Monday, 17 June 2013

1,2,3


"The world owes most to India in the realm of mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity. The success of Indian mathematics was mainly due to the fact that Indians had a clear conception of the abstract number as distinct from the numerical quantity of objects or spatial extension."
A.L. Basham, noted Australian historian

In the year 1911, noted Vedic scholar Bharati Krishna Tirthaji, a scholar of history, mathematics, Sanskrit and philosophy. and had made a comprehensive study of the four Vedas, Rigveda, Atharvaveda, Yajurveda, and Samaveda. Studying these texts for years, he was able to reconstruct a series of mathematical formulae, called Sutras. He continued the study for 7 years and compiled them together in a major single volume, which got published five years after his death, Vedic Mathematics, in the year 1965.

Repeated attempts of a few British mathematicians finally bore results duting the years 1981 to 1987, when Vedic mathematics started being taken seriously. A number of London and Indian schools took it up as subjects, and intellectuals started delving more time and energy into the same.

The Content:
The entire Vedic mathematics is divided into 16 Sutras or formulae, which when translated to english and analyzed, makes up 19 major aphorisms and 14 sub-aphorisms. It would be a bit too ambitious to include each one of them here, I would like to pick up a few simpler ones  which would strengthen my point..


Mental Multiplication:
So, what do you do when you are to multiply, say, 78X92?
You jot down the numbers hurrily on a notepad, do a quick 8X2, write down 6, carry over 1...blah blah blah...something like this
    78
    92
  156
702X
7176
Because thats what was taught in schools. Now, what Vedic Maths asks you to do is, think beyond the obvious(am I sounding like some management Guru?)
The nearest 10s base to 78 (and 92) is 100
Step 1) We subtract 100 from both numbers
78 - 100 = -22
92 - 100 = -8
Step2) Add 78 and 92 and subtract 100 from it 78+92-100=70
Step3) Multiply -22 and -8  -22 X -8 = 176
Step4) Carry the 1 from 176 and add it to the result obtained in Step 2 70+1 = 71
Step5)Concatenate the two 71 and 76=7176
And this can be done mentally, which is almost impossible in the first approach. A similar approach could be taken up for two digits or three digit numbers

Mental Squaring:
What would you do if someone asks you to calculate the area of a 42m X 42 m land? Again take out your notepad and scribble?
Or maybe take the above approach and solve it out much quicker?
Or maybe take another better and much interesting approach?
Step 1)Round of 42 to the nearest 10s, ie 40.
Step 2)Now add the remaining amount, ie 2 to 42 ie 44
Step 3) Multiply 40 and 44(much easier), ie 1760
Step4)Now take the number from step 2, ie 2 and square it, ie 4. Add the number to result of Step 3, ie 1764


Cubing a two digit number:
What would you do if someone asks you to find the volume of a 25X25X25 box?
Consider ab=25(where a=2, b=5)
Step 1)Cube a, is 8
Step 2)Divide b by a, ie 5/2=2.5
Step 3) Now write four subsequent products of a with the result of Step 2 and prepare a matrix
8    20     50     125
Step 4) Double the number at 2nd and 3rd place and add them at their subsequent places. Carry over the leftmost digit if the sum is of two digits
8    20     50     125
      40     100
8    60     150   125
8    60     162    5
8    76     2        5
15     6    2         5
The answer is 15625

Multiply and two 2-digit numbers:
If the base 100 method(the first in this blog), still looks tougher to compute mentally, or if you want to explore some more of it, here is another
Consider you have to multiply 12X34. Prepare a matrix of the two numbers.
1     2
3     4
Step1) Multiply ac, ie 1X3=3
Step 2)Multiply bd, ie 2X4=8
Step 3)Add ad and bc, ie 4 and 6=10
Step 4)Prepare another matrix mentally with the results of Step1, 3 and 2 respetively
3     10     8
Step 5) Carry over any extra digit to the left
4   0   8
The Answer is 408

More practical usage of Vedic Maths: Convert kilo to pounds:
Often people switch to Google in the blank of an eye when asked to fill up a form with weight as pounds(when they are more familiar with kilo). Or they would switch to their cellphones.
Well, its much easier to do it mentally, and a better way to keep the mind healthy.
If we have to convert 85 kilo to pounds,
Step 1) Double the kilos, 85X2=170
Step 2) Divide the answer by 10, ie 170/10=17
Step 3) Add the two numbers, 170+17=187, and thats the answer.(to the nearest integer)

Adding to time:
Whats the fastest way to calculate if the current time is 4:15, and someone asks you to calculate the time 2 hours 55 minutes later?
You first add the minutes and then the hours, which is quite simple as such, but then what would you say about this
Step1) Add 415 and 255, ie 670
Step 2) Add 40 to the answer, ie 670+40=710,and 7:10 is the answer

Concept of infinity and zero:
Two concepts highly useful in almost every practical application of maths in daily lives and even for astronomical calculations.
Infinity finds its first usage in the Yajurveda. Vedic men had several terms to describe what is infinity, ananta, purnam, asamkhya being few of them. Consider the following shloka out of the Yajur Veda,


पूर्णमदः पूर्णमिदम पूर्णत पूर्णमुदच्यते
पूर्णस्य पूर्णमादाय पुर्नामेवावासिश्यते 


From infinity is born infinity. When infinity is taken out of infinity, only infinity is left.
Till then, the Greeks used to distinguish between numbers with positional systems, like 27,207,270 would be represented as 27, 2 7, 27 . this system did not provide much flexibility to them to write large numbers with regular instances of 0.
Similarly, Romans didnt have the concept of 0, and had to write numbers like 101,000 as 101MMM.
AtharvaVeda described how the vale of a single digit number increases by 10 by writing 0 in front of it.

Trigonometry:
A fact iterated in the movie Namaste London, Trigonometry even got its name from Vedic mathematics, the word being Tri(three)-kon(angle)-mati(perimeter). Though, now the concepts have already been discovered and have been in use since years, The circular nature of Sin, Cos and Tan finds its mention in the Vedas.
The fact that Sinx/Cosx = Tanx finds its mention in the Vedas.

Currently, as you are reading all of this, researches are being carried on, and undertaken, including the effects of Vedic mathematics on children. Major research is being done on how to develop more powerful and simpler application of Vedic mathematics in geometry, calculus, etc.
What makes Vedic mathematics different from other schools and branches of theoretical and practical mathematics, is the flexibility of Vedic mathematics in providing them freedom with creating their own methods and breaking the "correct answer" jinx.
Vedic Mathematics provides us with quick and fast one-line formulae which speeds up mental calculation. It is a mental tool which not only helps a person solve complex problems quickly, but with repeated practice, also helps a person concentrate better.

Its absolute pity, that in spite of it being such a great marvel as "Vedic Mathematics", some elitist, from within the Indian sub-continent itself, claim it to be a farce. They say that they dont find any such reference in Vedas, and that it was a result of imagination of Tirthaji himself.
The Vedas, primarily, have been known to reveal the true knowledge and meaning of the verses, the hidden secrets to those who are worthy. While this may appear to be a line straight out of a Dan Brown book, it is a mighty known fact that Vedas are written in a cryptic language and a mere translation would mean nothing or may produce some relevant results. The Vedas are believed not to reveal the true meaning to the reader, but rather help the reader find certain answers, which others wont be able to see or even validate.
The irony is, that while the western world is embracing and opening up itself to the charms and secrets of Vedic Mathematics, there are Indians themselves, who claim the Vedic Mathematics to be a lie.
Nothing is greater a tragedy than to not believe in your achievements while the world celebrates them

Realists, as always, would claim that Vedas do not actually teach mathematics on the face of it, but the fact is Vedic mathematics is gradually making a stronghold in the education system of the entire world and is soon becoming a force to reckon.

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I would like to end the post as of now, and would like to know what you thought about it. If you are on Facebook and are interested in such topics, please click on the link below and like the page which comes up.Khoj-In Search of Lost Signs

11 comments:

  1. Thank you for this! Great information.
    From ShivaFan

    ReplyDelete
    Replies
    1. Namaste ShivaFan,
      Thanks a lot for reading through the post and liking the content

      Delete
  2. I learn some of the quick methods but this is awesome. i mean should be part of course

    ReplyDelete
    Replies
    1. Some of the western schools and colleges have already included this as a course in their primary and higher education system. A few private ones in India have also embraced Vedic maths and the students are reaping its benefits. However, a majority of all our schools need to include this as a part of the course

      Delete
  3. Replies
    1. Namaste Mukesh Sir!!
      Thanks a lot for liking the post

      Delete
  4. great :-)

    and its just the tip of the iceberg, there are methods for almost everything .. squares, square-roots, remainder theorem, solving quadratics and so on ...
    vedic maths uses devnagri alphabets for numerals with many-one mapping .. and there are slokas with numerical and philosophical meanings deciphered .. !!
    for example .. there is a sloka which gives the value of 'pi' upto 32 decimal digits ..

    ReplyDelete
    Replies
    1. Namaste!
      I agree, this is just the tip of the ice berg. There are methods much more complex, yet simple to solve bigger and more difficult problems like those of trigonometry and differential equations.
      Regarding the rest of your post, keep watching the space for more...:)

      Delete
  5. Vedic maths is based on sixteen sutra's or principles . These principles are general in nature and can be applied in many ways . In practice, the vedic system is used to solve difficult problems or huge sums in more effective and easy way.These method are just a part of a complete system of mathematics which is far more systematic than the modern system taught now. The simplicity of vedic mathematics helps us to solve the calculations mentally with sifficient practice.
    Vedic maths is highly helpful in cracking competitive exams .There are many vedic math online course one of them is http://www.wiziq.com/course/1507-vedic-mathematics-complete-certified-course So if anybody is intrusted to learn vedic math online can visit the link.

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