It is common knowledge that India’s contribution to Mathematics is huge. They invented the decimal system. Even Zero is attributed to Indians, although there has been some contention in recent times.

Today I want to share with you an interesting information I found in an ancient text called Sulbasutras (source). Vedic religion involved various forms of fire rituals which in turn involved constructing alters in specific dimensions and shapes. Sulbasutras contain rules for constructing these alters. Interestingly, all that we know about Vedic mathematics are contained in these texts. This led some historians to conclude that mathematics evolved in Vedic times as a means of finding solutions to problems in religions rites.

I was surprised to discover Pythagoras theorem is these texts. It should be noted that, these texts date from about the 15^{th} to the 5^{th} century BC. The Baudhayana Sulbasutra written in 800 BC gives a special case of the theorem

*The rope which is stretched across the diagonal of a square produces an area double the size of the original square.*

(Please note that all measurements are in terms of ropes. In fact the term Sutra itself means a rope or thread)

Can you relate the above statement to the Pythagoras theorem. If you draw a diagonal across a square, each half would be a right angle triangle with two sides equal. (see the diagram below)

Now if you were to draw a square with D as the side, what would it’s area be. D^{2}, right? Which is exactly what this theorem states, the area of the diagonal square will be double that of the original square.

A^{2} + A^{2} = D^{2}

=> 2A^{2} = D^{2 }^{}^{}^{ }

^{}Double the area of the Square with side A = The area of the Square with side D^{}

The Katyayana Sulbasutra written in 200 BC however, gives a more general version

*The rope which is stretched along the length of the diagonal of a rectangle produces an area which the vertical and horizontal sides make together.*

* *

Please refer to the diagram above. ABCD is the rectangle we are considering. BD is the diagonal. ABPQ is a square who side is equal to the AB side of the rectangle. ADYX is another square constructed from the AD side of the rectangle. BDFE is the square constructed from the diagonal. What this theorem says is

The area of BDFE = Sum of the areas of (ABPQ+ ADYX)

ð BD^{2} = AB^{2} + AD^{2}

If you think of ADB as a right angle triangle, we arrive at Pythogoras theorem. While it uses triangle as a reference, Sulbasutras use rectangles and squares. Understandable, because the intent was to build alters for rituals.It should however be noted that these texts do not contain proofs for these theorems, unlike Pythagoras theorem which has a clearly documented proof.

If you are interested in knowing more about Vedic mathematics this site provides a good overview.

on October 5, 2007 at 9:15 am |Vedic MathsHi!

Check out the Pythagoras Theorem on this website in the tutorials page http://www.vedicmathsindia.org you can calculate the 2 sides of a right angled triangle given 1 side of a right angled triangle.

Very simple method without using trignometry.

Thanks

Gaurav

http://www.vedicmathsindia.org

on October 6, 2007 at 11:59 am |rajagopal sukumarInteresting find. Even babylonians have laid claim to the Pythogoras theorem. It seems to be generally agreed upon that the theorem predates Pythogoras.

Please refer to this page on the wikipedia:

http://en.wikipedia.org/wiki/Pythagorean_theorem

It talks about the sulba sutra also.

on October 8, 2007 at 2:17 am |archana raghuramThanks for the link, Sukumar. I will check it out.

Thanks Mr.Vedic maths. I will look it up.

on October 9, 2007 at 8:08 pm |SaraswathiOh very interesting Archana!! I looked up the site for Vedic Mathematics and found it pretty impressive. I had never known before that Vedic Mathematics was so comprehensive.

on October 10, 2007 at 1:36 am |archana raghuramThank you Saraswathi.

on October 11, 2007 at 6:02 pm |SaraswathiHey archana,

In my blog you had mentioned that competitiveness need not essentially bring out excellence in people. Can you explain that a bit in detail? I was really intrigued by that statement and wanted to know the other side of the coin 🙂

I think I read somewhere about competitiveness not bringing out the best in people but can’t recollect where…

on October 12, 2007 at 4:07 am |archana raghuramDefinitely Saraswathi. I will respond to you over the weekend.

on October 12, 2007 at 6:44 am |SaraswathiOh sure Archana:)

on October 12, 2007 at 9:57 pm |SaraswathiOh I loved your side of explanation for competition….i guess we have to have passion towards our own work+respect for others work which truly leads to a united environment.N ya I totally agree about the writing part. I have been writing since two years and though I haven’t got many comments/traffic it never really stopped my passion for writing.I get your point when you say you write for the sheer thrill of it:) Thanks for taking time out to explain that part. It really put me to thinking:)

on October 13, 2007 at 1:47 am |archanaraghuramThank you Saraswathi. I am glad you asked me the question. It made me think through the subject. Very thought provoking.

on October 13, 2007 at 10:56 am |TatQuirks about theorems don’t qualify to be rigorous, until meticulously proved.

Vedic math may have a system of its own, quite independent of western math. We don’t need the latter to ratify the former.

With necessary respect for the discovery of vedic math in late 1910s by a godman, I would want to add this caveat…

Please refer to the end of TIFR Professor’s page at http://www.math.tifr.res.in/~dani/

on October 13, 2007 at 3:44 pm |archana raghuramThanks Tat. I will check out the link.

on June 28, 2010 at 5:23 pm |adogeotlytrerHi! I’m Georgia, i live in Thessaloniky Greece and I’m glad to finally be a member here!

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