Origin of Vedic Mathematics
Origin of Vedic Maths or Vedic Ganit
At the beginning of the twentieth century, when there was a great interest in the Sanskrit texts in Europe, Bharati Krsna Swamiji 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 Swamiji, 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, which you can find in the book named Vedic Mathematics by Bharati Krsna Tirthaji. These sutras 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. The term Vedic Mathematics now refers to a set of sixteen mathematical formulae or sutras and their corollaries derived from the Vedas.
You can find more details about Origin of Vedic Maths here at wikipedia - http://en.wikipedia.org/wiki/Bharati_Krishna_Tirtha's_Vedic_mathematics
Base Method of Multiplication
Base method of multiplication derived from Vedic Mathematics can be applied for multiplication of two numbers close to 100.
This post in is in continuation of an earlier post named "Vedic Multiplication of two numbers close to hundred". Though you can understand this post stand alone, yet I'll recommend you to read the linked post before reading this one.
In this post I'll explain how to multiply two numbers lesser than the base (in this case 100). In the earlier post it was about both numbers more than 100.
Trick to Find Square of Numbers from 51 to 59
I’ll share with you one simple method of finding the square of numbers between 50 and 60. Like many other Vedic Mathematics methods, in this method also, we will get the answer in two parts. Since the numbers are in 50s and square of 50 is 2500, we will just use 25 in our calculations, ignoring the zeros.
- To get the first part of the answer, add the digit at the units place to 25 and write the sum
- To get the second part, calculate the square of units place digit and write it
It’ll be easier to understand this with an example.
Vedic Multiplication Trick
Multiplication Method - multiplying 2 numbers starting with same digit(s)
This vedic maths trick will help you in multiplying two numbers when these numbers start with the same digit. For example 34 x 37; see their ten’s digit (starting digit) is same. Another example can be 234 x 232, see their hundred’s and ten’s digits (starting two digits) are same.
In one of the earlier post a similar method was described. In that like this trick the starting digit(s) should be same but at the same time the sum of digit at unit’s place should be 10 – please check that out - Vedic multiplication
Vedic Division by Nine
Friends, this time it has been a long time I have written a post. I badly wanted to write one but because of very busy schedule I couldn't.
This post is one of the many areas where Vedic Mathematics really surpasses traditional methods as you shall soon see. This post is about dividing any number by 9.
We will start by taking an example
Divide 200103002 by 9
Division in Vedic Mathematics
There are so many shortcuts for multiplication but hardly any shortcuts for division. Nandeesh has translated a Sanskrit Sutra to reduce long division to one line short-cut. Join me in thanking him for his great efforts.
Long Division reduced to one-line shortcut
Example 1: 716769 ÷ 54.
Reduce the divisor 54 to 5 pushing the remaining digit 4 “on top of the flag” (Dhvajanka so to say).
Corresponding to the number of digits flagged on top (in this case, one), the rightmost part of the number to be divided is split to mark the placeholder of the decimal point or the remainder portion.
Let us walk through the steps of this example:
716769 ÷ 54 = 13273.5
Finding Cube Root – Vedic Maths Way
This is an amazing trick which was always appreciated by the audience I have addressed in various workshops. This awe inspiring technique helps you find out the cube root of a 4 or 5 or 6 digits number mentally.
Before going further on the method to find the cube root, please make a note of the following points –
1) Cube of a 2-digit number will have at max 6 digits (99^3 = 970,299). That implies if you are given with a 6 digit number, its cube root will have 2 digits.
2) This trick works only for perfect cubes, it will not work for any arbitrary 6-digit
3) It works only for integers
Find the remainder – Vedic Algebra
Vedic Algebra
I have got a mail from some QuickerMaths follower, to illustrate usage of Vedic Mathematics in branches of mathematics other than arithmetic. This post is for that purpose only. Here I am highlighting the usage of Vedic Mathematics in finding out the remainder when an algebraic expression is divided by another.
Finding out the remainder becomes extremely easy using Vedic Maths.
So lets begin with a simple example -
Find the remainder when
x3 + 4x2 + 6x - 7 is divided by (x + 5)
Solution:
Vedic Mathematics Techniques for Finding HCF
Vedic Maths Trick to find the HCF of Algebraic Expressions
To appreciate the Vedic Maths process of finding the HCF you first need to know the other methods taught in school. I am giving you two other methods to compare with.
Example 1: Find the H.C.F. of x^2 + 5x + 4 and x^2 + 7x + 6.
Checking of Calculations: Casting Out Nines
While doing arithmetic calculations, we should normally check our calculation. But the checking should not be as tedious as the original problem. To solve this problem I am explaining below a very frequently used method which is discussed in Vedic Mathematics as well as by many other mathematicians.
Vedic Sutra: Vedic Mathematics Technique
Beejank: The Sum of the digits of a number is called Beejank. If the addition is a two digit number, then these two digits are also to be added up to get a single digit.
Find the Beejank of 632174.
As above we have to follow
632174 --> 6 + 3 + 2 + 1 + 7 + 4 --> 23 --> 2 + 3 --> 5
But a quick look gives 6 & 3 ; 2 & 7 are to be ignored because 6+3=9,2+7=9.
Hence remaining 1 + 4 --> 5 is the beejank of 632174.
Checking of Addition
Thumb Rule: Whatever we do to the number, we also do to their digit sum: then the result we get from the digit sum of the number must be equal to the digit sum of the answer.
For example: The number: 12+45+96+75+25 =253
The digit sum = 3+9+6+3+7 =28=10=1
Answer’s digit sum: 2+5+3 =10=1 (verified)
Another example: 3.5+23.4+17.5 = 44.4
The digit sum: 8+9+13=8+9+4=21=3
Answer’s digit sum: 12=3 (verified)
Casting Out Nines
This method is also known as "casting-out-nines". The method involves converting each number into its "casting-out-nines" equivalent, and then redoing the arithmetic. The casting-out-nines answer should equal the casting-out-nines version of the original answer. Below are examples for using casting out nines to check addition.
We get the casting-out-nines equivalent of a number by adding up its digits, and then adding up those digits, until you get a one digit number. If our answer is 9, then that becomes 0. As a short cut, we don't have to add in any of the 9's in our work, as these are the equivalent of 0. We can just "cast out" those 9's. For example, 19 becomes 1, without even adding 1 and 9 and getting 10, and then adding 1 and 0 and getting 1. As a further short cut, we can group numbers together which add up to 9, and replace them with 0. 2974 becomes 4, because we can cast out the 9 and the 2+7 (which is also 9 or 0). Well, let's try an arithmetic problem:
137892 3
+ 92743 + 7
------ --
230635 1
3+7=10, casting out 9 we get 1.
This rule is also applicable to subtraction, multiplication and up to some extent to division also
In the next post I will explain the use of this method for all of them.
Who is behind QuickerMaths?
I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more
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Recent Comments
watchman was paid for awaking not for sleeping so that he can see dreams.. – 05Feb12
as a night watchman he shouldnt have slept at night to get that dream... – 04Feb12
Can u plz give me clarity in ur solution Kaush sir..... – 04Feb12
thanks for these tricks. Are these from the book "quicker maths by m.tyra" ? – 03Feb12
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