An Ancient Indian Numbering System I learnt While Studying Sanskrit

 

"क  ट  प  य"

(Katpayādi System)

It is an ancient Indian method which helps to express/memorize numbers in the form of words or verses. A related verse-

नज्ञावचश्च शून्यानि संख्या: कटपयादय:। 

मिश्रे तूपान्त्यहल् संख्या न च चिन्त्यो हलस्वर: ॥

Meaning = न ,ज्ञ ,अ have zero value (0), क, ट, प, य have 1 number. The number of consonants that follow each of these groups in the alphabet ranges from 2 to 9. Ex:

क=1 ख=2 ग=3... झ=9 Etc.

ट= 1 ठ=2 ड=3... ध=9 Etc. (as mentioned in image)

It is written in the above verse that without worrying about endings, vowels and mixed consonants have no value.

One of the rules of this system is that words are read from right to left while numbers go from left to right.

E.g. If we want to represent the number of the word Ram, it is 52. (म=5; रा=2)

Also, the number of the word Kautilya is 111.

Long ago people used to name children based on their date of birth using Katpayādi system.

Katpayādi system was also used in mathematics by our grate scholars -

Shankar Verman's Sād·ratna·mālā uses the Kaṭapayādi system in which the first verse of Chapter 4 ends with the line:

(स्याद्) भद्राम्बुधिसिद्धजन्मगणितश्रद्धा स्म यद् भूपगी:

By splitting the consonants in the relevant phrase, calculating it and applying the numbering system then reversing the digits to descending order of places, gives  314159265358979324 which gives the value of pi (π) up to 17 decimal places. (Mentioned in above image)

 गोपीभाग्यमधुव्रात-शृङ्गिशोदधिसन्धिग॥

 खलजीवितखाताव गलहालारसंधर॥

Similarly this verse tells us the value of pi (π) up to 31 decimal places. which is - 31415926535897932384626433832792