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| Rahmathullah, KSEB Division Office, Alappuzha, Mob: 09496232044 |
Pythagorus theorem has found many intrepid enthusiasts ready to prove it. Rahmathullah, however, is not a member of that long list. Rather, he has devised a method by which the one can get the approximate length of the hypotenuse without actually doing the square root operation.
His finding has been accepted by the Association of Mathematics Teachers of India, Chennai and Kerala Mathematics Association.
So what is special about the discovery of Rahmathullah. He has found a way to make a good approaximation of the hypotenuse using simpler operations of division and multiplication.
If z is the length of the hypotenuse, then z2 = x2 + y2, which is the Pythagorus theorem. However, his approaximation goes like this:
Let k be the quotient and m the reminder when x2 is divided by 2y. Let a = y+k and b = m – k2, then a+(b/(2a+b/2a)) is an approximate value of z, the hypotenuse. For example, take x = 3 and y = 4. Now x2/2y is 9/8. So the quotient k = 1 and reminder m = 1. Therefore a = y+k = 4 + 1 = 5 and b = m – k2 = 1 – 12 = 0. Now hypotenuse z = a+(b/(2a+b/2a)) = 5+(0/(10+0/10)) = 5 + 0 = 5, which agrees with the Pythagorus theorem that 52 = 32 + 42.
Rahmathulla is a Senior Assistant in the Division Office of Kerala State Electricity Board at Alappuzha. He has worked on refining his methodology since 1986.
Courtesy: Mathrubhumi, March 18, 2014
