अंक
aank un chihnoan ko kahate haian jinase ginatiyaan soochit ki jati haian, jaise 1, 2, 3. . .4. svayan ginatiyoan ko sankhya kahate haian. yah nirvivad hai ki adim sabhyata mean pahale vani ka vikas hua aur usake bahut kal pashchath lekhan kala ka pradurbhav hua. isi prakar ginana sikhane ke bahut samay bad hi sankhyaoan ko aankit karane ka dhang nikala gaya hoga. vartaman samay tak bache hue abhilekhoan mean sabase prachin aank misr (eejipt) aur mesopoteshiya ke mane jate haian. inaka rachanakal 3,000 eesa poorv ke asapas raha hoga. ye aank chitralipi (hairogliphiks) ke roop mean haian. inamean kisi aank ke lie chi diya, kisi ke lie phool, kisi ke lie kudal adi banae jate the. keval aank hi nahian, shabd bhi chitralipi mean likhe jate the. right|border kuchh deshoan mean aankoan ke lie khapachchiyoan par khaanchean banae jate the, kahian kh diya se biandiyaan banaee jati thian, kahian kh di athava p di lakiroan se kam liya jata tha. prachin mesopotemiya mean kh di rekhaoan ka prayog hota tha, jo sanbhavat: kh di aanguliyoan ki dyotak haian:
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1 2 3
itihas
brahmi lipi mean, jo prachin bharat mean prachalit thi, inhian sankhyaoan ke lie bean di rekhaean prayukt hoti thian. pandit sudhakar dvivedi ka vichar tha ki hamare adhikaansh nagari aankoan ki akritiyaan pushpoan se li gee haian. parantu shilalekhoan mean se roop kahian bhi nahian mile haian. isalie aankoan ki yah utpatti keval kalpana hi jan p dati hai. agami prishth ki sarani mean aankoan ke ye roop dikhae ge haian ki bharat ke vividh shilalekhoan mean milate haian. yoonaniyoan mean 1 se 6 tak ke lie pahale kh di rekhaean prayukt hoti thian. pichhe paanch, das adi ginatiyoan ke lie prayukt shabdoan ke pratham akshar likhe jane lage. tritiy shatabdi eesa poorv ke lekhoan mean yah pranali milati hai. tadanantar varnamala ke kram se lie ge akshar 9 tak ki kramagat sankhyaoan ke lie prayukt hote the, aur 10, 20 adi 90 tak, aur phir 100, 200 adi tak ke lie shesh akshar prayukt hote the.
roman aank
roman paddhati, jisamean 1, 2, . . . ke lie I, II, III, IV, V, VI...likhe jate the, aj tak bhi tho di-bahut prachalit hai. sanh 260 eesa poorv mean yah paddhati (kuchh herapher ke sath) prachalit avashy thi, kyoanki us samay ke shilalekhoan mean yah vartaman hai. rom ka samrajy itani door tak phaila hua tha aur itane samay tak shaktiman bana raha ki usaki lekhan paddhati ka prabhutv ashcharyajanak nahian hai. apane samay ki any aank paddhatiyoan se roman aank paddhati achchhi bhi thi, kyoanki isamean char akshar V, N, L, aur C tatha ek kh di rekha se pratidin ke vyavahar ki sabhi sankhyaean likhi ja sakati thian. pichhe D tatha M ke upayog se paryapt b di sankhyaoan ka likhana bhi sanbhav ho gaya. ek, do aur tin ke lie itani hi kh di rekhaean khianchi jati thian. V se paanch ka bodh hota tha. mamasen ne 1850 mean bataya ki V vastut: khule panje ka chitriy pratik hai aur ek ulata tatha ek sidha V milane se do-paanch arthath das (X) bana. is siddhaant se adhikaansh vidvanh sahamat haian. C sau ke lie roman shabd seandam ka pahala akshar hai aur M hajar ke lie roman shabd mili ka pahala akshar hai. b di sankhya ke baeean or chhoti sankhya likhakar donoan ka aantar soochit kiya jata tha, jaise (IV = 4). roman aankoan se bahut b di sankhyaean nahian likhi ja sakati thian. avashyakata p dane par (1) se 1,000 ((1)) se 10,000, (((1))) se 1 lakh soochit kar liya jata tha, parantu jab unhoanne 260 eesa poorv mean karshejiv logoan par apani vijay ke lie kirti stanbh banaya aur us par 23,00,000 likhana p da to unhean (((1))) ko 23 bar likhana p da.
yukatan (meksiko aur madhy amarika ke prayadvip) mean prachinamay sabhyata atyant vikasit avastha mean thi. vahaan ek, do, tin ityadi biandiyoan se 1, 2, 3, . . . soochit kie jate the, bean di rekha se 5, chakr se 20, ityadi. is pranali mean likhi gee kuchh sankhyaean niche dikhaee gee haian:
aankoan ke lie vishesh chihhn
center chin mean prachin kal se hi aankoan ke lie vishesh chihhn the. yoorop mean prachalit aankoan 1, 2, 3,. . . ki utpatti ke lie kee siddhaant bane, parantu ab pashchaty vidvanh bhi manate haian ki unaka mool prachin bharatiy paddhati brahmi hai, yadyapi deshakal ki vibhinnata se kee aankoan ke roop mean kuchh vibhinnata a gee hai. 2 aur 3 spasht roop se brahmi ke do aur tin, arthath = aur 0, ke ghasitakar likhe ge roop haian. isake atirikt kee any yooropiy aankoan ke roop brahmi aankoan se milate haian. udaharanat: 1, 4 aur 6 ashok ke shilalekhoan ke 1, 4 aur 6 se milate-julate haian. 2, 4, 6, 7 aur nanaghat ke aankoan se bahut kuchh milate haian; 2, 3, 4, 5, 6, 7 aur 9 nasik ki gufaoan ke aankoan ke sadrish haian. parantu yooropiy logoan ne in aankoan ko sidhe bharatiyoan se nahian paya. unhoanne inhean arab valoan se sikha. isilie ye aank yoorop mean arabi (arebik) aank kahe jate haian. poorvokt pramanoan ke adhar par vaijnanik ab unhean hiandoo-arebik aank kahate haian.
shoony ka prayog
ashok ke shilalekh tisari shatabdi eesa poorv ke haian aur nanaghat ke shilalekh lagabhag 100 varsh bad ke haian. inamean hamare aankoan ke prachin roop ab bhi dekhe ja sakate haian. inamean shoony ka prayog nahian milata. athavian shatabdi se bharat mean shoony ke prayog ka pakka praman milata hai. aj sansar ki adhikaansh bhashaoan mean 1 se 9 tak ke aankoan ke lie svatantr aank haian. phir 1 mean 0 lagakar 10 banaya jata haian. bad ke samast aank das ko adhar manakar banae jate haian, jaise:
13 = 10+3
17=10+7
adhunik sankhya paddhati
isi tathy ko ham ganit ki bhasha mean is prakar kahate haian ki hamari sankhya paddhati dashaanshik hai. ham oopar dekh chuke haian ki ginane ki adim paddhati yogatmak thi. do lakiroan ka arth do hota tha aur tin lakiroan ka tin. kiantu adhunik sankhya paddhati yogatmak bhi hai aur gunanatmak bhi. dekhie:
45 = 4´ 10+5
68=6´ 10+8
91=9´ 10+1
spasht hai ki 45 mean 4 ka sankhyatmak man to 4 hi hai, kiantu apani sthiti ke karan usaka man 40 hai. is prakar 40 mean 5 jo dane se 45 prapt hota hai. sthanoan ke man ikaee, dahaee, saik da adi prasiddh haian. jab kisi sthan mean koee aank nahian rahata tab vahaan shoony (0) likh diya jata hai. jab tak shoony ka avishkar nahian hua tha tab tak sthanik manoan ka prayog bhali-bhaanti nahian ho pata tha. shoony ka avishkar prachin bharatiyoan ne hi kiya tha. shoonyarahit pranaliyoan mean (jaise roman paddhati mean) b di sankhyaoan ka likhana bahut kathin hota hai, aur b di sankhyaoan ko b di sankhyaoan se guna karana to pray: asanbhav ho jata hai.[1]
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tika tippani aur sandarbh
sanbandhit lekh