India has a rich history of intellectual progress and knowledge cultivation that has spanned many ages. At the core of this extensive academic heritage lies the field of mathematics, a discipline that has been highly esteemed and revered since ancient times, particularly during the era of the ancient Vedas.
Over the course of millennia, this complex discipline has been diligently refined and perfected, with each generation meticulously preserving, enhancing, and passing down this invaluable reservoir of knowledge to the next. This unwavering commitment to mastering and disseminating mathematical principles underscores India’s enduring role as a vibrant center for intellectual exploration and scholarly dialogue.
Amidst the numerous contributions to mathematics, Vedic mathematics stands out as a distinctive collection of efficient and expeditious techniques for solving mathematical arithmetic problems. This system is built upon 16 sutras or principles, each representing a word formula that encapsulates a natural approach to solving a wide range of mathematical challenges.
The credit for the inception of this remarkable technique goes to the renowned scholar Shri Bharathi Krishna Tirthaji Maharaj, who was a luminary in the fields of Sanskrit, Mathematics, History, and Philosophy. His groundbreaking work infuses mathematical solutions with simplicity and speed, introducing a fresh dimension to the field and exemplifying India’s ingenious mathematical spirit.
Below are the 16 Vedic Maths Sutras with brief explanations:
1. Ekadhikena Purvena (One more than the previous one): This sutra is useful for cases where the number is close to the base, like 10, 100, 1000, etc. It is mainly used in finding squares of numbers near these bases.
2. Nikhilam Navatashcaramam Dashatah (All from 9 and the last from 10): This sutra is helpful when you are subtracting a number from a large round number like 10, 100, 1000, etc.
3. Urdhva-Tiryakbhyam (Vertically and crosswise): This sutra is useful for multiplication of numbers where the multipliers are more than the number 10. It can also be applied for the multiplication of numbers close to bases (10, 100, 1000, etc).
4. Paravartya Yojayet (Transpose and adjust): This sutra is used in division. It makes any type of division simple.
5. Shunyam Saamyasamuccaye (When the sum is the same that sum is zero): This sutra is used in solving simultaneous linear equations where the coefficients of the variables are the same. The sum (or, difference) of the coefficients in the variables of these equations is zero.
6. Anurupye – Sunyamanyat (If one is in ratio, the other one is zero): Used in solving simultaneous linear equations, this sutra comes into play when the coefficients of one variable are in the same ratio to each other as the independent terms.
7. Sankalana-vyavakalanabhyam (By addition and by subtraction): This sutra is used to solve a special type of simultaneous linear equations where the coefficients of ‘x’ and ‘y’ are interchanged.
8. Purana Puranabhyam (By the completion or non-completion): When the given data is incomplete, this method helps us to find the complete data first and then solve the problem.
9. Chalana-Kalanabhyam (Differences and Similarities): This sutra is mainly used for solving the problems where differentiation is involved.
10. Yaavadunam (As much as the extend): This sutra is useful in the operations involving ‘0’. It helps in case of multiplication.
11. Vyashtisamanstih (Part and Whole): This is applied to find the product of two numbers when one number is far away from the base. It is also useful in solving complex numbers and statistics.
12. Shesanyankena Charamena (The remainders by the last digit): This one helps in finding the remainders of division problems. It’s used when we divide a number by 9.
13. Sopaantyadvayamantyam (The ultimate and twice the penultimate): Applicable when the multiplication of numbers whose last digits together make 10 and the remaining digits are identical.
14. Ekanyunena Purvena (One less than the previous one): This sutra is used for the multiplication of numbers whose last digits add up to 10 and the preceding numbers are the same.
15. Gunitasamuchyah (The product of the sum is the sum of the product): This sutra is used in solving problems related to algebra and geometry.
16. Gunakasamuchyah (The factor of the sum is the sum of the factor): This sutra can be applied in factorization and solving algebraic equations.
