Hindu Contribution to Mathematics

[Vinod2070]

Guys, I think we can do "baal ki khaal nikalanaa" for all we want on the issue of Hindu/Indian etc. That would be an interesting topic as well but here it is a bit off topic.

For the purpose of this discussion, there is no disconnect between the two terms. The mathematicians involved were practicing religious folks devoted to both the religion and maths. Let's get on with the topic.

 

[johnee]

This post is off-topic.

 

[johnee]

Guys, I think we can do "baal ki khaal nikalanaa" for all we want on the issue of Hindu/Indian etc. That would be an interesting topic as well but here it is a bit off topic.

For the purpose of this discussion, there is no disconnect between the two terms. The mathematicians involved were practicing religious folks devoted to both the religion and maths. Let's get on with the topic.

Thanx for the timely reminder. Lets get on the topic, now.

Here is a good method from vedic maths that will make the multiplications easy:

NIKHILAM NAVATAS’CHARAMAM DASATAH

The formula simply means : “all from 9 and the last from 10”

The formula can be very effectively applied in multiplication of numbers, which are nearer to bases like 10, 100, 1000 i.e., to the powers of 10(eg: 96 x 98 or 102 x 104). The procedure of multiplication using the Nikhilam involves minimum number of steps, space, time saving and only mental calculation. The numbers taken can be either less or more than the base considered.

Case (i) : when both the numbers are lower than the base.
Find 97 X 94. Here base is 100. Now following the rules, the working is as follows: 97 is 3 less than the nearest base 100. and 94 is 6 less than the same nearest base 100. Hence 3 and 6 are called deviations from the base. Always the base should be same for the two numbers.

=91/18=9118
Note: Here '/' signifies just a seperation and has nothing to do with division.
In genreal, let N1 and N2 be two numbers near to a given base in powers of 10, and D1 and D2 are their respective deviations from the base. Then N1 X N2 can be represented as:

Case ( ii) : When both the numbers are higher than the base.
The method and rules follow as they are. The only difference is the positive deviation. Instead of cross – subtract, we follow cross – add.104 X 102. Base is 100.

Note: We are considering 04x02=08 and appending '08' and not just '4x2=8'. This is done because, we need to consider two digits in deviation as it the base 100 has two zeros. If the deviation is near 1000 then we need to consider 3 digits in the deviation (eg, 004 and not just 4).

Case ( iii ): One number is more and the other is less than the base.
In this situation one deviation is positive and the other is negative. So the product of deviations becomes negative. So the right hand side of the answer obtained will therefore have to be subtracted. To have a clear representation and understanding a vinculum is used. It proceeds into normalization. 13 X 7. Base is 10

10/(-9)=91 how?

10/(-9) should be read as 'one zero, nine bar'. Here 'one' and 'zero' are in normal form. 'nine' is in complement form. so, when we bring a carry from normal form to complment form, '10' becomes '9' and '9-bar' becomes '1'( 10's complement of 9). Hence 10/(-9)-91.

Another example would be 94/(-3)=93/7=937.

Find the following products by Nikhilam formula.
1) 7 X 4 2) 93 X 85 3) 875 X 994 4) 1234 X 1002


5) 1003 X 997 6) 11112 X 9998 7) 1234 X 1002 8) 118 X 105

 

[Vinod2070]

Again, my 2 cents on the issue are that Hinduism (sic) being a 5000 year old faith system has undergone massive changes over a long period. It is quite correct to say that the current practices may be quite different from practices 1000 years back, 2000 years back and so forth. Massive corruptions also came in the religion and several attempts were made even thousands of years back to reform the religion or way of life or whatever we may want to call it.

I think any religion this old will go through many of the same issues. We can probably look at the concept of "panths" or path to God that we have. So we are all Indians but many of us have chosen different paths o God. That doesn't change our identity of being Indians or our origins. Some feel that that common identity can be called Hindu but that can be confused with the religion as well. Some will see no contradictions in this.

I don't think we need to care a damn about the origin of the term Hinduism. We understand it in the context of the belief system of the majority of Indian people now and we don't care what the Persians may think of that.

 

[Dark_Prince]

LOL hahhhahahha where did my post disappear? I clearly explained how word Hindu belongs to all citizens irrespective to their religion as mostly everyone has Vedic lineage!!

I searched for the post and its not there, Not even in deleted section!

 

[johnee]

Dark Prince,
Lets get back on the topic:

Here is a method(very very easy one) for multiplying any number with eleven:

Multiplying a number by 11 in Vedic Maths.

To multiply any 2-figure number by 11 we just put
the total of the two figures between the 2 figures.
26 x 11 = 286
Notice that the outer figures in 286 are the 26
being multiplied.
And the middle figure is just 2 and 6 added up.
So 72 x 11 = 792

Try these for practise:
Multiply by 11:
1) 43 =
2) 81 =
3) 15 =
4) 44 =
5) 11 =

Now, next example:

77 x 11 = 847
This involves a carry figure because 7 + 7 = 14
we get 77 x 11 = 7147 = 847.

Try these for Practise:
Multiply by 11:
1) 11 x 88 =
2) 11 x 84 =
3) 11 x 48 =
4) 11 x 73 =
5) 11 x 56 =

Three-digit number multiplication with eleven:

234 x 11 = 2574
We put the 2 and the 4 at the ends.
We add the first pair 2 + 3 = 5.
and we add the last pair: 3 + 4 = 7.

Try these for practise:
Multiply by 11:
1) 151 =
2) 527 =
3) 333 =
4) 714 =
5) 909 =

 

[Vinod2070]

^^ Can you check again? The thread was merged and demerged and I think some posts didn't make their way back earlier.

 

[Dark_Prince]

^^ Can you check again? The thread was merged and demerged and I think some posts didn't make their way back earlier.

I hv checked and its not there! Not a Prob! Thanks!

 

[Dark_Prince]

Nice 11 ka quna!clap

 

[Vinod2070]

I hv checked and its not there! Not a Prob! Thanks!

Were you not talking of this post?

Yusufji,

What this articles tries to signify is the contribution of the Hindu people, who lived across Hindu/Sindhu river, when whole of India was Hindu (including localized cultures). The contributions are during pre-dominantly Golden Hindu period, and credit attributes to all Indian's, as majority can trace their lineage (ancestry) to Vedic Hindu Culture!!

 

[johnee]

Guys, appreciate the genius of our rishis, appreciate the knowledge mine that is our veda/purana/upanishad/itihaas and appreciate our great civilization and its progress. The methods of calculation taught in vedic system by the wise rishis seem to be more advanced than the rudimentary ones we are taught today.

Here are a few famous quotes:

"Access to the Vedas is the greatest privilege this century may claim over all previous centuries."

-- Julius Robert Oppenheimer

"Wherever we direct our attention to Hindu literature the notion of infinity presents itself."

-- Sir William Jones

"In the history of the world the Vedas fill a gap which no literary work in any other language could fill. I maintain that to everybody who cares for himself for his ancestors for his intellectual development a study of the Vedic literature is indeed indispensable."

-- Professor F. Max Muller

Ok, lets get back to the maths: Here is a method from the treasure trove of vedas to divide any number by 9 upto any number of decimals. Interestingly, you dont even have to know the 9 table to calculate this. Anyone, who knows simple addition can do this. So here is the Vedic method of dividing a number by 9:

Vedic Maths


Method of dividing by 9


23 / 9 = 2 remainder 5
The first figure of 23 is 2, and this is the answer.
The remainder is just 2 and 3 added up!
43 / 9 = 4 remainder 7
The first figure 4 is the answer
and 4 + 3 = 7 is the remainder - could it be easier


Try these for practise:
Divide by 9:
1) 61 / 9 = and remainder=
2) 33 / 9 = and remainder=
3) 44 / 9 = and remainder=
4) 53 / 9 = and remainder=
5) 80 / 9 = and remainder=


Dividing a 3-digit number:

134 / 9 = 14 remainder 8
The answer consists of 1,4 and 8.
1 is just the first figure of 134.
4 is the total of the first two figures 1+ 3 = 4,
and 8 is the total of all three figures 1+ 3 + 4 = 8.

Try these for practise:
6)232 = and remainder=
7) 151 = and remainder=
8) 303 = and remainder=
9) 212 = and remainder=
10) 2121 = and remainder=

Dividing a more sophisiticated number:

842 / 9 = 812 remainder 14 = 92 remainder 14
Actually a remainder of 9 or more is not usually
permitted because we are trying to find how
many 9's there are in 842.
Since the remainder, 14 has one more 9 with 5
left over the final answer will be 93 remainder 5

Try these for practise:

1) 771 / 9 = and remainder=
2) 942 / 9 = and remainder=
3) 565 / 9 = and remainder=
4) 555 / 9 = and remainder=
5) 2382 / 9 = and remainder=
6) 7070 / 9 = and remainder=

Decimals Equivalents of Fractions:

We can easily remember the decimal equivalents of any fraction whose denominator is 1. So here is the list:

1/9 = .111...
2/9 = .222...
3/9 = .333...
4/9 = .444...
5/9 = .555...
6/9 = .666...
7/9 = .777...
8/9 = .888...

lets go back to the division.

Here is an example:

942/9.

First find the remainder, which is obtained by adding all the digits. So, remainder of 942/9= 9+4+2=15.
But 15 is greater than 9. So, substract 15 from 9, we get 6. This is the actual remainder. But now, we will have to add 1 to the quotient we get. So, 1 is the carry over.

So, Remainder=6
and carry over=1

Now, the quotient.

left digit is obtained by adding all the digits upto the last-but-one digit.
=> 9+4=13.
But we had a carry over of 1. So, add it.
=> 13+1=14.
So, 4 is the left digit and 1 is the carry.

Lets find the next digit:

The next digit is nothing but 9 itself. But we had a carry of 1. So add it. 9+1=10.

So, arrange the two numbers side by side. 10 and 4. The quotient is 104.


Now, 942/9 gives us quotient as 104 and remainder as 6.


If we want to find the decimals also, then we need to divide the remainder further with 9.

Here the remainder is 6. So, 6/9 would give us the decimal part. But we know the decimal equivalents of fractions, isnt it?

6/9= .66666....

so, we have got the decimal part. Append it to the quotient.

That means 942/9= 104.6666....


Now, go back and complete all the divisions upto their decimal values.

 

[VOCvangoens]

Was pre-modern Indian algebra more advanced than pre-modern Chinese algebra?

 

[Nuvneet Kundu]

Though Hindu enthusiasts have gone overboard claiming various ‘scientific’ discoveries were made in ancient India, there is some tinge of truth in those claims. The problem is they are mixing metaphysics with physics. Vedas didn't discover the 'Laws of Gravity'. But it did have a sense of 'Gravity'. And laws, if any, were framed by the frame of reference prevalent in that age. Those don't have to withstand the scrutiny of time today. We Indians have to keep our heritage alive, not by ludicrous over enthusiastic claims, but by maintaining the same sense of wonder. But we should not get bullied either, by those who are more articulate, and to whom, anything Indian seem deficient. For them, we have to rise in erudition to counter their claims.

 

[A chauhan]