There is an old Tamil Poem which actually tells something similar to Pythagoras Theorem.
This peom may be written earlier than the Pythagoras period. No facts about that.
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
Hmmm, Works well with most of the numbers.
Thanks to the unknown Tamil poet!
This peom may be written earlier than the Pythagoras period. No facts about that.
Odiya Neelamthannai
Orettu Koorathaakki
Koorilae Onru thalli
Kunrathil paathi serthal
Varuvathu karnam thaanae.
Orettu Koorathaakki
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
Hmmm, Works well with most of the numbers.
Thanks to the unknown Tamil poet!
tats bhodaiyanar
ReplyDeleteThank you Sathish. If you know any other information about this poet, You are most welcome to post here.
DeleteWell. The wiki page of the Tamil poet is this.
ReplyDeletehttp://en.wikipedia.org/wiki/Baudhayana
@Ilanthiraiyan : i'm collecting information regarding this bodhaiyanar theorem for my maths project , i'd like to clarify whether bodhaiyanar was a tamil poet or sanskrit poet , and is there any proof for this thoerem , what did he actually stated by this theorem , fact says that he stated
ReplyDelete"The area produced by the diagonal of a rectangle is equal to the sum of area produced by it on two sides. " this statement just relates with the formula ac^2 = ab^2 + bc^2, but this doesn't coincide with the formula what actually mentioned ie . , c = (a - a/8) + (b/2)
Baudhayana has contributed to the texts called shulba sutra. These texts are in Sanskrit.
DeleteSo, He should be a Sanskrit poet. One of his followers in south India should have translated his theorem in Tamil.
It is weird, that the statement of Area equaling with those of diagonal and of other two sides does not relate to the formula c= (a-a/8)+(b/2).
Also I see that this formula does not work for other higher numbers (For eg: 65, 72, 97 )
Perhaps a more deep research on this subject will reveal us a better and a fool proof alternative for the pythagorean theorem.
dīrghasyākṣaṇayā rajjuḥ pārśvamānī, tiryaḍam mānī,
ReplyDeletecha yatpṛthagbhūte kurutastadubhayāṅ karoti.
This is the Sanskrit couplet which could have been translated in Tamil.
It good, Tamil always ancient for any innovation.
ReplyDeleteits good one without root we can find, also for (8,15,17) for this one we got answer 17.125
ReplyDeleteGreat
ReplyDeleteTamil is always great
ReplyDelete