Consonants have numerals assigned as per the above table.A consonant without a vowel is to be ignored.Įxplanation: The assignment of letters to the numerals are as per the following arrangement (In Devanagari, Kannada, Telugu & Malayalam respectively) In a conjunct consonant, the last of the consonants alone will count. The nine integers are represented by consonant group beginning with ka, ṭa, pa, ya. Translation: na (न), nya (ञ) and a (अ)-s, i.e., vowels represent zero. Miśre tūpāntyahal saṃkhyā na ca cintyo halasvaraḥ Nanyāvacaśca śūnyāni saṃkhyāḥ kaṭapayādayaḥ Rules and practices įollowing verse found in Śaṅkaravarman's Sadratnamāla explains the mechanism of the system. Some Pali chronograms based on the Ka-ṭa-pa-yā-di system have been discovered in Burma. The Ka-ṭa-pa-yā-di system is not confined to India. It is preserved in the Sarasvati Bhavan Library of Sampurnanand Sanskrit University, Varanasi. However, on a Sanskrit astrolabe discovered in north India, the degrees of the altitude are marked in the Kaṭapayādi system. Not much is known about its use in north India. Geographical spread of the use Īlmost all evidences of the use of Ka-ṭa-pa-yā-di system is from south India, especially Kerala. There is no definitive evidence whether the Ka-ṭa-pa-yā-di system originated from Āryabhaṭa numeration.
bhaṭīya, is known to have used a similar, more complex system to represent astronomical numbers.Therefore, sometime in the early first millennium is a reasonable estimate for the origin of 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. In some astronomical texts popular in Kerala planetary positions were encoded in the Kaṭapayādi system. Some argue that the system originated from Vararuci. The oldest available evidence of the use of Kaṭapayādi (Sanskrit: कटपयादि) system is from Grahacāraṇibandhana by Haridatta in 683 CE.