VEDIC SCIENCE
nterest
in Vedic maths is growing in the field of education where math’s
teachers are looking for a new and better approach to the subject. Even
students at IIT (Indian Institute of Technology) are said to be using
this ancient technique for quick calculations. No wonder, a recent Convocation
speech addressed to the students of IIT, Delhi, Indian Minister for
Science & Technology, stressed the significance of Vedic math’s,
while pointing out the important contributions of ancient Indian
mathematicians, such as Aryabhatta, who laid the foundations
of algebra, Baudhayan, the great geometer, and Medhatithi and Madhyatithi,
the saint duo, who formulated the basic framework for numerals.
Few of Vedic examples (The Magic of Vedas)
(VEDIC MATH’S FORMULAE):- THERE ARE 16 SUTRA’S
| SUTRA | MEANING | |
| 1 | Ekadhikina Purvena | By one more than the previous one |
| COROLLARY: Anurupyena | ||
| 2 | Nikhilam Navatashcaramam Dashatah | All from 9 and the last from 10 |
| COROLLARY: Sisyate Sesasamjnah | ||
| 3 | Urdhva-Tiryagbyham | Vertically and crosswise |
| COR: Adyamadyenantyamantyena | ||
| 4 | Paraavartya Yojayet | Transpose and adjust |
| COR: Kevalaih Saptakam Gunyat | ||
| 5 | Shunyam Saamyasamuccaye | When the sum is the same that sum is zero. |
| COROLLARY: Vestanam | ||
| 6 | (Anurupye) Shunyamanyat | Sankalana-vyavakalanabhyam |
| COROLLARY: Yavadunam Tavadunam | ||
| 7 | Sankalana-vyavakalanabhyam | By addition and by subtraction |
| COR: Yavadunam Tavadunikritya Varga Yojayet | ||
| 8 | Puranapuranabyham | By the completion or non-completion |
| COROLLARY: Antyayordashake'pi | ||
| 9 | Chalana-Kalanabyham | Differences and Similarities |
| COROLLARY: Antyayoreva | ||
| 10 | Yaavadunam | Whatever the extent of its deficiency |
| COROLLARY: Samuccayagunitah | ||
| 11 | Vyashtisamanstih | Part and Whole |
| COROLLARY: Lopanasthapanabhyam | ||
| 12 | Shesanyankena Charamena | The remainders by the last digit |
| COROLLARY: Vilokanam | ||
| 13 | Sopaantyadvayamantyam | The ultimate and twice the penultimate |
| COR: Gunitasamuccayah Samuccayagunitah | ||
| 14 | Ekanyunena Purvena | By one less than the previous one |
| COROLLARY: Dhvajanka | ||
| 15 | Gunitasamuchyah | The product of the sum is equal to the sum of the product |
| COROLLARY: Dwandwa Yoga | ||
| 16 | Gunakasamuchyah | The factors of the sum is equal to the sum of the factors |
| COROLLARY: Adyam Antyam Madhyam | ||
| 1 | EKADHIKENA PURVENA The Sutra (formula) Ekadhikena Purvena means: “By one more than the previous one”. |
| i)
Squares of numbers ending in 5 :
Now we relate the sutra to the ‘squaring of numbers ending
in 5’. Consider the example 252.
Here the number is 25. We have to find out the square of the number.
For the number 25, the last digit is 5 and the 'previous' digit
is 2. Hence, 'one more than the previous one', that is, 2+1=3.
The Sutra, in this context, gives the procedure 'to multiply the
previous digit 2 by one more than itself, that is, by 3'. It becomes
the L.H.S (left hand side) of the result, that is, 2 X 3 = 6.
The R.H.S (right hand side) of the result is 52, that is, 25.
|
|
| Thus: - 252 = 2 X 3 / 25 = 625. | |
| In the same way, | |
| 352= 3 X (3+1) /25 = 3 X 4/ 25 = 1225; | |
| 652= 6 X 7 / 25 = 4225; | |
| 1052= 10 X 11/25 = 11025; | |
| 1352= 13 X 14/25 = 18225; | |
| Algebraic proof: | |
| a) Consider (ax + b)2 ? a2. x2 + 2abx + b2. | |
| This identity for x = 10 and b = 5 becomes | |
| (10a + 5)2 = a2 . 102 + 2. 10a . 5 + 52 | |
| = a2 . 102 + a. 102 + 52 | |
| = (a 2+ a ) . 102 + 52 | |
| = a (a + 1) . 102 + 25. | |
| Clearly 10a + 5 represents two-digit numbers 15, 25, 35, -------,95 for the values a = 1, 2, 3, -------,9 respectively. In such a case the number (10a + 5)2 is of the form whose L.H.S is a (a + 1) and R.H.S is 25, that is, a (a + 1) / 25. | |
| Thus any such two digit number gives the result in the same fashion. | |
| Example:
45 = (40 + 5)2, It is of the form (ax+b)2
for a = 4, x=10 and b = 5. giving the answer a (a+1) / 25 that is, 4 (4+1) / 25 + 4 X 5 / 25 = 2025. |
|
| b) Any three digit number is of the form ax2+bx+c for x = 10, a ? 0, a, b, c ? W. | |
| Now (ax2+bx+ c) 2 = a2 x4 + b2x2 + c2 + 2abx3 + 2bcx + 2cax2 | |
| = a2 x4 +2ab. x3+ (b2 + 2ca)x2+2bc . x+ c2. | |
| This identity for x = 10, c = 5 becomes (a . 102 + b .10 + 5)2 | |
| = a2.104 + 2.a.b.103 + (b2 + 2.5.a)102 + 2.b.5.10 + 52 | |
| = a2.104 + 2.a.b.103 + (b2 + 10 a)102 + b.102+ 52 | |
| = a2.104 + 2ab.103 + b2.102+ a . 103 + b 102 + 52 | |
| = a2.104+ (2ab + a).103 + (b2+ b)102 +52 | |
| = [ a2.102 + 2ab.10 + a.10 + b2 + b] 102+ 5 | |
| = (10a + b) ( 10a+b+1).102 + 25 | |
| = P (P+1) 102 + 25, where P = 10a+b. | |
| Hence any three digit number whose last digit is 5 gives the same result as in (a) for P=10a + b, the ‘previous’ of 5. | |
| Example : 1652 = (1 . 102 + 6 . 10 + 5)2. | |
| It is of the form (ax2 +bx+c)2 for a = 1, b = 6, c = 5 and x = 10. It gives the answer P(P+1) / 25, where P = 10a + b = 10 X 1 + 6 = 16, the ‘previous’. The answer is 16 (16+1) / 25 = 16 X 17 / 25 = 27225. | |
| Similar to this other sutra’s has there benefits and mathematic implications to solve the problems. | |
| The other degree programs under this department will be | |
| Course & Duration | |
| BSc/ M B A in Moral science, a 3/ 2 years program | |
| BSc/ M B A in Human psychology a 3/ 2 years program | |
| BSc/ M Sc in Botany a 3/ 2 years program | |
| M B A in Human behavior (Marketing) |