Vedic Math Ancient Sutras - Basic Mental Math

The latest research in Vedic Math suggests that there are sixteen ancient Vedic Sutras which have been expanded upon by an additional thirteen sub-Sutras or math corollaries.

A brief discussion on each of these is in order.

The 16 Vedic Math Sutras as applicable to mathematics:

1. "Ekadhikena Purvena" (By one more than the previous one) The working of the Sutra is quite simple. In the case of the vulgar fraction 1/19 whose denominator ends with 9, in the normal method 18 steps are required. But with this Sutra it can be accomplished in only one step. The actual calculations and steps are beyond the scope of this writing. This is just to show the ease with which we can apply Vedic mathematics to everyday calculations as well as for solving complex equations.

2. "Nikhilam Navatascaramam Dasatah" (All from 9 and the last from 10) This is a cryptic Sutra for multiplying numbers. According to Vedic Math multiplication tables are not required beyond the 5 multiplied by 5. It is claimed that with this sutra multiplication becomes a Childs play.

3. "The Urdhva Tiryaghyam Sutra" (Vertically and crosswise multiplications) This is another short Sutra for multiplication

4. "Paravartya Yojayet" (Transpose and apply) This Sutra is used to solve simple equations

5. "Sunyam Samyasamuccaye" i.e. If the Samuccaya is the same (on both sides of the equation, then) that Samuccaya is (equal to) zero This Sutra is used to solve special type of equations. "Samuccaya" is a technical term which has several meanings in different contexts. In fact, a single word taking on different meanings is the beauty of Sanskrit text. At the same time it is also confusing and confounding to those who have not mastered the language. If looked at it from different angles, Sanskrit is a boon as well as a bane. Misunderstanding and misinterpreting is quite common among scholars. In as much as the scriptures are concerned, the meaning of words becomes all the more important.

6. "(Anurupye ) Sunyamanyat" ( If one is in ratio the other one is zero) There are some simultaneous equations which may involve large numbers and may therefore seem hard to solve, but owing to certain ratios between the coefficients can be readily and easily solved using this Sutra.

7. "Sankalana-vyavakalanabhyam"

8. "Puranapuranabhyam"

9. "Calana-kalanabhyam"

The above three Sutras are used in solving different types of quadratic equations.

10. "Yavadunam" This Sutra is used for squaring and cubing.

11. "Vyastisamastih"

12. "Sesanyankena Caramena"

13. "Sopantyadvayamantyam"

14. "Ekanyunena Purvena"

15. "Gunitasamuccayah"

16. "Gunakasamuccayah"