Sunday, January 19, 2014

PI in India

PI in India

The value of pi is being used in India from ancient times. It gives us an insight about how evolved our past was.

There is a shloka, a hymn to Lord Krishna or Shiva, which gives the value of pi upto 31 decimal places. 

Its amazing that our forefathers used an encryption technique to easily remember it. What is more astonishing is that they needed pi upto 31 places!

Science and spirituality both moved together in this land.

Importance of Pi
Pi deals with circles and circles are very important in many fields. Pi is a very important number in the fields of :

  • geometry and trigonometry, 
  • complex number and analysis, 
  • number theory, 
  • probability and statistic physics, 
  • engineering and geology.
  • computers and many more
We would hardly find a person of scientific quest unaware of pi and its significance.

What is Pi?
π is commonly defined as the ratio of a circle's circumference C to itsA diagram of a circle, with the width labeled as diameter, and the perimeter labeled as circumferencediameter d:
 \pi = \frac{C}{d}

The ratio C/d is constant, regardless of the circle's size.
In decimal form, the value of pi isapproximately 3.14.
Pi is an irrational number, meaning that its decimal form neither ends nor becomes repetitive.
 pi = 3.1415….infinitely

chaturadhikaM shatamaShTaguNaM dvAShaShTistathA sahasrANAm AyutadvayaviShkambhasyAsanno vr^ttapariNahaH.
[gaNita pAda, 10] Aryabhatiyam (499 CE)
“Add 4 to 100, multiply by 8 and add to 62,000. This is approximately the circumference of a circle whose diameter is 20,000.”
i.e. \pi \approx \frac{62,832}{20,000} = 3.1416
correct to four places.
Even more important however is the word "Asanna" - approximate, indicating an awareness that even this is an approximation.

Aryabhatta called it an approximate (asanna) value to mean that not only is this an approximation but that the value is incommensurable (or irrational).

It is quite a sophisticated insight, because the irrationality of pi was proved in Europe only in 1761 by Lambert!

Katapayadi Encryption
gopiibhaagya madhuvraataH shruMgashodadhi saMdhigaH .
khalajiivitakhaataava galahaalaa rasaMdharaH
This shloka, a hymn to Lord Krishna or Shiva, gives the value of pi upto 31 decimal places.

Pi using Katapayadi Encryption
Katapayadi system is used to encode numbers in many shlokas

ga - 3 pii - 1 bhaa - 4 gya - 1 ma - 5 dhu - 9 ra - 2 ta -6 shru - 5 ga - 3 sho - 5 da - 8 dhi - 9 sa - 7 dha - 9 ga - 3 kha - 2 la - 3 jii - 8 vi - 4 ta - 6 kha - 2 ta - 6 va - 4 ga - 3 la - 3 ra - 2 sa - 7 dha - 9 ra – 2

pi = 3.1415926535897932384626433832792

So we needed pi upto 31 decimal places! What is more amazing is that we knew encryption! Science and spirituality both were important and both moved together. 

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