aaryabhat

aaryabhat

Pune mein aaryabhat ki moorti 476-550
janm 0 December 476
ashmak, Maharashtra, Bhaarat
mrutyoo 0 December 550(550-12-00) (umr 74)
nivaas Flag of India.svg Bhaarat
raashtreeyata Flag of India.svg bhaarateeya
kshetr praacheen ganitjnya, jyotishvid, khagolajnya
sansthaaeain naalanda vishvavidyaalaya
prasiddh kaarya aaryabhateeya, aaryabhatt siddhaant, pai ka anveshan

aaryabhat (476-550) praacheen Bhaarat ke ek mahaan jyotishvid aur ganitjnya the. inhonne aaryabhateeya granth ki rachana ki jismein jyotishshaastr ke anek siddhaanton ka pratipaadan hai. isi granth mein inhonne apna janmasthaan kusumapur aur janmakaal shak sanvat 398 likha hai. Bihar mein vartamaan Patna ka praacheen naam kusumapur tha lekin aaryabhat ka kusumapur dakshin mein tha, yeh ab lagbhag siddh ho chuka hai.

ek anya maanyata ke anusaar unka janm Maharashtra ke ashmak desh mein hua tha. unke vaigyaanik kaaryon ka samaadar rajdhani mein hi ho sakta tha. at: unhonne lambi yaatra karke aadhunik Patna ke sameep kusumapur mein avasthit hokar raajasaannidhya mein apni rachanaaeain poorn ki.

anukram

aaryabhat ka janm-sthaan

yadyapi aaryabhat ke janm ke varsh ka aaryabhateeya mein spasht ullekh hai, unke janm ke vaastavik sthaan ke baare mein vivaad hai. kuchh maanate hain ki ve narmada aur godaavari ke madhya sthit kshetr mein paida hue the, jise ashmaaka ke roop mein jaana jaata tha aur ve ashmaaka ki pehchaan madhya Bhaarat se karte hain jisme Maharashtra aur madhya pradesh shaamil hai, haalaaainki aaranbhik bauddh granth ashmaaka ko dakshin mein, dakshinaapath ya dakkhan ke roop mein varnit karte hain, jabki anya granth varnit karte hain ki ashmaaka ke log alekjeindar se lade honge, is hisaab se ashmaaka ko uttar ki taraf aur aage hona chaahiye.[1]

ek taaja adhyayan ke anusaar aaryabhat , Kerala ke chaamravattam (10uttara51, 75poorva45) ke nivaasi the. adhyayan ke anusaar asmaka ek jain pradesh tha jo ki shravanabelagol ke chaaron taraf faila hua tha aur yahaaain ke patthar ke khambon ke kaaran iska naam asmaka pada. chaamravattam is jain basti ka hissa tha, iska pramaan hai bhaarataapujha nadi jiska naam jainon ke pauraanik raaja bhaarata ke naam par rakha gaya hai. aaryabhatt ne bhi yugon ko paribhaashit karte vakt raaja bhaarata ka jikr kiya hai- dasageetika ke paanchavein chhand mein raaja Bhaarat ke samay tak beet chuke kaal ka varnan aata hai. un dinon mein kusumapura mein ek prasiddh vishvavidyaalaya tha jahaaain jainon ka nirnaayak prabhaav tha aur aaryabhatt ka kaam is prakaar kusumapura pahuainch saka aur use pasand bhi kiya gaya.[2]

haalaaainki ye baat kaafi had tak nishchit hai ki ve kisi na kisi samay kusumapura uchch shiksha ke liye gaye the aur kuchh samay ke liye vahaan rahe bhi the.[3] bhaaskar I (629 E.) ne kusumapura ki pehchaan paataliputr (aadhunik Patna) ke roop mein ki hai. gupt saamraajya ke antim dinon mein ve vahaan raha karte the. yeh vah samay tha jise Bhaarat ke svarnim yug ke roop mein jaana jaata hai, vishnugupt ke poorv buddhagupt aur kuchh chhote raajaaon ke saamraajya ke dauraan uttar poorv mein hoonon ka aakraman shuroo ho chuka tha.

aaryabhatt apni khagoleeya pranaaliyon ke liye sandarbh ke roop mein Sri Lanka ka upayog karte the aur aaryabhateeya mein anek avsaron par Sri Lanka ka ullekh kiya hai.[tathya vaanchhit]

krutiyaaain

aaryabhat dvaara rachit teen granthon ki jaankaari aaj bhi upalabdh hai. dashageetika, aaryabhateeya aur tantr. lekin jaankaaron ke anusaar unhone aur ek granth likha tha- 'aaryabhatt siddhaant'. is samay uske keval 34 shlok hi upalabdh hain. unke is granth ka saatave shatak mein vyaapak upayog hota tha. lekin itna upayogi granth lupt kaise ho gaya is vishay mein koi nishchit jaankaari naheen milti.[4]

unhonne aaryabhateeya naamak mahatvapoorn jyotish granth likha, jismein vargamool, ghanamool, samaantar shreni tatha vibhinn prakaar ke sameekaranon ka varnan hai. unhonne apne aaryabhatteeya naamak granth mein kul 3 prushthon ke sama sakane vaale 33 shlokon mein ganitvishyak siddhaant tatha 5 prushthon mein 75 shlokon mein khagol-vigyaan vishyak siddhaant tatha iske liye yantron ka bhi niroopan kiya.[5] aaryabhatt ne apne is chhote se granth mein apne se poorvavarti tatha pashchaadvarti desh ke tatha videsh ke siddhaanton ke liye bhi kraantikaari avadhaaranaaeain upasthit ki.

unki pramukh kruti, aaryabhateeya, ganit aur khagol vigyaan ka ek sangrah hai, jise bhaarateeya ganiteeya saahitya mein bade paimaane par uddhat kiya gaya hai aur jo aadhunik samay mein bhi astitv mein hai. aaryabhateeya ke ganiteeya bhaag mein ankaganit, beejaganit, saral trikonamiti aur goleeya trikonamiti shaamil hain. isame satat bhinn (kainteenyood frekshans), dvighaat sameekaran (kvadretik ikveshans), ghaat shrrunkhala ke yog (sams of power series) aur [[jyaaon ki ek taalika (Table of Sines) shaamil hain.

aarya-siddhaant, khagoleeya gananaaon par ek kaarya hai jo ab lupt ho chuka hai, iski jaankaari hamein aaryabhatt ke samakaaleen varaahamihir ke lekhanon se praapt hoti hai, saath hi saath baad ke ganitjnyaon aur tippaneekaaron ke dvaara bhi milti hai jinmein shaamil hain brahmagupt aur bhaaskar I. aisa prateet hota hai ki ye kaarya puraane soorya siddhaant par aadhaarit hai aur aaryabhateeya ke sooryodaya ki apeksha ismein madhyaraatri-diwas-ganana ka upayog kiya gaya hai. isame anek khagoleeya upakaranon ka varnan shaamil hai, jaise ki nomon(shanku-yantr), ek parachhaai yantr (chhaaya-yantr), sanbhavat: kon maapi upakaran, ardhavruttaakaar aur vruttaakaar (dhanur-yantr / chakr-yantr), ek belanaakaar chhadi yasti-yantr, ek chhatr-aakar ka upakaran jise chhatr- yantr kaha gaya hai aur kam se kam do prakaar ki jal ghadiyaaain- dhanushaakaar aur belanaakaar.[1]

ek teesara granth jo arabi anuvaad ke roop mein astitv mein hai, al ntf ya al nanf hai, aaryabhatt ke ek anuvaad ke roop mein daava prastut karta hai, parantu iska sanskrut naam agyaat hai. sanbhavat: 9 vi sadi ke abhilekhan mein, yeh faarasi vidvaan aur bhaarateeya itihaasakaar Abu rehaan al-birooni dvaara ullekhit kiya gaya hai.[1]

aaryabhateeya

mukhya lekh aaryabhateeya

aaryabhatt ke kaarya ke pratyaksh vivran sirf aaryabhateeya se hi gyaat hain. aaryabhateeya naam baad ke tippaneekaaron dvaara diya gaya hai, aaryabhatt ne swayam ise naam nahi diya hoga; yeh ullekh unke shishya bhaaskar pratham ne ashmakatantr ya ashmaaka ke lekhon mein kiya hai. ise kabhi kabhi aarya-shat-asht (arthaat aaryaabhaatt ke 108)- jo ki unke paath mein chhandon ki sankhya hai- ke naam se bhi jaana jaata hai. yeh sootr saahitya ke samaan bahut hi sankshipt shaili mein likha gaya hai, jahaaain pratyek pankti ek jatil pranaali ko yaad karne ke liye sahaayata karti hai. is prakaar, arth ki vyaakhya tippaneekaaron ki vajah se hai. samooche granth mein 108 chhand hai, saath hi parichyaatmak 13 atirikt hain, is poore ko chaar padon athva adhyaayon mein vibhaajit kiya gaya hai :

  • (1) geetikpaad : (13 chhand) samay ki badi ikaaiyaaain - kalp, manvantar, yug, jo praarambhik granthon se alag ek brahmaand vigyaan prastut karte hain jaise ki lagadh ka vedaang jyotish, (pehli sadeeisavi poorvainame jeevaaon (sign) ki taalika jya bhi shaamil hai jo ek ekal chhand mein prastut hai. ek mahaayug ke dauraan, grahon ke paribhraman ke liye 4. 32 million varshon ki sankhya di gayi hai.
  • (2) ganitpaad (33 chhand) mein kshetramiti (kshetr vyavahaar), ganit aur jyaamitik pragati, shanku/ chhaayaaeain (shanku -chhaaya), saral, dvighaat, yugapat aur anishchit sameekaran (kuttak) ka samaavesh hai.
  • (3) kaalakriyaapaad (25 chhand) : samay ki vibhinn ikaaiyaaain aur kisi diye gaye din ke liye grahon ki sthiti ka nirdhaaran karne ki vidhi. adhik maas ki ganana ke vishay mein (adhikmaas), kshaya-tithiyaan. saptaah ke dinon ke naamon ke saath, ek saat din ka saptaah prastut karte hain.
  • (4) golapaad (50 chhand): aakaasheeya kshetr ke jyaamitik /trikonamiteeya pahaloo, kraantivrutt, aakaasheeya bhoomadhya rekha, aasanthi, pruthvi ke aakaar, din aur raat ke kaaran, kshitij par raashichkreeya sanketon ka badhna aadi ki visheshataaen.

iske atirikt, kuchh sanskaranon ant mein krutiyon ki prashansa aadi karne ke liye kuchh pushpikaaen bhi jodte hain.

aaryabhateeya ne ganit aur khagol vigyaan mein padya roop mein, kuchh naveenataaeain prastut ki, jo anek sadiyon tak prabhaavashaali rahi. granth ki sankshiptata ki charam seema ka varnan unke shishya bhaaskar pratham (bhaashya , 600 aur) dvaara apni sameekshaaon mein kiya gaya hai aur apne aaryabhateeya bhaashya (1465) mein neelakanth somayaaji dvaara.

aaryabhat ka yogadaan

bhaaratake itihaas mein jise 'guptakaal' ya 'suvarnayug' ke naam se jaana jaata hai, us samay Bhaarat ne saahitya, kala aur vigyaan kshetron mein abhootapoorv pragati ki. us samay magadh sthit naalanda vishvavidyaalaya jnyaaanadaan ka pramukh aur prasiddh kendra tha. desh videsh se vidyaarthi jnyaaanaarjan ke liye yahaaain aate the. vahaaain khagolashaastr ke adhyayan ke liye ek vishesh vibhaag tha. ek praacheen shlok ke anusaar aaryabhat naalanda vishvavidyaalaya ke kulapati bhi the.

aaryabhat ka Bhaarat aur vishv ke jyotish siddhaant par bahut prabhaav raha hai. Bhaarat mein sabse adhik prabhaav Kerala pradesh ki jyotish parampara par raha. aaryabhat bhaarateeya ganitjnyaon mein sabse mahatvapoorn sthaan rakhate hain. inhonne 120 aaryaachhandon mein jyotish shaastr ke siddhaant aur usase sambandhit ganit ko sootraroop mein apne aaryabhateeya granth mein likha hai.

unhonne ek or ganit mein poorvavarti aarkimideej se bhi adhik sahi tatha sunishchit pai ke maan ko niroopit kiya[k] to doosari or khagolavijnyaaan mein sabse pehli baar udaaharan ke saath yeh ghoshit kiya gaya ki swayam pruthvi apni dhuri par ghoomti hai.[kh]

aaryabhat ne jyotishshaastr ke aajkal ke unnat saadhanon ke bina jo khoj ki thi, unki mahatta hai. koparniks (1473 se 1543 i.) ne jo khoj ki thi usaki khoj aaryabhat hajaar varsh pehle kar chuke the. "golapaad" mein aaryabhat ne likha hai "naav mein baitha hua manushya jab pravaah ke saath aage badhta hai, tab vah samajhta hai ki achar vruksh, paashaan, parvat aadi padaarth ulti gati se ja rahe hain. usi prakaar gatimaan pruthvi par se sthir nakshatr bhi ulati gati se jaate hue dikhaai dete hain." is prakaar aaryabhat ne sarvapratham yeh siddh kiya ki pruthvi apne aksh par ghoomti hai. inhonne satayug, treta, dvaapar aur kaliyug ko samaan maana hai. inke anusaar ek kalp mein 14 manvantar aur ek manvantar mein 72 mahaayug (chaturyug) tatha ek chaturyug mein satayug, dvaapar, treta aur kaliyug ko samaan maana hai.

aaryabhat ke anusaar kisi vrutt ki paridhi aur vyaas ka sambandh 62,832 : 20,000 aata hai jo chaar dashamlav sthaan tak shuddh hai.

aaryabhat ne badi-badi sankhyaaon ko aksharon ke samooh se niroopit karne keetyant vaigyaanik vidhi ka prayog kiya hai.

ganit

sthaaneeya maan pranaali aur shoonya

sthaan-moolya ank pranaali, jise sarvapratham teesari sadi ki bakhshaali paandulipi mein dekha gaya, unke kaaryon mein spasht roop se vidyamaan thi.[6] unhonne nishchit roop se prateek ka upayog naheen kiya, parantu fraanseesi ganitjnya George ifrah ki daleel hai ki rikt gunaank ke saath, das ki ghaat ke liye ek sthaan dhaarak ke roop mein shoonya ka gyaan aaryabhatt ke sthaan-moolya ank pranaali mein nihit tha.[7]

haalaanki, aaryabhatt ne braahmi ankon ka prayog naheen kiya tha; vaidik kaal se chali aa rahi sanskrut parampara ko jaari rakhate hue unhonne sankhya ko niroopit karne ke liye varnamaala ke aksharon ka upayog kiya, maatraaon (jaise jyaaon ki taalika) ko smarak ke roop mein vyakt karna. [8]

aparimeya (irreshanal) ke roop mein pai

aaryabhatt ne pai () ke sanniktan par kaarya kiya aur shaayad unhein is baat ka gyaan ho gaya tha ki pai irreshanal hai. aaryabhateeyam (ganitpaad) ke doosare bhaag vah likhte hain:

chaturaadhikan shatamashtagunan dvaashashtistatha sahastraanaam.
ayutadvayasya vishkambhasya aasannau vruttaparinaah:.
100 mein chaar jodein, aath se guna karein aur fir 62000 jodein. is niyam se 20000 paridhi ke ek vrutt ka vyaas gyaat kiya ja sakta hai.
(100 + 4) * 8 + 62000/20000 = 3.1416

iske anusaar vyaas aur paridhi ka anupaat ((4 + 100) × 8 + 62000) / 20000 = 3.1416 hai, jo paaainch mahatvapoorn aankadon tak bilkul sateek hai.

aaryabhatt ne aasann (nikat pahunchana), pichhle shabd ke theek pehle aane wala, shabd ki vyaakhya ki vyaakhya karte hue kaha hai ki yeh na keval ek sanniktan hai, varan yeh ki moolya atulaneeya (ya irreshanal) hai. yadi yeh sahi hai, to yeh ek atyant parishkrut drushtikon hai, kyonki Europe mein paai ki tarkaheenata ka siddhaant laimbart dvaara keval 1761 mein hi siddh ho paaya tha.[9]

aaryabhateeya ke arabi mein anuvaad ke pashchaat (poorv.820 E.) beejaganit par al khvaarijmi ki pustak mein is sanniktan ka ullekh kiya gaya tha.[1]

kshetramiti aur trikonamiti

ganitpaad 6 mein, aaryabhatt ne trikon ke kshetrafal ko is prakaar bataaya hai-

tribhujasya falaashaarirm samadalaakoti bhujardhasamavarg:

iska anuvaad hai: ek trikon ke liye, ardh-paksh ke saath lamb ka parinaam kshetrafal hai.[10]

aaryabhatt ne apne kaam mein dvijya (sign) ke vishay mein charcha ki hai aur usako naam diya hai ardh-jya iska shaabdik arth hai "ardh-tantri" . aasaani ki vajah se logon ne ise jya kehna shuroo kar diya. jab arabi lekhakon dvaara unke kaam ka sanskrut se arabi mein anuvaad kiya gaya, to unhonne isko jiba kaha (dhvanyaatmak samaanata ke kaaranavash) . chooainki, arabi lekhan mein, svaron ka istemaal bahut kam hota hai, isliye iska aur sankshipt naam pad gaya jb . jab baad ke lekhakon ko ye samajh mein aaya ki jb jiba ka hi sankshipt roop hai, to unhonne vaapis jiba ka istemaal karna shuroo kar diya. jiba ka arth hai "khoh" ya "khaai" (arabi bhaasha mein jiba ka ek takaneeki shabd ke aalaava koi arth naheen hai). pashchaat mein baarahaveen sadi mein, jab kreemona ke gheraardo ne in lekhanon ka arabi se laitin bhaasha mein anuvaad kiya, tab unhonne arabi jiba ki jagah uske letin samakaksh saainas ko daal diya, jiska shaabdik arth "khoh" ya khaai" hi hai. aur uske baad angreji mein, saainas hi sign ban gaya.[11]

anishchit sameekaran

praacheen kal se bhaarateeya ganitjnyaon ki vishesh roochi ki ek samasya rahi hai un sameekaranon ke poornaank hal gyaat karna jo ax + b = cy svarup mein hoti hai, ek vishay jise vartamaan samay mein daayofaintaain sameekaran ke roop mein jaana jaata hai. yahaaain aaryabhateeya par bhaaskar ki vyaakhya se ek udaaharan dete hain:

vah sankhya gyaat karo jise 8 se vibhaajit karne par sheshafal ke roop mein 5 bachata hai, 9 se vibhaajit karne par sheshafal ke roop mein 4 bachata hai, 7 se vibhaajit karne par sheshafal ke roop mein 1 bachata hai.

arthaat, bataaen N = 8x+ 5 = 9y +4 = 7z +1. isse N ke liye sabse chhota maan 85 niklata hai. saamaanya taur par, daayofaintaain sameekaran kathinta ke liye badnaam the. is tarah ke sameekaranon ki vyaapak roop se charcha praacheen vaidik granth sulb sootr mein hai, jiske adhik praacheen bhaag 800 E.pu. tak puraane ho sakte hain. aisi samasyaaon ke hal ke liye aaryabhatt ki vidhi ko kuttak vidhi kaha gaya hai. kuṭaaṭaaaka kootatak ka arth hai peesana, arthaat chhote chhote tukadon mein todna aur is vidhi mein chhoti sankhyaaon ke roop mein mool khandon ko likhne ke liye ek punaraavarti kalanavidhi ka samaavesh tha. aaj yeh kalanavidhi, 621 isavi pashchaat mein bhaaskar ki vyaakhya ke anusaar, pehle kram ke daayofaintaain sameekaranon ko hal karne ke liye maanak paddhati hai, aur ise aksar aaryabhatt elgoridm ke roop mein jaana jaata hai.[12] daayofaintaain sameekaranon ka istemaal kriptolauji mein hota hai aur aaraesae sammalen, 2006 ne apna dhyaan kuttak vidhi aur sulvasootr ke poorv ke kaaryon par kendrit kiya.

beejaganit

aaryabhateeya mein aaryabhatt ne vargon aur ghanon ki shrrunkhala ke suruchipoorn parinaam pradaan kiye hain.[13]

aur

khagol vigyaan

aaryabhatt ki khagol vigyaan pranaali audaayak pranaali kahalaati thi, (Sri Lanka, bhoomadhya rekha par udaya, bhor hone se dinon ki shuruaat hoti thi.) khagol vigyaan par unke baad ke lekh, jo satahi taur par ek dviteeya model (ardh-raatrika, madhyaraatri), prastaavit karte hain, kho gaye hain, parantu inhe aanshik roop se brahmaguptake khaanadaakhaadyaaka mein hui charchaaon se pun: nirmit kiya ja sakta hai. kuchh granthon mein ve pruthvi ke ghoornan ko aakaash ki aabhaasi gati ka kaaran bataate hain.

saur pranaali ki gatiyaaain

prateet hota hai ki aaryabhatt yeh maanate the ki pruthvi apni dhuri ki parikrama karti hai. yeh Sri Lanka ko sandarbhit ek kathan se gyaat hota hai, jo taaron ki gati ka pruthvi ke ghoornan se utpann aapekshik gati ke roop mein varnan karta hai.

jaise ek naav mein baitha aadmi aage badhte hue sthir vastuon ko peechhe ki disha mein jaate dekhta hai, bilkul usi tarah Sri Lanka mein (arthaat bhoomadhya rekha par) logon dvaara sthir taaron ko theek pashchim mein jaate hue dekha jaata hai. [achalaani bhaani samaanpaashaachimaagaani - golaapada .9]

parantu agala chhand taaron aur grahon ki gati ko vaastavik gati ke roop mein varnit karta hai: "unke udaya aur ast hone ka kaaran is tathya ki vajah se hai ki provektar hava dvaara sanchaalit gruh aur esterisms chakr Sri Lanka mein nirantar pashchim ki taraf chalaayamaan rahate hain.

lanka (Sri Lanka) yahaaain bhoomadhya rekha par ek sandarbh bindu hai, jise khagoleeya ganana ke liye madhyaahn rekha ke sandarbh mein samaan maan ke roop mein le liya gaya tha.

aaryabhatt ne saur mandal ke ek bhookeindreeya model ka varnan kiya hai, jisme soorya aur chandrama gruhachakr dvaara gati karte hain, jo ki parikrama karta hai pruthvi ki. is model mein, jo paaya jaata hai pitaamahaasiddhaant (E. 425), pratyek grahon ki gati do grihchakron dvaara niyantrit hai, ek chhota manda (dheema) gruhachakr aur ek bada sheegra (tej) gruhachakr. [14] pruthvi se doori ke anusaar grahon ka kram is prakaar hai : chandrama, budh, shukr, sooraj, mangal, bruhaspati, shani aur nakshatr[1]

grahon ki sthiti aur avadhi ki ganana samaan roop se gati karte hue binduon se saapeksh ke roop mein ki gayi thi, jo budh aur shukr ke maamale mein, jo pruthvi ke chaaron or ausat soorya ke samaan gati se ghoomate hain aur mangal, bruhaspati aur shani ke maamale mein, jo raashichkr mein pruthvi ke chaaron or apni vishisht gati se gati karte hain. khagol vigyaan ke adhikaansh itihaasakaaron ke anusaar yeh dvi gruhachakr wala model pre-tolemik greek khagol vijnyaaanake tatvon ko pradarshit karta hai.[15] aaryabhatt ke model ke ek anya tatv sighroka, soorya ke sambandh mein buniyaadi grahon ki avadhi, ko kuchh itihaasakaaron dvaara ek antarnihit soorya kendrit model ke chinh ke roop mein dekha jaata hai.[16]

grahan

unhonne kaha ki chandrama aur grah soorya ke paraavartit prakaash se chamakate hain. maujooda brahmaandavijnyaaan se alag, jisme grahanon ka kaarak chhadm grah nispand bindu raahoo aur ketu the, unhonne grahanon ko pruthvi dvaara daali jaane waali aur is par girne waali chhaaya se sambaddh bataaya.is prakaar chandragahan tab hota hai jab chaaaind pruthvi ki chhaaya mein pravesh karta hai (chhand gola. 37) aur pruthvi ki is chhaaya ke aakaar aur vistaar ki vistaar se charcha ki (chhand gola. 38-48) aur fir grahan ke dauraan grahan vaale bhaag ka aakaar aur iski ganana.baad ke bhaarateeya khagolavidon ne in gananaaon mein sudhaar kiya, lekin aaryabhatt ki vidhiyon ne pramukh saar pradaan kiya tha. yeh gananaatmak misaal itni sateek thi ki 18 veen sadi ke vaigyaanik guilaum le jeintil ne, paandicheri ki apni yaatra ke dauraan, paaya ki bhaarateeyon ki ganana ke anusaar 1765-08-30 ke chandragrahan ki avadhi 41 second kam thi, jabki uske chart (dvaara, tobias mayor, 1752) 68 second adhik darshaate the.[1]

aaryabhatt ki ganana ke anusaar pruthvi ki paridhi 39,968.0582 kilometer hai, jo iske vaastavik maan 40,075.0167 kilometer se keval 0.2% kam hai. yeh sanniktan yoonaani ganitjnya, eraatosatheinnas ki sanganana ke oopar ek ullekhaneeya sudhaar tha,200 E.) jinka ganana ka aadhunik ikaaiyon mein to pata naheen hai, parantu unke anumaan mein lagbhag 5-10% ki ek truti avashya thi.[17]

nakshatron ke aavartakaal

samay ki aadhunik angreji ikaaiyon mein joda jaaye to, aaryabhatt ki ganana ke anusaar pruthvi ka aavartakaal (sthir taaron ke sandarbh mein pruthvi ki avadhi)) 23 ghante 56 minute aur 4.1 second thi; aadhunik samay 23:56:4.091 hai. isi prakaar, unke hisaab se pruthvi ke varsh ki avadhi 365 din 6 ghante 12 minute 30 second, aadhunik samay ki ganana ke anusaar ismein 3 minute 20 second ki truti hai. nakshatr samay ki dhaaran us samay ki adhiktar anya khagoleeya pranaaliyon mein gyaat thi, parantu sanbhavat: yeh sanganana us samay ke hisaab se sarvaadhik shuddh thi.

soorya keindreeyata

aaryabhatt ka daava tha ki pruthvi apni hi dhuri par ghoomti hai aur unke grah sambandhi gruhachakr modelon ke kuchh tatv usi gati se ghoomate hain jis gati se soorya ke chaaron or grah ghoomate hain. is prakaar aisa sujhaav diya jaata hai ki aaryabhatt ki sangananaaeain antarnihit soorya kendrit model par aadhaarit theen, jisme gruh soorya ka chakkar lagaate hain.[18][19] ek sameeksha mein is soorya kendrit vyaakhya ka vistrut khandan hai. yeh sameeksha bi.L. vaan dar vaarden ki ek kitaab ka varnan is prakaar karti hai "yeh kitaab bhaarateeya gruh siddhaant ke vishay mein agyaat hai aur yeh aaryabhatt ke pratyek shabd ka seedhe taur par virodh karta hai,".[20] haalaaainki kuchh log yeh sveekaar karte hain ki aaryabhatt ki pranaali poorv ke ek soorya kendrit model se upaji thi jiska gyaan unako naheen tha.[21] yeh bhi daava kiya gaya hai ki ve grahon ke maarg ko andaakaar maanate the, haalaaainki iske liye koi bhi praathamik saakshya prastut naheen kiya gaya hai.[22] haalaaainki saamos ke eristaarchus (teesari shataabdi E.poo.) aur kabhi kabhaar pontas ke heraaklids(chauthi shataabdi E.poo.) ko soorya kendrit siddhaant ki jaankaari hone ka shreya diya jaata hai, praacheen Bhaarat mein gyaat greek khagolashaastr(paulisa siddhaant - sanbhavat: alekjndriya ke kisi paul dvaara) soorya kendrit siddhaant ke vishay mein koi charcha naheen karta hai.

viraasat

bhaarateeya khagoleeya parampara mein aaryabhatt ke kaarya ka bada prabhaav tha aur anuvaad ke maadhyam se isne kai padosi sanskrutiyon ko prabhaavit kiya. islaami svarn yug (E. 820), ke dauraan iska arabi anuvaad vishesh prabhaavashaali tha. unke kuchh parinaamon ko al-khvaarijmi dvaara uddhrut kiya gaya hai aur 10 veen sadi ke arabi vidvaan al-birooni dvaara unhein sandarbhit kiya gaya gaya hai, jinhonne apne varnan mein likha hai ki aaryabhatt ke anuyaayi maanate the ki pruthvi apni dhuri par ghoomti hai.

sign (jya), kosaain (kojya) ke saath hi, varasaain (ukramaajya) ki unki paribhaasha, aur vilom sign (utkram jya), ne trikonamiti ki utpatti ko prabhaavit kiya. ve pehle vyakti bhi the jinhonne sign aur varasaain (1 - kosaeks) taalikaaon ko, 0 degree se 90 degree tak 3.75 ° antaraalon mein, 4 dashamlav sthaanon ki sookshmata tak nirmit kiya.

vaastav mein "sign " aur "kosaain " ke aadhunik naam aaryabhatt dvaara prachalit jya aur kojya shabdon ke glat (apabhransh) uchchaaran hain. unhein arabi mein jiba aur kojiba ke roop mein uchchaarit kiya gaya tha. fir ek arabi jyaamiti paath ke laitin mein anuvaad ke dauraan kremona ke jeraard dvaara inki glat vyaakhya ki gayi; unhonne jiba ke liye arabi shabd 'jeb' liya jiska arth hai "poshaak mein ek tah", L saainas (si.1150).[23]

aaryabhatt ki khagoleeya ganana ki vidhiyaan bhi bahut prabhaavashaali thi. trikonamitik taalikaaon ke saath, ve islaami duniya mein vyaapak roop se istemaal ki jaati thi. aur anek arabi khagoleeya taalikaaon (jij) ki ganana ke liye istemaal ki jaati thi. vishesh roop se, arabi Spain vaigyaanik al-jharkaali (11veen sadi) ke kaaryon mein pai jaane waali khagoleeya taalikaaon ka laitin mein toledo ki taalikaaon (12veen sadi) ke roop mein anuvaad kiya gaya aur ye Europe mein sadiyon tak sarvaadhik sookshm panchaang ke roop mein istemaal mein rahi.

aaryabhatt aur unke anuyaayiyon dvaara ki gayi tithi ganana panchaang athva hindu tithiptr nirdhaaran ke vyaavahaarik uddeshyon ke liye Bhaarat mein nirantar istemaal mein rahi hain, inhe islaami duniya ko bhi preshit kiya gaya, jahaaain inse jalaali tithiptr ka aadhaar taiyaar kiya gaya jise 1073 mein umar khayyaam sahit kuchh khagolavidon ne prastut kiya,[24] jiske sanskaran (1925 mein sanshodhit) aaj Iran aur Afghanistan mein raashtreeya calendar ke roop mein prayog mein hain. jalaali tithiptr apni tithiyon ka aankalan vaastavik saur paaragaman ke aadhaar par karta hai, jaisa aaryabhatt (aur praarambhik siddhaant calendar mein tha).is prakaar ke tithi patra mein tithiyon ki ganana ke liye ek panchaang ki aavashyakta hoti hai. yadyapi tithiyon ki ganana karna kathin tha, par jalaali tithiptr mein gregori tithiptr se kam mausami trutiyaan thi.

Bhaarat ke pratham upagrah aaryabhatt, ko unka naam diya gaya.chandra khadd aaryabhatt ka naam unke sammaan svarup rakha gaya hai. khagol vigyaan, khagol bhautiki aur vaayumandaleeya vigyaan mein anusandhaan ke liye Bhaarat mein naineetaal ke nikat ek sansthaan ka naam aaryabhatt prekshan vijnyaaanan anusandhaan sansthaan (eaaraaaies) rakha gaya hai.

antarskool aaryabhatt ganit pratiyogita unke naam par hai.[25] baisils aaryabhatt, isaro ke vaigyaaniko dvaara 2009 mein khoji gayi ek baikteeriya ki prajaati ka naam unke naam par rakha gaya hai.[26]

tippniyaaain

k. ^ chaturadhikan shatamashtagunan dvaashashtistatha sahasraanaam.
ayutadvayavishkambhasyaasanno vrutt-parinaah:.. (aaryabhateeya, ganitpaad, shlok 10)

kh. ^ anulomagatirnausth: pashyatyachalan vilomagan yadvat.
achalaani bhaani tadvat samapashchimgaani lankaayaam.. (aaryabhateeya, golapaad, shlok 9)

(arth-naav mein baitha hua manushya jab pravaah ke saath aage badhta hai, tab vah samajhta hai ki achar vruksh, paashaan, parvat aadi padaarth ulti gati se ja rahe hain. usi prakaar gatimaan pruthvi par se sthir nakshatr bhi ulati gati se jaate hue dikhaai dete hain.)

sandarbh

  1. a aa i E u oo Ansari, S. M. R. (March 1977). "Aryabhata I, His Life and His Contributions". Bulletin of the Astronomical Society of India 5 (1): 10–18. http://hdl.handle.net/2248/502. abhigman tithi: 2007-07-21.
  2. [5] ^ aaryabhatt ki kathit galati- unke paryevekshan ke sthaan par prakaash, varttamaan vigyaan, granth .93, 12, 25 December 2007, peepi 1870 -73.
  3. Cooke (1997). "The Mathematics of the Hindus". pp. 204. "Aryabhata himself (one of at least two mathematicians bearing that name) lived in the late fifth and the early sixth centuries at Kusumapura (Pataliutra, a village near the city of Patna) and wrote a book called Aryabhatiya."
  4. "aaryabhatt" (echateeemael). hindi nauvels. http://www.hindinovels.net/2008/03/ch-59b-hindi.html. abhigman tithi: 2009.
  5. "ganit-shaastr ke vikaas ki bhaarateeya parampara" (peeechapi). bhaarateeya saahitya sangrah. http://pustak.org/bs/home.php?bookid=4545. abhigman tithi: 2009.
  6. pi.Z. ingarmaan, 'paanini-box form', eseeem ke sanchaar 10(3)(1967), pi.137
  7. A universal history of numbers: From prehistory to the invention of the computer (1998). G Ifrah. John Wiley & Sons.
  8. Dutta, Bibhutibhushan & Avadhesh Narayan Singh (1962), History of Hindu Mathematics, Asia Publishing House, Bombay, ISBN 81-86050-86-8 (reprint)
  9. Indian Mathematics and Astronomy: Some Landmarks, (1994/1998). S. Balachandra Rao. Jnana Deep Publications,. aai॰aऍsa॰abee॰aऍna॰ 81-7371-205-0.
  10. Roger Cooke (1997). "The Mathematics of the Hindus". History of Mathematics: A Brief Course. Wiley-Interscience. aai॰aऍsa॰abee॰aऍna॰ 0471180823. "Aryabhata gave the correct rule for the area of a triangle and an incorrect rule for the volume of a pyramid. (He claimed that the volume was half the height times the area of the base)."
  11. Howard Eves (1990). An Introduction to the History of Mathematics (6th Edition, p.237). Saunders College Publishing House, New York.
  12. amartya ke datta, anishchit bahupadeeya sameekaran: kootatak, pratidhvani, October 2002.poorv ke sinhaavalokan bhi dekhein: "praacheen Bhaarat mein ganit,"
  13. Boyer, Carl B. (1991). "The Mathematics of the Hindus". A History of Mathematics (Second san॰). John Wiley & Sons, Inc.. pa॰ 207. aai॰aऍsa॰abee॰aऍna॰ 0471543977. "He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes."
  14. Pingree, David (1996), "Astronomy in India", written at London, in Walker, Christopher, Astronomy before the Telescope, British Museum Press, 123-142, ISBN 0-7141-1746-3 peepi. 127-9.
  15. oto nyoogebaar, "praacheen aur madhyakaaleen khagol vigyaan mein gruh sancharan siddhaant", script meinthameinteeka, 22(1956): 165-192; oto nyoogebaar mein pun: prakaashit, khagol vigyaan aur itihaas: chayanit nibandh, New York: sprinjar-verlag, 1983, peepi. 129-156.aaiesabeeen 0-387-90844-7
  16. hyoog tharaston, praarambhik khagol vigyaan, New York: sprinjar-verlag, 1996, peepi.178-189.aaiesabeeen 0-387-94822-8
  17. "di round arth", enaeesae, 12 December 2004, 24 January 2008 ko vaapas.
  18. bhaarateeya soorya kendreekaran ki avadhaaran ki vakaalat bi.L. vaan dar vaardan dvaara ki gayi hai, Das heliozentrische System in der griechischen, persischen und indischen Astronomie . jureech mein necharafaurachenaden geselkaaft.jureech : kameeshanasverlag leeman eji, 1970.
  19. bi.L. vaan dar vaardan, "soorya kendrit pranaali greek, faarasi aur hindu khagol vigyaan mein", David A King aur George saleeba, idi., fraam deefrent to ikvant: E.S. kainedi ke sammaan mein praacheen aur madhyakaaleen nikat poorv mein vigyaan ke itihaas ke paathon ka ek granth, New York ekedami of science ke varshkramik itihaas, 500(1987), peepi.529-534.
  20. [40] ^ noel sverdlov, "sameeksha: bhaarateeya khagol vigyaan ka lupt smrutichinh" isis, 64 (1973): 239-243.
  21. denis dayuk, " Bhaarat mein sam pad : praacheen bhaarateeya grah sambandhi modelon ka ganiteeya aadhaar."sateek vigyaan ke itihaas ka puraalekh 59 (2005): 563-576, N. 4 http://people.scs.fsu.edu/~dduke/india8.pdf.
  22. [43] ^ J J O'kaunar aur E ऍf robartasan, aaryabhatt the eldar, maik tutor history of maithamaitiks archive:'
    "He believes that the Moon and planets shine by reflected sunlight, incredibly he believes that the orbits of the planets are ellipses."
  23. Douglas Harper (2001). "Online Etymology Dictionary". http://www.etymonline.com/. abhigman tithi: 2007-07-14.
  24. "Omar Khayyam". The Columbia Encyclopedia, Sixth Edition.. (2001-05). abhigman tithi: 2007-06-10
  25. "Maths can be fun". the hindu. 2006-02-03. http://www.hindu.com/yw/2006/02/03/stories/2006020304520600.htm. abhigman tithi: 2007-07-06.
  26. straitosfiyr mein nae sookshmajeevon ki khoj. 16 March 2009.isaro.

anya sandarbh

  • Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience. aai॰aऍsa॰abee॰aऍna॰ 0471180823.
  • vaaltar yoojeen Clark, the Āaaryabhaṭaaīaayaof Āaaryabhaṭaaa, ganit aur khagol vigyaan par ek praacheen bhaarateeya kaarya, Chicago vishvavidyaalaya press (1930); pun: prakaashit: kessinger prakaashan (2006), aaiesabeeen 978-1425485993.
  • kaak, subhaash si.(2000)'bhaarateeya khagol vigyaan ka 'janm aur praarambhik vikaas' mein Selin, Helaine (2000), Astronomy Across Cultures: The History of Non-Western Astronomy, Kluwer, Boston, ISBN 0-7923-6363-9
  • shukla, krupa shankar. aaryabhatt: bhaarateeya ganitjnya aur khagolavid. nai Delhi: bhaarateeya raashtreeya vigyaan academy, 1976
  • Thurston, H. (1994), Early Astronomy, Springer-Verlag, New York, ISBN 0-387-94107-X

yeh bhi dekhein

baahari kadiyaaain