Vedic Mathematics

My first impression while writing about this topic was Vedic mathematics must be maths used during vedic period ....I think many will have such impression when u just read the topic...

But...........

VEDIC MATHEMATICS  is a book written by Indian monk Jagadguru Swami Sri Bharati Krishna Tirtha Sankaracarya of Govardhan Matha, Puri.

● His vast and versatile learning, his spiritual and educational attainments, his wonderful research achievements in the field of Vedic mathematics and his consecration of all these qualifications to the service of humanity as such. 

● His Holiness, better known among his disciples by the beloved name 'Jagadguru ' or ' Gurudev' , was born of highly learned and pious parent in March, 1884.

● Jagadguru, named as Venkatraman in his early days, was an exceptionally brilliant student and invariably won the first place in all the subjects throughout his educational career. He was awarded the title of ' SARASWATI' by the Madras sanskrit association in July, 1899.

● His public life under the guidance of late Hon'ble Sri Gopal krishna Gokhale , C.I.E in 1905 in connection with the National education Movement and the South African Indian issue. 

● His inclination towards Vedas was very much and the definition of Veda given by Sri Swami ji is.

" The very word 'VEDA' has this derivational meaning I.e. the FOUNTAINHEAD and ILLIMITABLE store house of all the knowledge "

VEDAS:

The vedas are wellknown as four in number 

1. Rigveda 

2. Samaveda 

3. Yajurveda 

4. Atharvaveda 

And have four Upavedas and the Six Vedangas.

● Swami ji naturally regarded mathematics or the science of calculations and computation to fall under this category. The Sixteen sutras on which the vedic mathematics is based form part of a Parisista of the Atharvaveda. 

1. Ekadhikena purvena 

     Meaning::  By one more than the previous 

 Very useful in finding the products of number .

2. Nikhilam Navatashcaramam Dashatah

     Meaning:: All from 9 and last from 10

3. Urdhav-Tribhagyam

    Meaning:: Vertically and crosswise

4. Paravartya Yojayet

    Meaning:: Transpose and adjust 

5. Sunyam Samyasamuccaye

    Meaning:: When the sum is same .That the                              sum is zero.

6. Anurupye Sunyamanyat

     Meaning:: If one is in the ratio the other is               equal to zero. This also used to                                 solve algebraic equations. 

 7. Sankalana vyavakalanabhyam

     Meaning:: By addition and subtraction. Mainly                          used for algebraic equations. 

 8. Puranapuranabhyam

     Meaning:: By completion and non completion. 

 9. Chalana kalanabhyam

     Meaning:: Difference and similarity. Mainly                                used in calculus to find square                                  roots of quadratic equations. 

10. Yavadunam

      Meaning:: Whatever is the extent of its                                       deficiency .

11. Vyastisamastih

      Meaning:: Part and whole. 

12. Sesanyankena Caramena

      Meaning :: The remainder by last digit.

13. Sopantyadvayamantyam

       Meaning:: The ultimate and twice the                                          penultimate. 

14. Ekanyunena Purvena 

       Meaning:: By one less than the previous. 

15. Gunitasamuccayah

        Meaning:: The product of the sum is equal                                 to the sum of product 

16. Gunakasamuccayah 

        Meaning:: The factor of the sum is equal to                               the factors.

Swami ji wants " Mathematics without tears " and using these sutras your mental calculations will definitely increase and u don't have to learn squares or use long traditional methods of multiplication and division and much more......

 

 Keep smiling and keep learning..😊😊😊

Multiples and Sub - Multiples

This is the continued part of previous post I.e, Multiplication. 

How to solve numbers with minimal calculations or mentally .Here we will discuss some more cases , where numbers are just half the base(10)

Or we can say near 5,50,500,5000,50000 etc.

Case 1.

41 x 41

Here we will take base as 50 (100÷2)

41-9

41-9

---------

41-9/9×9

32/81

But as we have assumed base as 50 because numbers are closer to 50. Base 50 is half of 100, so we will divide the answer by 2.

32÷2/81

16/81

= 1681 is answer.

       Or

Another way to solve the same problem .

41x41

Assume base as 10 

10 x 5=50

41-9

41-9

---------

32/81

X 5/

---------

160/81

As we have taken base 10 . So 8 will be carried over.

168/1

1681 answer. 

Why we have multiplied the above with 5. So if u are wondering then the answer is because we have taken the base as 10 and the number are closer to 50 base and to make it 50 we have multiplied it by 5.  Thus we have to multiply the answer  by 5.

 Or

Another way if you want to assume base as 40 because numbers are 41 x 41

Then 10 x 4= 40

So,

41 + 1

41 + 1

----------

41+1/1×1

42/1

×4

--------

168/1

1681 answer. 

EXAMPLE::

1. 49 x 49

Working  base 100/2

49-1

49-1

--------

48/01

÷ 2

----------

24/01=2401

  Or

Working base 10x5

49-1

49-1

-----------

48/1

×5

-----------

240/1

2401 answer.

Example 2

23 x 21

Working base 10 x 3= 30

23 - 7

21 - 9

-------------

23-9/ 7x9

14/63

×3

-------------

42/63

6 will be carried over because of base 10 

48/3

483

Or

Working base 10x2

Then

23+3

21+1

---------

24/3

×2

--------

48/3

483 answer.

● Direct short cut for square. Using the first corollary which is arising out of the 'Nikhilam ' Sutra means : whatever the extent of its deficiency, lessen it still further to that very extent and also set up  the square of that deficiency. 

 A. 9x9 

9-1

9-1

-------

9-1/1×1

8/1

81

B. 7 x 7

 (7-3)/3^2

4/9=49

C. 11^2 = (11+1)/1^2=121

D. 12^2=(12+2)/2^2= 144

E. 13^2 =(13+3)/3^2=169

F. 14^2 =(14+4)/4^2= 18/16=196

G . 15^2 =(15+5)/5^2= 20/25=225

And so on.....

In the next post we will learn how to write table quickly ... by using simple techniques  of the same sutra....rather than memorizing it....

Keep learning. Keep smiling 😊😊😊

 

learning table of 9 in seconds.

This post is really interesting to write as we all must have struggled in our childhood while learning tables or youngs student must be ....as its tedious task to learn so many tables....so here we have some techniques or ways to solve tables in less time.

The First case.

The annexed table of products produced by the single digit multiplier 9 gives us the necessary clue to an understanding of the sutra:

The meaning of the sub corollary thus fits in smoothly I.e, that the multiplicand has to be decreased by 1 and as for the right hand side , that is mechanically available by the subtraction of the left hand side from 9 which is practically a direct application of the Nikhilam Sutra.

● 9 x 2

(2-1)/(9-(2-1))

1/9-1

1/8

18 answer.

● 9 x 3

(3-1)/9-(3-1)

2/7

27 answer.

The second case::

● 11 x 99

(11 - 1)/99-(11-1) = 1089

● 12 X 99

( 12-1)/99-(12-1)=1188

And so on.....

Keep learning keep smiling 😊😊