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.
Example:
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:
RESOURCES:
Vedic Mathematics by Sri Bharati Krisna Tirthaji
http://www.vedamu.org/Mathematics/course.asp
http://www.sanalnair.org/articles/vedmath/intro.htm
http://www.vedicganita.org/ganitsutras.htm
http://hinduism.about.com/library/weekly/aa062901a.htm
http://www.vedicmaths.org/
http://www.hinduism.co.za/vedic.htm
Mathemagics by Arthur Benjamin and Michael B. Shermer
http://en.wikipedia.org/wiki/Vedic_math
http://www.tifr.res.in/~vahia/dani-vmsm.pdf
http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html