Sulabha Sutras (Easy Principles, Rules) : Sulbasutras: Mathematics and Engineering.
For more details click for Online Reference, or read B Datta, The science of the Sulba (Calcutta, 1932).
Vedic altars had to be built very precisely. The sutras contain formulae without derivations. (My thinking is that the derivations must have been taught ‘guru-mukhena’ by the guru, directly.)
- The method of constructing a square of area equal to a given rectangle is exact.
- Constructing a square of area equal to that of a given circle, is an approximation.
Baudhayana, Apastamba, Katyayana, and Manava are some of the authors of these sutras. (I have heard my father say that we traditionally belong to the Apastamba Sutra school, this has to be stated in the pravara.)
Western historians date Baudhayana at a 800 BCE, Pythagoras around 500 BCE and Katyayana at 200 BCE. (kAtyAyana the author of SuklaYajurVidhanaSastra, is the grand disciple of Saunaka as per the SaDgurusiSyA. So my date for him is around 3000 BCE.)
Baudhyana : The rope which is stretched across the diagonal of a square produces an area double the size of the original square.
Katyayana : 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.
(Sutras can mean the rope for measuring an altar.)
Pythagoras : The square on the hypotenuse is equal to the sum of the squares on the other two sides, in a right angled triangle.
Apastamba : gave a sutra for computing the square root of 2 : Increase a unit length by its third and this third by its own fourth less the thirty-fourth part of that fourth.
√2 = 1 + 1/3 + 1/(3 
4) – 1/(3 4 34) = 577/408 = 1.414215686 when computed to 9 decimal places.
Compare this with the present value of √2 = 1.414213562, and you can see that the value agrees to 5 decimal places.
The different constructions in the Sulabha Sutras, lead to different approximations for Pi.
Baudhayana’s : methods of constructions lead to the following approximations for Pi : 676/225, 900/289 and 1156/361
Manava : 25/8 (Western date given for Manava is 750 BCE)
Others : 2.99, 3.00, 3.004, 3.029, 3.047, 3.088, 3.1141, 3.16049 and 3.2022
In schools we are now taught 22/7.
Interestingly, in sanskrit sutra means both thread and principle!
For more details click for Online Reference, or read B Datta, The science of the Sulba (Calcutta, 1932).
Authorship and Copyright Notice : Satya Sarada Kandula : All Rights Reserved.
While I don’t agree with the western version of the Aryan Theory or their chronology, I think, you might find these links useful.
The Sacred Laws of the Âryas, Part I (SBE 2) George Bühler translator [1879] (Sacred Books of the East, Vol. 2) (Apastamba, Gautama)
The Sacred Laws of the Âryas, Part II (SBE 14) George Bühler translator [1879] (Sacred Books of the East, Vol. 14) (Vasistha, Baudhayana)
