*We learnt the Pythagoras theorem in 7th grade:*

 *We learnt the Pythagoras theorem in 7th grade:* 

*Did you know that there is an alternate, simple and ancient Indian  method to compute hypotenuse?*

The Tamil kings, centuries before the dawn of the Common Era had built dams,  dykes, palaces and great cities during the Sangam era. How did the architects in those times design and build  the great turrets in temples and the great dams,canals, highways, etc.

Upon searching it was revealed that finding the hypotenuse of a right-angle triangle can be done independent of the Pythagoras theorem, (which enunciates that sum of the square of both sides of the right angle will be equal to the square of the hypotenuse, of the triangle). 

It is a simple task to find the square of a number, but finding the square root of a number is not so easy. There is no simple formula to find the square root of a number.

*An ancient Tamil mathematician/poet _Pothayanar_, who lived 800 years before the Common Era*, had 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 fractions. 

Here is the English translation of the quatrain:

Divide the horizontal into eight,           

Delete one portion, and add the remaining, to half of vertical to result you’ve got. The answer would be hypotenuse of the triangle

The Tamil poem by poet _Pothayanar_ is :

ஓடும் நீளம் தனை ஒரேஎட்டுக்

கூறு ஆக்கி கூறிலே ஒன்றைத்

தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால்

வருவது கர்ணம் தானே

    —– போதையனார்

The advantage of the ancient theorem is that  there is no need to use a square / square root function.

But before we jump to conclusions let us see how this ancient and simple 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 and B to be the horizontal and perpendicular 

sides respectively. 

If we are to divide A 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

Say A=8 and B=6

By Pythagoras theorem, C equals

√ (8x8+6x6) = √ (64+ 36)

= √100 =10.

Now, according to the quatrain :

C should be 7/8 A+ ½ B 

 7/8 of A (8) = 7 and ½ of B (6) =3 

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

*Second* with 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.

 *Third* with A= 12 and B= 5 then 

By Pythagoras theorem 

C= √ (12x12) + (5x5) 

= √(144+ 25) 

√169 =13.

According to the ancient Tamil quatrain :  the hypotenuse becomes 7/8A + 1/2B

7/8(12) = 10.5

1/2 (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. 

The discoveries of the Greek scientists and mathematicians spread far and wide along with their conquests in the world.  

Unfortunately, in ancient India,  many great intellectuals, and their knowledge / findings were  lost to the world owing to various reasons and events. 

Our schools teach the  Pythagoras Theorem to our children. They should also teach _Pothayanar's_ theorem as an alternate and easier method, as explained above