pai

greek akshar pai
yadi kisi vrutt ka vyaas 1 ho to usaki paridhi pai ke baraabar hogi.

pai ya π ek ganiteeya niytaank hai jiska sankhyaatmak maan kisi vrutt ki paridhi aur uske vyaas ke anupaat ke baraabar hota hai. is anupaat ke liye π sanket ka prayog sarvapratham san 1706 mein William jons ne sujhaaya. iska maan lagbhag 3.14159 ke baraabar hota hai. yeh ek aparimeya raashi hai.

pai sabse mahatvapoorn ganiteeya evam bhautik niytaankon mein se ek hai. ganit, vigyaan evam injeeniyri ke bahut se sootron mein π aata hai.[1]

anukram

itihaas

puraatan

2589–2566 E. poorv bane geeja ki mahaan piraamid ka parimaap 1760 kyoobit aur oonchaai 280 kyoobit thi; jiska anupaat 1760/280 ≈ 6.2857 pai ke maan ke lagbhag 2 guna hai. is anupaat ke aadhaar par, kuchh misravidya maanate hain ki piraamid banaane vaale π ka gyaan rakhate the aur vrut ke gunadharmon ko nigmit karne vaale piraamid jaan - boojhakar banaae.[2] anya maton ke anusaar π se sambandhit uparokt sujhaav keval sanyog hai, kyonki iska koi pramaan upalabddh naheen hai ki piraamid banaane vaalon ko π ke baare mein jaankaari thi aur choonki piraamid ki vimaaen anya kaarakon par bhi nirbhar karti hain.[3]

π ke sheeghraatisheeghr likhit sannikt misr aur baabil mein mile hain, ye donon maap 1 pratishat ki shuddhata ke saath hain. baabil mein E. poorv 1900-1600 dinaank waali kle goli par jyaamiteeya kathan hai ki π ka nihit arth 25/8=3.1250 hai.[4] misr mein E. poorv 1650 dinaankit, en:Rhind Papyrus, parantu yeh E. poorv 1850 dinaankit ek lekhapatr ki pratilipi hai jismein vrut ke kshetrafal ka sootr diya gaya hai jo π ko (16/9)2 ≈ 3.1605 ke rup mein upayog karta hai.[4]

bhaarateeya ganit mein pai

Bhaarat mein E. poorv 600 mein shulb sootron (sanskrut granth jo ganitiya gananaaon mein bahut pahuainche hue hain.) mein π ko (9785/5568)2 ≈ 3.088 likha gaya hai.[5] E. poorv 159 athva shaayad isse bhi pehle mein bhaarateeya srot π ko ≈ 3.1622 likhte the.[6]

aaryabhat ne nimnalikhit shlok mein pai ka maan diya hai-

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 dashamlav ke paaainch ankon tak bilkul teek hai.

shankar varman ne sadratnamaala mein pai ka maan nimnalikhit shlok mein diya hai, jo katapayaadi pranaali ka upayog karke likha gaya hai-

bhadraambuddhisiddhajanmaganitshraddha sm yad bhoopagi:
= 31415926535897932384626433832795 (ikatees dashamlav sthaanon tak, 3 ke baad dashamlav maaniye.)

29 March 2015 ko Bhaarat ke Rajasthan raajya ke mohacha gaanv ke raajaveer meena ne pai ka dashamlav ke baad 70000 anko tak maan 9 ghante 27 minit mein sunaakar ginij book mein apna record banaaya[verification needed]

sandarbh

  1. Howard Whitley Eves (1969). An Introduction to the History of Mathematics. Holt, Rinehart & Winston. http://books.google.com/books?id=LIsuAAAAIAAJ&q=%22important+numbers+in+mathematics%22&dq=%22important+numbers+in+mathematics%22&pgis=1.
  2. "ham yeh nishkarsh nikaal sakte hain yadyapi praacheen misravidyon ke anusaar π ka shuddh maan naheen praapt kiya ja sakta, vyavahaarik jeevan mein unhonein iska prayog kiya." Verner, M. (2003). The Pyramids: Their Archaeology and History. , p. 70.
    Petrie (1940). Wisdom of the Egyptians. , p. 30.
    See also Legon, J. A. R. (1991). "On Pyramid Dimensions and Proportions". Discussions in Egyptology 20: 25–34. http://www.legon.demon.co.uk/pyrprop/propde.htm. .
    See also Petrie, W. M. F. (1925). "Surveys of the Great Pyramids". Nature Journal 116 (2930): 942–942. Bibcode 1925Natur.116..942P. doi:10.1038/116942a0.
  3. misravidya: roji, korinna, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2004, pp 60–70, 200, ISBN 9780521829540.
    Skeptics: Shermer, Michael, The Skeptic Encyclopedia of Pseudoscience, ABC-CLIO, 2002, pp 407–408, ISBN 9781576076538.
    See also Fagan, Garrett G., Archaeological Fantasies: How Pseudoarchaeology Misrepresents The Past and Misleads the Public, Routledge, 2006, ISBN 9780415305938.
    For a list of explanations for the shape that do not involve π, see Roger Herz-Fischler (2000). The Shape of the Great Pyramid. Wilfrid Laurier University Press. pp. 67–77, 165–166. aai॰aऍsa॰abee॰aऍna॰ 9780889203242. http://books.google.co.uk/books?id=066T3YLuhA0C&pg=67,.
  4. a aa Arndt & Haenel 2006, prushth 167
  5. Arndt & Haenel 2006, prushth 168–169
  6. Arndt & Haenel 2006, prushth 169

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