Katapayadi system

Kaṭapayādi system (Devanagari: कटपयादि, also known as Paralppēru, Malayalam: പരല്‍പ്പേര്) of numerical notation is an ancient Indian alphasyllabic numeral system to depict letters to numerals for easy remembrance of numbers as 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 Kaṭapayādi (Sanskrit: कटपयादि) system is from Grahacāraṇibandhana by Haridatta in 683 CE. It has been used in Laghu·bhāskarīya·vivaraṇa written by Śaṅkara·nārāyaṇa in 869 CE.

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.

Aryabhata, in his treatise Ārya·bhaṭīya, is known to have used a similar, more complex system to represent astronomical numbers. There is no definitive evidence whether the Ka-ṭa-pa-yā-di system originated from Āryabhaṭa numeration.

Almost all evidences of the use of Ka-ṭa-pa-yā-di system is from South India, especially Kerala. Not much is known about its use in North India. 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.

The Ka-ṭa-pa-yā-di system is not confined to India. Some Pali chronograms based on the Ka-ṭa-pa-yā-di system have been discovered in Burma.

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

नञावचश्च शून्यानि संख्या: कटपयादय:।
मिश्रे तूपान्त्यहल् संख्या न च चिन्त्यो हलस्वर:॥