Shunyam Saamyasamuccaye

*When the samuccaya is the same that samuccaya is zero*
Shunyam Saamyasamuccaye is the fifth

sutra of

Vedic mathematics. Its corollary is

Vestanam.

What follows is a

*brief* and

*incomplete* summary of the math shortcuts this sutra contains:

**The Many Definitions of "Samuccaya"**:

*Any Common Term*: The most simple (but incomplete) definition of samaccaya is to call it any term that is common to all the parts of a problem, such as Z in the equation

**1z + 3z = 5z + 6z**. Z would be the samaccaya, and in using this sutra we would assume z = 0

Another example would be the equation

**3(z + 1) = 5(z + 1)** The common term here is (z + 1), so in using this sutra we would assume z + 1 = 0, meaning z = -1

*The Product of the Independent Terms*:

We'll use this equation as our example:

**(1 + z) (2 + z) = (3 + z) (4 + z)**
Using this sutra, we would simplify the problem as

** 1 x 2 = 3 x 4** then as

**2 = 12** (which, obviously, is not true), so we would then assume z must equal zero for this equation to make sense.

*The sum of the two Denominators with the same Numerators*:

Example:

** 1/(3z - 1) + 1/(z - 1) = 0**
Because the numerator is 1 in both fractions, this definition of summaccaya tells us to combine the denominators and rewrite the equation as

**4z - 2 = 0**
The next step is to solve it like any algebra equation:

4z = 2

**z = 1/2**
"When the samuccaya is the same that samuccaya is zero" can also be applied to some other algebra problems and some problems involving

cubes. To learn more about Shunyam Saamyasamuccaye, 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