Method of Inversion in Āryabhaṭīyam
Introduction
Inverse means the opposite effect of an action or a step. In Mathematics we have operations such as addition (+), subtraction (−), Multiplication (×), Division (÷) etc.The process in which the effect of one operation is inversed by another operation is termed as inverse operations.
Verse
गुणकारा भागहरा भागहरास्ते भवन्ति गुणकाराः ।
यः क्षेपः सोऽपचयोऽपचयः क्षेपश्च विपरीते ॥
Translation
In the method of inversion multipliers become divisors and divisors become multipliers, additive becomes subtractive and subtractive becomes additive[1].
Example
A number is multiplied by 2 , then increased by 1 , then divided by 5, then multiplied by 3, then diminished by 2, and then divided by 7 , the result (thus obtained) is 1. Say what is the initial number.
| Steps | Given Order | Steps | Reverse Order | ||
|---|---|---|---|---|---|
| 1 | Multiplied by 2 | ↓ | 6 | Divided by 2 | ↑ |
| 2 | Increased by 1 | 5 | Subtracted by 1 | ||
| 3 | Divided by 5 | 4 | Multiplied by 5 | ||
| 4 | Multiplied by 3 | 3 | Divided by 3 | ||
| 5 | Diminished by 2 | 2 | Increased by 2 | ||
| 6 | Divided by 7 | 1 | Multiplied by 7 |
Result: 1
Starting from the last number 1, in the reverse order
See Also
आर्यभटीयम् में 'व्युत्क्रमण की विधि'
