Vedic Mathematics, as the name implies, is drawn from the Vedas, a Hindu scripture. The methodology used is simple and straight forward. It facilitates faster calculation speed. Arithmetic calculation can be without the need for extensive memorization of tables. Most of the times the calculations can be done mentally, obviating the need for writing them down. Vedic Mathematics can be applied to trigonometric problems. It can be used in astronomical calculations like the positions of planets.
There are sixteen Sutras, (Main rules are called Sutras) and thirteen sub Sutras (corollaries) in Vedic Mathematics. Jagadguru Swami Bharathi Krishna Thirtha (1884-1960) of Sri Govardhana Mutt, Puri , after extensive research rediscovered these sutras. Jagadguru writes (Vedic Mathematics XXXV)
“The Sutras (aphorisms) apply to and cover each and every part of each and every chapter of each and every branch of mathematics (including arithmetic, algebra, geometry- plane and solid, trigonometry- plane and spherical, conics-geometrical and analytical, astronomy, calculus-differential and integral etc.). In fact, there is no part of mathematics, pure or applied, which is beyond their jurisdiction.”
The following are the Sutras
| Sutra |
Translation |
| एकाधिकेन पूर्वेन | By one more than the one before |
| निखिलं नवतश्चरमं दशतः | All from 9 and the last from 10 |
| ऊर्ध्वतिर्यग्भ्याम् | Vertically and Cross-wise |
| परावर्त्य योजयेत् | Transpose and Apply |
| शून्यं साम्यसमुच्चये | If the Samuccaya is the same it is zero |
| आनुरूप्ये शून्यं अन्यत् | If one is in Ratio the other is zero |
| संकलन व्यवकलनाभ्यां |
By Addition and by subtraction |
| पूरणापूरणाभ्यां |
By the completion or Non-completion |
| चलनकलनाभ्याम् |
Differential Calculus |
| यावदूनं |
By the Deficiency |
| व्यष्टिसमष्टिः |
Specific and general |
| शेषाण्यडेन चरमेण |
The Remainders by the last digit |
| सोपान्त्यदयमन्त्यं |
The ultimate and twice the penultimate |
| एकन्यूनेन पूर्वेन |
By one less than the one before |
| गुणितसमुच्चयः |
The Product of the Sum |
| गुणकसमुच्चयः |
All the Multipliers |
The Trachtenberg speed system of Basic Mathematics is somewhat similar to vedic Mathematics. Jackaow Trachtenberg, a Russian Born Engineer discovered this method. He derived the whole system while being detained in a Nazi concentration camp.
Let us start examining the vedic sutras one by one. There is no special meaning attached to the order in which the sutras are discussed.
The sutra एकाधिकेन पूर्वेन meaning “By one more than the previous one ” is applied in practice as under:
To find the answer for the mathematical sum 1/19 to an accuracy of 18 digits. Answer = 0.052631578947368421
Step 1 : The number which is previous to the last digit 9 is 1 (1 9) and therefore one more than that is 2
Step 2 : Divide the numerator 1 by 2. The quotient is 0 and reminder is 1. Therefore the first decimal digit of the answer should be 0
Step 3 : Take the quotient 0 and Prefix the reminder 1 to it to get the number 10. Divide that by to get quotient 5 and reminder as 0. The second digit of the answer is therefore 5
Step 4 : The reminder in previous step is 0 and when prefixed to get quotient 5 we get the digit 5. Divide that by 2 to get Quotient 2 and reminder 1. The third digit of the answer is therefore 2
Step 5 : Divide 12 ( prefix reminder 1 to quotient 2) by 2 to get 6 as quotient and reminder 0. The fourth decimal of the answer is 6.
Step 6 : Divide 6 (reminder 0 prefixed to quotient 6 is 6) by 2 to get 3 as quotient and 0 as reminder. Therefore the fifth decimal of the answer is 3.
Repeat the same procedure to get the answer, 0.052631578947368421.
It can be seen that the digits after the first 9 digits are complements of 9.
Therefore one need to workout only the first 9 decimal digits and then subtract each from 9, starting with first decimal digit and write down the result.
That is simple !!!