Elegant dissection proofs for algebraic identities in Nīlakaṇṭha’s Āryabhaṭīyabhāṣya

Abstract

Renowned Indian astronomer and mathematician Nīlakaṇṭha Somayājī is well known for his innate ability to provide ingenious proofs. In his elaborate commentary on Āryabhaṭīya called Āryabhaṭīyabhāṣya, we find elegant upapattis or rationales for three algebraic identities involved in calculating cubes and cube-roots. In this paper, we detail these upapattis which may be called dissection proofs in the modern parlance. Incidentally, Nīlakaṇṭha’s simple, yet concise and convincing demonstrations are pertinent in the context of mathematics pedagogy as well.