Varga

Varga refers to squaring. It is one of the parikarmas or basic operations as reckoned in Indian treatises on mathematics. Squaring is a simple operation - multiply a number by itself. It is also well known. However, it is also one of the most heavily used operations. It is required at a fundamental level in geometry to find the area of various figures. Practically speaking, it occurs in numerous problems in Indian texts related to mathematics and astronomy, such as the computation of planetary locations and that of latitude, to name a few. These problems have geometric solutions, hence this is not surprising. The geometric connection of squaring was fundamental to the understanding of this operation by Indian authors.

For small numbers, multiplying the two numbers directly is the easiest way of finding the number’s square. However, with large numbers, which are common in astronomy, this can be cumbersome. As this was a very common operation, there was a need for simplifying operations when dealing with very large numbers.

One of the methods envisaged by Indian authors was to split the number into chunks and find squares individually. This is well known today as it was back then and was commonly used in manual computations.

Let’s say we want to compute the square of 102. The steps are as follows:

• Split this into 50 and 52

• Multiply these numbers together. This gives 2600

• Multiply this by 4. We get 10400.

• Add to this the square of the difference of the original numbers. The difference is 2. Its square is 4. Add it to the above number.

The final answer is 10404. These methods enable quick calculation of the varga.