aryabhata kii saain table

aryabhata kii saain table khagoliya granth aryabhattiya mein dee gaee chaubis sankhyaon kaa ack samooh haye, jise paanchvin shatabdi key bhaaratiya ganitshastri aur khagolshastri aryabhata (476-550 CE) dwara ack vritt key chapon key ack nishchit samooh key aadhe taaron kii ganana key liye rachit kiya gayaa haye. aryabhatiya key adhyaay 1 "dashgitika" mein 12vein schlock mein sankhyaon kaa samooh dikhaai detaa haye. yeh ganitiya talika key aadhunik arth mein ack talika naheen haye; yaani, yeh panktiyon aur stambhon mein vyavasthit sankhyaon kaa ack samooh naheen haye. aryabhata kii talika bhee paaramparik arthon mein trikonamitiya saain function key moolyon kaa ack samooh naheen haye; yeh archmint mein vyakt trikonamitiya saain key moolyon key pahale antar kii ack talika haye, aur iss vajah seey talika koo "aryabhata kii saain-antar kii talika" key roop mein bhee sandarbhit kiya jaataa haye.
aryabhata kii mez ganit key itihas mein pahali saain table thee. hipparcus kii abb khou gaee mez (see. 190 eesaa poorv-see. 120 eesaa poorv) aur mainlouse (see. 70-140 CE) aur tolemy key loga (c. aeye. dee. 90-see. 168) sabhi taaron kii mejein theen aur aadhe taaron kii naheen.
aryabhata kii mez pracheen bhaarat kii maanak saain table key roop mein bunny rahee. iss talika kii sateekta mein sudhaar karane key liye lagaatar prayaas kiye gaye. inn prayason kii parinati sangamagram key madhav (see. 1350-see. 1425), khagol vigyaan aur ganit key keral school key sansthaapak, aur saat yaa aathh dashamlav sthaanon key liye sateek moolyon key saath madhav dwara ack saain table kaa saaraneekaran.
ganit key kuchh itihaskaron ney tark diyaa haye kii aryabhattiya mein dee gaee saain table pracheen yunan key ganitvidon aur khagolvidon dwara nirmit pahale kii aisee taalikaon kaa ack roopaantaran thaa. david pingri, joe pracheen kaal mein sateek vigyaan key america key agrani itihaskaron mein seey ack they, iss tarah key drishtikon key ack pratipaadak they. iss parikalpana koo maanate hue, jee. jey. tommer likhate hain, "bhaarat mein yunani khagoliya model key sabse pahale aagaman key liye shayed hii koee dastavej maujood haye, yaa usa mamle key liye kii way model kaise dikhate. isaliye yeh pataa lagaana bahut mushkil haye kii hamaare paas joe aaya haye vaha sanchaarit gyaan kaa pratinidhitva kartaa haye, aur bhaaratiya vaigyaanikon key saath kyaa mool haye. ... sachchai shayed donon kaa ack ulajha huaa mishran haye."
mez.
aadhunik sanketanon mein.
aryabhata key sanskrit padya mein kootbaddh moolyon koo aryabhata mein samajhaai gaee sankhyaatmak yojana kaa upayog karke kootbaddh kiya jaa sakata haye, aur kootbaddh sankhyaaen neeche dee gaee talika mein soochibaddh hain. talika mein, aryabhata kii saain table key liye praasangik konn maap dusare collum mein soochibaddh hain. teesare stambh mein oopar dee gaee devnagari lipi mein sanskrit kavita mein nihit sankhyaaen hain. devnagari koo padhane mein asamarth upayogkartaon kii suvidha key liye, inn shabd-sankhyaon koo iso 15919 lipyantaran mein chauthe collum mein punah prastut kiya gayaa haye. agale stambh mein yeye sankhyaaen hindu-arabi ankon mein hain. aryabhata kii sankhyaaen saain key moolyon mein pahala antar hain. saain (yaa adhik sateek roop seey, "jiyaa") kaa sambandhit moolya usa antar taka key antar koo jodkar praapt kiya jaa sakata haye. iss prakaar "jiyaa" kaa maan isake anuroop haye
18°45′ kaa yog 225 + 224 + 222 + 219 + 215 = 1105 haye. aryabhata kii gananaon kii sateekta kaa aaklan karane key liye, "jya" key aadhunik moolya talika key antim stambh mein diye gaye hain.
bhaaratiya ganitiya parampara mein, ack konn kaa saain (yaa "jiyaa") sankhyaon kaa anupaat naheen haye. yeh ack nishchit rekha khand kii lambai haye, ack nishchit aadhaa-taar. iss tarah kii taalikaon key nirmaan key liye aadhar vritt kii trijya mool mapdand haye. aitihaasik roop seey, iss mapdand key liye vibhinn moolyon kaa upayog karke kaee taalikaon kaa nirmaan kiya gayaa haye. aryabhata ney apani saain table kii ganana key liye aadhar vritt kii trijya key moolya key roop mein sankhya 3438 koo chunaa haye. iss mapdand key chayan kaa tark konn maap mein ack vritt kii paridhi koo maapane kaa vichaar haye. khagoliya gananaon mein doori koo degree, minut, sekand aadi mein maapa jaataa haye. iss maap mein, ack vritt kii paridhi 360° = (60 × 360) minut = 21600 minut haye. vritt kii trijya, jisaki paridhi 21600 minut haye, 21,600/2π minut haye. aryabhata koo gyaat maan π = 3.1416 kaa upayog karke isaki ganana karane parr vritt kii trijya lagbhag 3438 minut hoe jaati haye. aryabhata kii saain table aadhar vritt kii trijya key liye iss moolya parr adharit haye. yeh abhee taka sthaapit naheen kiya gayaa haye kii aadhar trijya key liye iss moolya kaa upayog karane vaalaa pahala vyakti kaun haye. lekin aryabhatiya sabse purana jeevit paath haye jisamen iss mool sthiraank kaa sandarbh haye.
aryabhata kii computational vidhi.
aryabhattiya key dusare khand, jiska sheershak ganitpad haye, mein ack chhand haye joe saain table kii ganana key liye ack vidhi kaa sanket detaa haye. iss schlock key arth kii sahee vyakhya karane mein kaee aspashtataaen hain. udaaharan key liye, nimnalikhit cotts dwara dee gaee kavita kaa anuvaad haye jisamen varg koshthak mein shabd anuvaadak key sammilit hain naa kii kavita mein granthon key anuvaad.
yeh iss tathya kaa ullekh curr sakata haye kii saain falan kaa doosara vyutpann saain falan key rinaatmak key barabar haye.

