vaidik ganit (svaami bhaarati Krishna teerth dvaara virchit)

jagadguroo svaami bhaarati Krishna teerth dvaara virchit vaidik ganit ankaganiteeya ganana ki vaikalpik evam sankshipt vidhiyon ka samooh hai. ismein 16 mool sootr diye gaye hain. vaidik ganit ganana ki aisi paddhati hai, jisse jatil ankaganiteeya gananaaen atyant hi saral, sahaj va tvarit sambhav hain. svaameeji ne iska pranayan beesaveen shati ke aarambhik dinon mein kiya. svaameeji ke kathan ke anusaar ve sootr, jin par 'vaidik ganit' naamak unki kruti aadhaarit hai, atharvaved ke parishisht mein aate hain. parantu vidvaanon ka kathan hai ki ye sootr abhi tak ke gyaat atharvaved ke kisi parishisht mein naheen milte. ho sakta hai ki svaameeji ne ye sootr jis parishisht mein dekhe hon vah durlabh ho tatha keval svaameeji ke hi sajnyaaan mein ho. vastut: aaj ki sthiti mein svaameeji ki 'vaidik ganit' naamak kruti swayam mein ek naveen vaidik parishisht ban gayi hai.

anukram

vaidik ganit ke solah sootr

svaameeji ke ekamaatr upalabdh ganiteeya granth 'vaidik ganit' ya 'vedon ke solah saral ganiteeya sootr' ke bikhre hue sandarbhon se chhaaaintakar dau॰ vaasudev sharan Agrawal ne sootron tatha upasootron ki soochi granth ke aarambh mein is prakaar di hai—

1. ekaadhiken poorven
2. nikhilan navatashcharaman dashat:
3. oordhvatiryagbhyaam
4. paraavartya yojayet
5. shoonyan saamyasamuchchaye
6. (aanuroopye) shoonyamanyat
7. sankalanavyavakalanaabhyaam
8. pooranaapooranaabhyaam
9. chalanakalanaabhyaam
10. yaavadoonam
11. vyashtismashti:
12. sheshaanyaङaken charamen
13. sopaantyadvayamantchyam
14. ekanyoonen poorven
15. gunitsamuchchay:
16. gunakasamuchchay:

upasootr

  • aanuroopyen
  • shishyate sheshasanjnya:
  • aadhamaadhenaantyamantyen
  • kevalai: saptakan gunyaat
  • veshtanam
  • yaavadoonan taavadoonan
  • yaavadoonan taavadooneekrutya vargan ch yojayet
  • antyayorddashakeऽpi
  • antyayorev
  • samuchchayagunit:
  • lopanasthaapanaabhyaan
  • vilokanan
  • gunitsamuchchay: samuchchayagunit:
  • dhvajaaङak

vaidik ganiteeya sootron ki visheshataaeain

(1) ye sootr sahaj hi mein samajh mein aa jaate hain. unka anuprayog saral hai tatha sahaj hi yaad ho jaate hain. saari prakriya maukhik ho jaati hai.

(2) ye sootr ganit ki sabhi shaakhaaon ke sabhi adhyaayon mein sabhi vibhaagon par laagoo hote hain. shuddh athva prayukt ganit mein aisa koi bhaag naheen jismein unka prayog na ho. ankaganit, beejaganit, rekhaaganit samatal tatha goleeya trikaanamiteeya, samatal tatha ghan jyaamiti (vaishleshik), jyotirvijnyaaan, samaakal tatha avakal kalan aadi sabhi kshetron mein vaidik sootron ka anuprayog samaan roop se kiya ja sakta hai. vaastav mein svaameeji ne in vishyon par solah krutiyon ki ek shrrunkhala ka srujan kiya tha, jinmein vaidik sootron ki vistrut vyaakhya thi. durbhaagya se solah krutiyaaain prakaashit hone se poorv hi kaal-kavalit ho gain tatha svaameeji bhi brahmaleen ho gaye.

(3) kai paidiyon ki prakriyaavaale jatil ganiteeya prashnon ko hal karne mein prachalit vidhiyon ki tulana mein vaidik ganit vidhiyaaain kaafi kam samay leti hain.

(4) chhoti umr ke bachche bhi sootron ki sahaayata se prashnon ko maukhik hal kar uttar bata sakte hain.

(5) vaidik ganit ka sampoorn paathyakram prachalit ganiteeya paathyakram ki tulana mein kaafi kam samay mein poorn kiya ja sakta hai.

kuchh sootron ka parichay

ekaadhiken poorven

is sootr ka shaabdik arth hai : 'pehle vaale ki tulana mein ek adhik se'. yeh sootr 1/x9 (jaise.: 1/19, 1/29, aadi) ka maan nikaalne ke liye bahut upayogi hai. yeh sootr guna karne vaale aur bhaag karne vaale dono prakaar ke algoridm mein upayog mein liya ja sakta hai.

maan leejiye ki 1/19 ka maan nikaalna hai, arthaat x = 1 . gunan algoridm ka upayog karne ke liye (yeh daaeain se baaeain kaam karta hai) bhaajya (dividend) 1 hi parinaam ka sabse daayaaain ank hoga. iske baad is ank ko 2 se guna karein (arthaat: x + 1) aur gunanafal ko baaeain likhein. yadi gunanafal 10 se adhik aaye to (gunanafal – 10) ko likhein aur "1" haasil ban jaata hai jise agali baar guna karne par seedhe jod diya jaayega.

'ekaadhiken' aur 'poorven' mein truteeya vibhkti (karan) hai jo yeh sanket karti hai ki yeh sootr guna ya bhaag par aadhaarit hai. kyonki yog aur ghataana mein dviteeya ya panchami vibhkti (to aur from) aati.

is sootr ka ek rochak upayog paaainch (5) se ant hone waali sankhyaaon ka varg nikaalne mein kiya ja sakta hai, jaise:

35×a35 = ((3×a3)+3),25 = 12,25 and 125×a125 = ((12×a12)+12),25 = 156,25

ya 'ekaadhiken poorven' ka prayog karte hue,

35×a35 = ((3×a4),25 = 12,25 and 125×a125 = ((12×a13),25 = 156,25

upapatti (Proof)

yeh sootr jahaaain aur , par aadhaarit hai, arthaat

baahari kadiyaaain