Recently I saw in facebook, an old tamil verse on a method to calculate the hypotenuse of a right-angled triangle. The facebook status linked the source to
The verse is given below.
ஓடும் நீளம் தனை ஒரேஎட்டுக்
கூறு ஆக்கி கூறிலே ஒன்றைத்
தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால்
வருவது கர்ணம் தானே.
- போதையனார்
What it tells is that the hypotenuse can be easily calculated using the following formula
Hypotenuse = 7/8 * Longer Side + 1/2 * Shorter side.
The highlight of this formula is that it gives a method to calculate hypotenuse using linear equation instead of the non-linear one given by Pythagoras!
Of course, these two cannot produce the same results. I just did a small calculation for smaller integer Pythagorean triples. It works for (3,4,5) and for (5, 12,13). But for other integer triplets, it produces approx. results closer to the one that can be obtained using Pythagoras theorem! I calculated the hypotenuse values using this equation for the triples from http://en.wikipedia.org/wiki/Pythagorean_triple The results can be seen here.
Some facts:
1. The formula gives accuracy above 94% for the triplets in consideration
2. The deviation from actual hypotenuse values is increased as the ratio of longer side to the hypotenuse is increased.
