Thread by @RajeAiyer

We learnt the Pythagoras theorem in 5th grade.

Did you know that there is an alternate,simple & ancient Indian method to compute hypotenuse :

The Tamizh kings,centuries before the dawn of the Common Era had built dams,dykes,palaces & great cities during the Sangam era.

How did the architects in those times design and build the great turrets in temples & 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 & simple formula works:
Let us take the 3 sides of the right-angle triangle to be A,B,& C, where C be the hypotenuse.
Let us take A & B to be the horizontal & perpendicular

sides respectively.
If we are to divide A into 8 parts & 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 :
*Firstly* Say A=8 and B=6

By Pythagoras theorem, C equals √(8x8+6x6) Which is √(64+ 36)= √100=10.
Now,according to the quatrain:
C should be 7/8 A+ ½ B
7/8 of A (8) = 7 & ½ of B (6) =3
Together they add up to give hypotenuse to be 7+3=10

*Second* let us try with taking A=28 and B=21 then
@

RajeAiyer
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 & 1/2B=1/2 (21) = 10.5
Thus 24.5 + 10.5=35.
*Third* let us try with taking 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) = 10.51/2 (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 & wide along with their conquests in the world.
Unfortunately,in ancient India, many great intellectuals,& their knowledge/findings were lost to the world owing to various reasons & events

Our schools teach the Pythagoras Theorem to our children.They should also teach Pothayanar's theorem as an alternate & easier method, as explained above.🙏

I m not a Maths buff. Just sharing here what was posted in FB.
No tough Maths questions to me :)
Happy sharing

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