Vilokanam: By Mere Observation

Vilokanam is the corollary to Shesanyankena Charamena, the twelfth sutra of Vedic mathematics.

This sutra is not a mathematical process like the other sutras and upsutras. This corallary serves to remind us to step back from a problem and observe it for an obvious solution or simplification.

Solve for x in the equation: x + ( 1/x ) = 10/3
By observation we see that 10/3 could be written as 3 1/3
That makes our equation: x + 1/x = 3 + 1/3
Therefore x = 3 or x = 1/3

So stepping back from the problem and merely observing it can sometimes lead to a fast solution. This is particularly true in the classroom setting, where algebra problems are usually set up such that the answer is a small whole number or a common fraction (such as 1/2).

Vilokanam can also be applied to algebra problems involving simultaneous equations, quadratic equations, etc., and to resolve certain algebraic equations into partial fractions. To learn more about Vilokanam, check out the resources below:

Vedic Mathematics by Sri Bharati Krisna Tirthaji
Mathemagics by Arthur Benjamin and Michael B. Shermer

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