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  Ka-Ta-Pa-Yadi System

The mnemonic major system i.e. peg system, to memorize numbers is 300 years old. A far superior system to memorize numbers, the 'ka-ta-pa-yadi system' also known as Paralppēru in Malayalam, is in use in India. It has got its roots in vedic era (6th century AD).

The 'ka-ta-pa-yadi system' of numerical notation is an ancient Indian system to depict letters to numerals for easy remembrance of  words or verses. Assigning more than one letter to one numeral and nullifying certain other letters as valueless, this system provides the flexibility in forming meaningful words out of numbers which can be easily remembered.

The oldest available evidence of the use of Katapayadi System is from Grahacāraṇibandhana by Haridatta, Kerala, in 683 CE. It has also been used in Laghubhāskariyavivarana written by Sankaranarayana in 869 CE.

A variation of it is extensively used by 'Aryabhatta II'.

In this system the letters are represented as

                  1       2        3      4        5       6         7         8       9       0
                 ka    kha     ga    gha     nga    ca      Cha     ja     jha    nya
                 Ta    Tha     Da    Dha    Na      ta       tha     da    dha    na
                 pa    pha     ba    bha    ma
                 ya    ra        la     va      Sha    sha     sa       ha

Like in the major system only consonant are considered to determine the numbers represented and vowels have no value; i.e., ga, ge, gi and gu all represent 3.

A beautiful example of the use of the system is in the following 'Sloka', which is in the praise of both god Krishna and god 'Shankara'.

                          గోపీ భాగ్య మధువ్రాత శ్రుజ్గిశోదరి సంధిగ

                          ఖల జీవిత ఖాతావగల హలార సంధర |

When converted into numbers in the system yields

3141592653589793238462643832792

which are the first 32 decimal places of '╥' value.

This system is very useful for Indians who do not have good English vocabulary in using the peg system.

They can easily find words to represent numbers to be memorized in their own language. Further, as all Indian languages are derived from ‘Sanskrit’ the system can be modified for their mother tongue.

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