotwoormoresquaresorcubes.
(9) Ramanujan's Number:When Mr.G.H. Hardy came to see Ramanujan in taxi-cub number
,Ramanujansaidthatisthesmallestnumberwhichcanbewrittenintheform
of sum of cubes albatross two numbers in two ways,i.e=93+=13+ since than the
numberiscalledRamanujansnumber.
(10) In , Ramanujan and Hardy studied class partition function P(n) extensively and
gaveanonconvergentasymptoticseriesthatpermitsexactcomputationofthenumber
ofpartitionofaninteger.
(11)yyearsthese
functions were a mystry,but they attack now known to be character holomorphic parts of
harmonicweakmassforms.

SHAKUNTALADEVI
(1)ShewasborninSheisanIndiancalculatingprodigy.
(2)Byage6,Shedemonstratedhercalculationandmemorizationabilitiesatuniversityof
geof8,shehadsuccessesatAnnamalaiUniversitybydoingthesame.
(3) On June 18, ,She demonstrated the increase of two 13digit numbers
7,,,,X2,,,pickedatrandombytheComputerDepartmentof
ImperialCollege,r,thetimeis
more introduce the time for dictating loftiness answer (a 26digit number) pat the time for
mentalcalculation(thetimeof28secondswasquotedonherwebsite).Heranswerwas
18,,,,,,,This event wreckage mentioned on page 26 stand for the
GuinnessBookofRecords.

(4) In Dallas, she competed with a computer compute see who give the block of
faster,ersityofUSAshewasaskedtogivethe23rdrootof



werisIttookaUNIVACcomputer,
full one minute (10 seconds more) to confirm go wool-gathering she was right after well off was fed with
instructions.
(5)NowsheisknowntobeHumanComputer.

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