Pythagorean theorem expressed without roots in an old Tamilian (Indian) statement There's an old Tamil statement that predicts the hypotenuse of a right angle triangle to a reasonable level of accuracy considering it doesn't involve roots. This is how it goes:

“Odum Neelam Thanai 
  Ore Ettu Kooru thaaki 
  Koorilae Ondrai Thalli
  Kundrathil Paadhiyai Saerthal 
  Varuvathu Karnam Thane”

This translates to something like -
"Subtract one eight of the length (longer side) from the length, and add a half of the height to get the hypotenuse". This approximates quite well to the hypotenuse. Seems like an interesting subject to elaborate on.  
Hypotenuse = 7/8* base + height/2    


How is 7/8*base + height/2 somewhat equivalent to sqrt(a^2 + b^2)


The method provides a not-so-great approximation when the two catheti are roughly of the same length. In this case, $$\frac{7}{8}a+\frac{1}{2}b\approx\frac{7}{8}a+\frac{1}{2}a=\frac{11}{8}a=1\mathrm.375 a\approx(1\mathrm.414...)a=\sqrt{2}{a}\approx\sqrt{a^2+b^2}.$$
