Thread by @anbezhil12

Alternate method to compute hypotenuse to Pythagoras theorem: The Tamilian land, centuries before the dawn of the common era had built dams and dikes, palaces and great cities during the Sangam era. The great turrets in temples and great highways cannot be built without any

knowledge about Pythagoras theorem. To find the hypotenuse of a right-angle triangle independent of the Pythagoras theorem, which enunciate that sum of the square of both sides of the right angle will be equal to the square of the hypotenuse, of the triangle has been known by our

ancestors. It is not a simple task to find the square of a number, but finding the square root of a number is a herculean task. There is no simple formula to find the square root of a number. An ancient Tamil mathematician/poet #Pothayanar, who had lived 800 years before the

common era, has given a quatrain of four lines articulating the method of finding the length of the hypotenuse of a right-angle triangle without the need to find the square or the square-root, only using the length of the sides, and simple fraction. Here is the English

translation of the quatrain.
Divide the horizontal to eight,
Delete one portion, and add the remaining,
To half of vertical to result you’ve got’
Available would-be hypotenuse of the triangle.
The Tamil poem by poet Pothayanar goes as follows;
ஓடும் நீளம் தனை

ஒரேஎட்டுக்
கூறு ஆக்கி கூறிலே ஒன்றைத்
தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால்
வருவது கர்ணம் தானே. – போதையனார்
The advantage of the ancient theorem is that one need not use a square root function which may be a bit cumbersome. But before we jump to conclusion let us see how our

new found formula works. Let us take the three sides of the right-angle triangle to be A, B, and C, where C be the hypotenuse. Let us take A to be the horizontal side. If we are to divide into eight parts and takeaway one eight, it would be 7/8A. The half of the vertical side

will be 1/2B. Thus, the result should be;
C= 7/8A + 1/2B
Let us give some numbers and try: Say A=8 and B=6

By Pythagoras theorem C equals √ (8x8+6x6) Which is √ (64+ 36) = √100 =10
According to the quatrain; C becomes 7/8A + ½ B
Now 7/8 of A = 7 and ½ of B =3 And

they add up to give hypotenuse to be 7+3=10

Now let us try with taking A=28 and B=21 then
By Pythagoras theorem C= √ (21x21+28x28)
C = √ (441+784)
which is =√1225 = 35
According to quatrain; hypotenuse becomes 7/8A + 1/2 B.
7/8 A=7/8 (28) = 24.5 and 1/2B= 1/2

(21) = 10.5
Thus 24.5 + 10.5= 35.
Now let us try with taking A= 12 and B= 5 then
By Pythagoras theorem C= √ (12x12) + (5x5) = (144+ 25) √169 =13.
According to the Tamil quatrain; hypotenuse becomes 7/8A + 1/2B
7/8(12) = 101/2 (5) = 2.5
Thus 10.5 +2.5 =13
Pothayanar

must have been a great mathematician, who got lost like fruit hidden in the foliage of the tree. All our ancient constructions of temples and palaces have been based on our superior knowledge in all areas. But the discoveries of the Greeks scientists and mathematicians became

more popular. Unfortunately, not only the great Indian intellectuals but also their findings were lost to the world. Let us in our thought thank Pothayanar for his discovery.
By Kumar Punithavel