The alphabetical notation system of Ᾱryabhaṭa for numerals and its applications
The wealth of ancient Indian Mathematical wisdom was so well developed that modern researchers are increasingly interested in discovering the knowledge of ancient India. The great mathematician and astronomer Āryabhața I (476-540 AD) wrote Āryabhațīyam in 499 AD. The text is divided into four chapters (pādas): 1. Gītikāpāda 2. Gaņitapāda 3. Kālakriyāpāda 4. Golapāda. The text mostly highlights the problems of Arithmetic, Algebra, Geometry, Trigonometry and Astronomy. In second verse of Gītikāpāda, alphabetical notation system for numerals is mentioned. Āryabhața I has classified alphabets into two parts- I. Varga (group) letters; they have been divided into 5 groups. II. Avarga; they are not classified into Vargas. The varga letters ka to ma have value from 1, 2, 3, 4, 5. Up to 25 and the avarga letters ya to ha have value 30, 40, 50, 60….up to 100. This notation system has been applied by Āryabhața I in his mathematical and astronomical calculations.
The research paper is aimed at determining astronomical and mathematical calculations through alphabetical notation system based on Sanskrit phonemes with examples & proofs from Āryabhațīyam and its commentaries.