Parikarmāṣṭaka - Fundamental Operations
Introduction
Arithmetic deals with calculations using numbers. Pāṭīgaṇita is the Samskrit word for arithmetic and geometry .Pāṭīgaṇita is formed by combining the words Pāṭī (slate) and gaṇita (mathematics). Since gaṇita was done using a board of a slate , it was called Pāṭīgaṇita. For all transactions using numbers will require the basic operations of addition, subtraction, multiplication, division, squaring etc. Ancient Indian Mathematicians mentioned eight fundamental operations together called as Parikarmāṣṭaka.
Definition
Parikarma means arithmetic operations and aṣṭaka means group of eight. Parikarmāṣṭaka signifies eight basic operations.
The eight fundamental operations are :
- Saṅkalanam (addition)
- Vyavakalanam (subtraction)
- Guṇana (multiplication)
- Bhājana (division)
- Varga (squaring)
- Varga-mūla (square root)
- Ghana (cubing) and
- Gana-mūla (cube root)
Addition and subtraction form the basis of all calculations. Bhāskara I mentions in the below shloka
संयोगभेदा गुणनागतानि शुद्धेः च भागः गतमूलमुक्तम् । व्याप्तं समीक्ष्य उपचयक्षयाभ्याम् विद्यात् इदम् द्व्यात्मकम् एव शास्त्रम् ॥
