vedic maths

The word vedic suggest that it is the maths originated from India. As far as I know it is the maths which makes the complex calculation simple as well as faster. Further I will show how to apply this in practice. Before that we will try to know some of it's  history and origin.

The ancient system of Vedic Mathematics was rediscovered from the Indian Sanskrit texts known as the Vedas, between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). At the beginning of the twentieth century, when there was a great interest in the Sanskrit texts in Europe, Bharati Krsna tells us some scholars ridiculed certain texts which were headed 'Ganita Sutras'- which means mathematics. They could find no mathematics in the translation and dismissed the texts as rubbish. Bharati Krsna, who was himself a scholar of Sanskrit, Mathematics, History and Philosophy, studied these texts and after lengthy and careful investigation was able to reconstruct the mathematics of the Vedas. According to his research all of mathematics is based on sixteen Sutras, or word-formulae.

Bharati Krsna wrote sixteen volumes expounding the Vedic system but these were unaccountably lost and when the loss was confirmed in his final years he wrote a single book: Vedic Mathematics, currently available. It was published in 1965, five years after his death. 

A copy of the book was brought to London a few years later and some English mathematicians took an interest in it. They extended the introductory material given in Bharati Krsna's book and gave many courses and talks in London. A book, Introductory Lecturees on Vedic Mathematics, was published in 1981.

Now let see how using a simple mental maths trick,this calculation can be done in a matter of seconds...

108 Squared    =   108 + 8 / 8 x 8
                     =   116 / 64
                     =   11,664

108 x 109 can be computed in one second by understanding this Pattern Recognition:

I add the excess of "8" to the other number "109" and then tag on the multiplication of those two excesses: "8" and "9".

108 x 109 = 109 + 8 / 8 x 9
                  =  117 / 72
                  =  11,772

To solve 98 Squared (98 x 98) we must first determine what Base we are in. It is close to 100, therefore we say Base 100. We must now choose one of the 16 Sutras to effectively solve the problem. It is called: "By The Deficiency":
"By whatever the deficiency, lessen it further by that much and set up the square thereof"
says one of the 16 Sutras. Sounds cryptic and meaningless yet it quickly solves the problem.
We get our answer by merely knowing how much is 100 less 98. Knowing that the deficiency is 2, we merely lessen 98 by 2 and then we tag on the squaring of that 2. As a one-line answer, the setting out would appear as thus:

98 Squared         = 98 ­- 2 / 2x2.   Simplifying it:
                        = 96 / _ 4
We almost have our answer. What we need to know is that since our Base is 100, it has 2 zeroes, therefore this fact governs the need for 2 spaces or 2 digits after the "forward slash" symbol ( / ). By inserting or inventing The Zero as a "Place Marker", the answer is achieved:
98 Squared         = 96 / 04
                        = 9,604.
(Perhaps the greatest invention of all time, the Hindu creation of the Zero was to change the world unimaginably as time passed on leading to the ability to send Vimana U.F.O craft and rockets into space, to supercomputers and thus the ancient and continuing battle between Michael and Lucifer:
Archangel Michael's Internal Light Vehicle Merkabah Time/Space Travel and Natural Spiritual Powers Versus Lucifer's daring invention of the External Merkabah or Artificial Technological Metal Spacecraft).

Observe similar examples:
97²        = 97 -­ 3 / 3x3
             = 94 / 09

96²        = 96 -­ 4 / 4x4
             = 92 / 16.
What if we enlarged our numbers to 998 Squared?
It is close to 1,000 so we say Base 1,000 and know to have 3 zeroes on the right hand side of the ( / ).
998²        = 998 -­ 2 / 2x2
               = 996 / _ _ 4
               = 996 / 004.
               = 996,004

Understanding this, you can be calculating digits in the millions:
9998²        = 9998 -­ 2 / 2x2
                 = 9996 / _ _ _ 4
(Since we are in Base 10,000 the 4 Zeroes determine the need for 4 digits after the ( / ).
                 = 9996 / 0004
                 = 99,960,004.

Generally theorems we studied in our colleges were not wrong but clumsy, and some of the western theorems were completely wrong or inadequate 

If we wanted to square the number 25, i.e. 25 x 25, we would conventionally take 3 lines of working out. Vedic Mathematics merely looks at the Question, applies one of the 16 Sutras, and solves it Mentally in One-Line. In this case, the Sutra at work is "By One More Than The Previous Digit". Observing that 25 is a 2 digit number, 5 is the last digit, but we are mainly interested in "the Previous Digit" which is 2. We say, mentally, "What is One more than Two?" It is 3. The word "By" in the Sutra really means "to multiply". The setting out for the first half of the answer is thus:
25² = 2 "By" 3 / ........
       = 2 x 3 / ........

To this we tag on the last digit "5" squared:
                             = 2 x 3 / 5 x 5
                             = 6 / 25
Thus the answer is 625. 
Similarly, all other numbers that end in 5, when squared, can be done instantly:
15² = 1 x 2 / 5 x 5          =  2 / 25    = 225
35² = 3 x 4 / 5 x 5          = 12 / 25   = 1,225

45² = 4 x 5 / 5 x 5          = 20 / 25   = 2,025
95² = 9 x 10 / 5 x 5        = 90 / 25   = 9, 025

Here is another simple Sutra,
the one that Bharati Krsna 

Tirthaji refers to as most widely used, called "Vertically and Crosswise" and solves all multiplication by application of a  pattern (which is registered by 

 the Right Brain as

Feminine-Natured Mathematics in contrast to the logical Male Left Brain style of moths you learnt at school.



For eg: To find 26 Multiplied by 31 in One-Line, we need to look at a Pattern,

viz: This  Sutra, known as: "Vertically and Crosswise" shows we will have

a 3-Digit Answer represented by the 3 short horizontal lines.
Here is how we traditionally write the setting out for "26 x 31":

  2 6
       x
  3 1

------

_ _ _
Notice there are 4 digits involved ( 2, 6, and 3, 1) and let them be represented by a small circle or dot and that explains the format seen in Fig 137e. This will help you to understand "CROSS ADDITION" which is shown as the middle part:

[ (2 x 1) + (6 x 3) ] and uses both multiplication and addition in the form of the letter "X" and corresponds to the "cross-over of the optical nerve in the brain" shown in Fig 137e below. (Here, the symbol "x" = Multiplication):

=         2 x 3      (2 x 1) + (6 x 3)       6 x 1

=           6                   ₂ 0                   6              (nb: the "2" of the “20” is carried over to the left hand side).             

=           8                      0                   6

= 806   

When scientists have a problem, say with electronic data, and they need to send it efficiently, the solution is invariably Compression. Digital Compression is a powerful Sutra that solves multiplication by 11 very quickly.

If we wanted to multiply 25 x 11 we merely add the two digits of the 25 and say "2 + 5" which is 7 and insert it between the two digits. Thus the answer is 275. Another way of showing this is to separate the two digits and insert their digital sum:

25 x 11      = 2   (2+5)   5
                 = 2      7      5

39 x 11   = 3   (3+9)   9
              = 3      ₁2     9    (nb, the "1" of the "12" gets carried over to the left)
              = 429