Katapayadi system

The oldest available evidence of the use of Kaṭapayādi (Sanskrit: कटपयादि) system is from Grahacāraṇibandhana by Haridatta in 683 CE.

[2] In some astronomical texts popular in Kerala planetary positions were encoded in the Kaṭapayādi system.

The first such work is considered to be the Chandra-vakyani of Vararuci, who is traditionally assigned to the fourth century CE.

Therefore, sometime in the early first millennium is a reasonable estimate for the origin of the Kaṭapayādi system.

[3] Aryabhata, in his treatise Ārya·bhaṭīya, is known to have used a similar, more complex system to represent astronomical numbers.

However, on a Sanskrit astrolabe discovered in North India, the degrees of the altitude are marked in the Kaṭapayādi system.

It is preserved in the Sarasvati Bhavan Library of Sampurnanand Sanskrit University, Varanasi.

Some Pali chronograms based on the Ka-ṭa-pa-yā-di system have been discovered in Burma.

[6] Following verse found in Śaṅkaravarman's Sadratnamāla explains the mechanism of the system.

[7][8] नञावचश्च शून्यानि संख्या: कटपयादय:। मिश्रे तूपान्त्यहल् संख्या न च चिन्त्यो हलस्वर:॥ Transliteration: nanyāvachaścha śūnyāni sankhyāḥ kaṭapayādayaḥ miśre tūpāntyahal sankhyā na cha chintyo halasvaraḥ Translation: na (न), ña (ञ) and a (अ)-s, i.e., vowels represent zero.

The nine integers are represented by consonant group beginning with ka, ṭa, pa, ya.

Explanation: The assignment of letters to the numerals are as per the following arrangement (In Devanagari, Kannada, Telugu & Malayalam scripts respectively) ఙ ങ vyāsastadarddhaṃ tribhamaurvika syāt This verse directly yields the decimal equivalent of pi divided by 10: pi/10 = 0.31415926535897932384626433832792 Traditionally, the order of digits are reversed to form the number, in katapayadi system.

These dates are generally represented as number of days since the start of Kali Yuga.