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 15th to the 5th 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. D2, right? Which is exactly what this theorem states, the area of the diagonal square will be double that of the original square.
A2 + A2 = D2
=> 2A2 = D2
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 BD2 = AB2 + AD2
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.