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JAIN MATHEMATICS AND KARMAVAD/139
TYPES OF MATHEMATICS
In the Sthananga-sutra, ten types of Mathematics are described in the chapter dealing with numerate terms. Mahapragya has presented a detailed note on this mathematical learning, which is complete in itself. This ancient mathematical style will be interesting for the readers.
1. Parikarma (Operators) -
In the Indian system, there are eight basic mathematical operations - (i) addition, (ii) subtraction, (iii) multiplication, (iv) division, (v) square, (vi) square-root, (vii) Cube, (viii) Cube-root. But, out of these operations, the majority of them were not employed effectively in the canonical texts.
According to Brahmagupta, there are twenty possible mathematical operations: (i) addition, (ii) subtraction, (iii) multiplication, (iv) division, (v) square, (vi) square-root, (vii) cube, (viii) cube-root, (ix-xiii) five rules for simplifying fractions, (xiv) the rule of three expressions, (xv) complex rule of three expressions, (xvi) rule of five expressions, (xvii) rule of seven expressions, (xviii) rule of nine expressions, (xix) rule of eleven expressions, (xx) rule of commutation.
From the ancient times, the Hindu mathematicians recognized that all the operations of mathematics are based on the two fundamental operations - addition and subtraction. The operations of doubling and halving were regarded important by the Egyptians, Greeks and Arabians, who were ignorant of the decimal system.
2. Calculations --
According to Brahmadatta, there are eight types of treatment in which the above mathematical operators can be used to perform calculations: (1) Mixed (Mishrak) - four basic operations viz. addition, subtraction,
multiplication and division. (2) Series (shredhi) - progressions (3) Area (Kshetra) - geometry of closed figures (4) Volume (Khata) - dealing with excavation and volumes involved
therein (5) Sets (Chati) - treatment of sets (6) Permutation-Combination (Krackchic) - statistical analysis
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