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போதையானர் (Vs Pythagoras)

September 7th, 2015 Leave a comment Go to comments

ஓடும் நீளம் தனை ஒரேஎட்டுக்
கூறு ஆக்கி கூறிலே ஒன்றைத்
தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால்
வருவது கர்ணம் தானே

Premise: Consider the Running length of the base of a right-angle triangle as “a” and the standing height “b” and hypotenuse is “c”. As per Pythagoras theorem we have c2 = a2 + b2[Update] Ensure that the triangle is rotated to have the base side longer than the height side.

Proof:  As per the poem we have to consider (7/8) of the base length, that is  (7a/8) and half of the height, which is (b/2) and sum them up to get the hypotenuse “c”

We have (7/8)a + (1/2)b = c => 7a + 4b = 8c.

Consider an easy example of 3, 4 and 5.  By Bodhaiyanar, we get 7*4+4*3 = 40 = 8*5 => c = 5.  We were able to find the hypotenuse without using square root operator in constant time.

Caveat: This algorithm works only for whole number hypotenuse values.  For others, it gives a quick and approximate estimate.

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