sankhya

sankhyaaen hamaare jeevan ke dharre ko nirdharit karti hain. jeevan ke kuchh aise kshetron mein bhi sankhyaaon ki ahamiyt hai jo itne aam naheen maane jaate. kisi dhaavak ke samay mein 0.001 saikind ka antar bhi use svarn dila sakta hai ya use isse vanchit kar sakta hai. kisi pahiye ke vyaas mein ek seinteemeetar ke hajaaravein hisse jitna fark use kisi ghadi ke liye bekaar kar sakta hai. kisi vyakti ki pehchaan ke liye usaka telephone number, raashan card par pada number, bank khaate ka number ya pareeksha ka rol number madadgaar hote hain.

anukram

sankhyaaon ka udbhav

sankhyaaen maanav sabhyata jitni hi puraani hain. aaksaford sthit eshamoliyn ajaayabaghar mein raajaadhikaar ka prateek ek misri shaahi dand (raayal mes) rakha hai, jis par 1,20,000 kaidiyon, 4,00,000 bailon aur 14,22,000 bakariyon ka rikaard darj hai. is rikaard se jo 3400 isa poorv se pehle ka hai, pata chalta hai ki praacheen kaal mein log badi sankhyaaon ko likhna jaante the. beshak sankhyaaon ki shurooaat misravaasiyon se bhi bahut pehle hui hogi.

aadimaanav ka ginti se itna vaasta naheen padta tha. rahane ke liye uske paas gufa thi, bhojan ped-paudhon dvaara ya fir hathiyaaron se shikaar karke use mil jaata tha. magar kareeb 10,000 saal pehle jab aadimaanavon ne gaaainvon mein bas kar kheti ka kaam aur pashupaalan aarambh kiya to unka jeevan pehle se kaheen adhik jatil ho gaya. unhein apne rojamarra ke kaaryakram ke saath apne saarvajanik evam paarivaarik jeevan mein bhi niymitta laane ki jaroorat mahasoos hui. unhein pashuon ki ginti karne, krushi upaj ka hisaab rakhane, bhoomi ki paimaaish tatha samay ki jaankaari ke liye sankhyaaon ki jaroorat padi. duniya ke vibhinn bhaagon mein jaise ki bebeelon, misr, Bhaarat, cheen tatha kai aur sthaanon par vibhinn sabhyataaon ka nivaas tha. in sabhi sabhyataaon ne sanbhavataya ek hi samay ke dauraan apni-apni sankhya-paddhatiyon ka vikaas kiya hoga. bebeelon nivaasiyon ki praacheen mitti ki pratimaaon mein sankhyaaen khudi milti hain.

tej dhaar waali patali dandiyon se ve geeli mitti par shanku aakaar ke prateek chihnon ki khudaai karte, baad mein inhein inton ki shakl de dete. ek (1), das (10), sau (100) aadi ke liye vishesh prateekon ka istemaal kiya jaata tha. in prateekon ki punaraavrutti dvaara hi ve kisi sankhya ko pradarshit karte jaise ki 1000 ko likhne ke liye ve prateek chinh ka sahaara lete. ya fir 100 ki sankhya ko das baar likhte the. bebeelonavaasi kaafi badi sankhyaaon ki ginti ve 60 ki sankhya ke maadhyam se hi karte, jaisa ki aajkal ham sankhya 10 ke maadhyam se apni ginti karte hain. misr ke praacheen nivaasi bhi badi sankhyaaon ki ginti karna jaante the tatha saal mein 365 din hone ki jaankaari unke paas thi.

sankhyaaon ka vikaas

moolat: sankhya ka matlab 'praakrutik sankhyaaon' se liya gaya tha. aage chalakar dheere-dheere 'sankhyaaon' ka kshetr vistrut hota gaya tatha poornaank, parimeya sankhya, vaastavik sankhya hote hue samishr sankhya tak pahuainch chuka hai.

sankhyaaon ke samuchchaya mein yeh sambandh hai:

praakrutik sankhya
poornaank
parimeya sankhya
vaastavik sankhya
samishr sankhyaaeain quaternions

sankhyaaon ka mahatva

ek aam aadmi ke jeevan ki nimnaankit sthitiyon ko dekhiye:

1. savere-savere alaarm ghadi ki aavaaj ek daftar jaane vaale ko jagaati hai. ''chhah baj gaye; ab uthana chaahiye.'' is tarah us vyakti ki dincharya ki shurooaat hoti hai.

2. bas mein conductor yaatri se kehta hai : ''chaalees paise aur deejiye.''

yaatri : ''kyon main to aapko sahi bhaada de chuka hoon.''

conductor : ''bhaada ab 25 pratishat badh gaya hai.'' yaatri : ''achha, yeh baat hai.''

3. ek gruhini kisi mahanagar mein doodh ke booth par ja kar kehti hai, ''mujhe do liter waali ek thaili deejiye.''

''mere paas do liter waali thaili naheen hai.''

''theek hai, tab ek liter waali ek thaili aur aadhe-aadhe liter waali do thailiyaan hi aap mujhe de deejiye.''

4. ek restaurant mein bill par najar daudaate hue ek graahak kehta hai : ''waiter ! tumane bill ke paise theek se naheen jode hain. bill 9.50 ki bajaae 8.50 Ru. ka hona chaahiye.''

''mujhe afosas hai, shreemaan !''

ye kuchh aisi sthitiyaaain hain jo sankhyaaon ke rojamarra ke jeevan mein istemaal ko darshaati hain.

inhein bhi dekhein

baahari kadiyaaain