Pythagoras Theorem in Tamil Poem

                

Pythagorean Theorem in Tamil poem 8th century AD by a TAMILAN but the same thing was told by Pythagoras in different manner at 10th century AD only-after 200years... . Baudhayana, (800 BCE) was the author of the Baudhayana sutras, which cover dharma, daily ritual, Vedic sacrifices, etc. He belongs to the Yajurveda School, and is older than the other sutra author Apastambha. He was the author of the earliest Sulba Sutra—appendices to the Vedas giving rules for the construction of altars—called the Baudhayana Sulbasutra. These are notable from the point of view of mathematics, for containing several important mathematical results, including giving a value of pi to some degree of precision, and stating a version of what is now known as the Pythagorean Theorem.

போதாயனர் என்பவர் கி. மு. எட்டாம் நூற்றாண்டில் வாழ்ந்த ஒரு இந்திய கணித மேதை. இவர் பையின் மதிப்பையும் செங்கோண முக்கோணத்தில் செம்பக்கத்தை வர்க்கம் வர்க்கமூலம் இல்லாமல் கண்டறியும் முறையையும் அறிந்தவர் என்றும் கூறப்படுகிறார்.

There is an old Tamil Poem which actually tells something similar to Pythagoras Theorem.

ஓடிய  நீளந்தன்னை  ஓரெட்டு  கூறதாக்கி  கூற்றிலே  ஒன்று  தள்ளி
குன்றத்தில்  பாதி  சேர்த்தால்  வருவது  கர்ணம்  தானே.

Poem in Romanized Tamil:

This peom may be written earlier than the Pythagoras period. No facts about that.

Odiya Neelamthannai Orettu Koorathakki Koorilae Onru thalli Kunrathil paathi serthal Varuvathu karnam thaanae.          

The meaning here in this poem is:

"Odiya Neelamthannai Orettu Koorathakki" - Divide greater length by 8.

"Koorilae Onru thalli" - Multiply by one less than 8, which is 7.

"Kunrathil paathi serthal" - Kunram means smaller length. Add half of the smaller length.

"Varuvathu karnam thaanae." - What we get is the hypotenuse , here represented as karnam.


Example 1:

According to Pythagoras theorem,

6² + 8² = 10²

Explanation from this poem...

greater length is 8, smaller is 6.

[7 * (8/8) ]+ (6/2) = 10

Example 2:

Pythagoras theorem,

4² + 3² = 5²

greater length is 4, smaller is 3.

[7 * (4/8) ] + (3/2) = 7 * (1/2) + 1.5 = 3.5 + 1.5 = 5

Somehow this unknown Tamil poet, got an Idea of what Pythagoras had also thought.

As it happens in most of the Indian literature, the thoughts of the poets and their great Ideas will only live in the form of poem or song, but no proof of a particular ideas (In this case Derivation for theorem) exists.

From the above poem, I would like to derive an equation to get the hypotenuse value of a right angled triangle.
 
Let the longer side be X.Shorter side be Y.
Hypotenuse be Z.
our equation goes like this...
[7 * (X/8) ] + Y/2 = Z
7X/8 + Y/2 = Z
Also we can write as,
Z = (7X + 4Y) / 8