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 शुद्धेश्च भागो गतमूलमुक्तम् ।
व्याप्तं समीक्ष्योपचयक्षयाभ्यां विद्यादिदं द्व्यात्मकमेव शास्त्रम् ॥ (Āryabhaṭīya-bhāṣya in Gaṇitapāda, p.43)
"All arithmetical operations resolve into two categories though usually considered to be four i.e, addition, subtraction, multiplication and division. The two main varieties are increase and decrease. Addition means to increase and subtraction means to decrease. These two varieties of operation penetrate the whole of mathematics. Multiplication and evolution ( square etc,) are particular kinds of addition and division and involution( square root etc) are particular kinds of subtraction. Every mathematical operations involves increase or decrease. Hence the whole of this science should be known as consisting truly of these two operations only."
Saṅkalana and Vyavakalana (Addition and Subtraction)
Addition is the first fundamental operation in mathema
