Scientific Contributions[or glories] of Ancient Tamils"/Part:02

The Ancient Tamil Poetry & Science/Geometry":
[The six parts Tamil article published in theebam.com on "பண்டைய தமிழ் பாடல்களில் விஞ்ஞானம்"[Science in the Ancient Tamil Poetries ] is the based for this English article "Scientific Contributions[or glories] of Ancient Tamils",but with substantial improvements,For Tamil articles refer :http://www.ttamil.com/theebam.com ] November /December 2016 ]


 

Ancient Tamils were highly knowledgeable and had high living standards in ancient times.They proved that from mathematics to medicine everything could be condensed within Tamil poetry and grammatical rules.These poetries are usually said to be the autobiography of ancient Tamils. The life, thought and aspirations of those people are portrayed in the  poetry they produced.For example, their mathematical skills wherein one out of eight lakh fractions was the least small quantity up to which they could calculate without a calculator or computer &  The theorem of Pythagoras spelt out in poetic form in Tamil much before his times as:"7/8 of Bigger side plus half of smaller side should equal to Hypotenuse./ஓடும் நீளம் தனை ஒரேஎட்டுக் கூறு ஆக்கி கூறிலே ஒன்றைத் தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால் வருவது கர்ணம் தானே".We had bronze casting just like we do today for our bronze statues ie the lost wax method of metal casting was used. Kurunthogai[குறுந்தொகை] 155 says:"The loud ploughmen who cleared the old forests and seeded the land in the morning return with their seed-bowls filled with flowers.The clear bells with wide mouths that were cast with wax in foundries, chime in the forest, dense with trees. ,...."/"முதைப்புனங் கொன்ற ஆர்கலி உழவர் விதைக்குறு வட்டி போதொடு பொதுளப் பொழுதோ தான் வந்தன்றே மெழுகு ஆன்று ஊது உலைப் பெய்த பகுவாய்த் தெண்மணி மரம் பயில் இறும்பின் ஆர்ப்ப...".

 

The Grand Anaicut built by Karikalan Chola in the 2nd century A.D. to harness the waters of the river kaveri was made of stone, the dam is 329 m long and 20 m wide and still very much in use.The amazing thing about this dam is that it doesn't have plaster or cement holding it in place.This damn's strength was studied in the 1800s and they found the "secret" which is the "curvy" dam [Arch dam].The curvey structure later found to take off the water pressure from the structure.There are documentation that the Egyptians visited this dam to study the structure.The structure build in the time when no modern engineering had exist.It shows Tamilan talent.It is very much like an arched entryway in building, where the weight is distributed to the sides.This curved dam concept is quite an engineering feat,considering the time when it was built – about 2000 years ago– Akananuru[அகநானூறு] 346 clearly Says:"...in the water that flows rapidly though a strong sluice gate of an curved dam ["....வருத்திக் கொண்ட வல்வாய்க் கொடுஞ்சிறை,மீது அழி கடு நீர் நோக்கிப் பைப்பயப் பார்வல் இருக்கும் பயங் கேழ் ஊர...."/வல்வாய்க் கொடுஞ்சிறை – curved dam with strong sluice gate,] created by farmers... "Also Sirupanatrupadai  [சிறுபாணாற்றுப்படை] 242 – 245 -  has a description of the sun being in the center,and surrounded by planets  – "வாள் நிற விசும்பின் கோள்மீன் சூழ்ந்த இளங்கதிர் ஞாயிறு எள்ளூம் தோற்றத்து விளங்கு பொற்கலத்தில் விரும்புவன பேணி ஆனா விருப்பின் தான் நின்று ஊட்டி", and this means "He himself will serve you unlimited quantities of desired foods with hospitality in golden bowls that shine in a manner that blames the blazing,tender-rayed sun surrounded by planets, in the shining, sword-colored, bright sky.".This book is from the second century A.D.and There is a reference in Nedunalvadai [நெடுநல்வாடை](72- 78)about professional men who are well read in the building art, who use thread to establish the perimeter of the palace that they built for their king:"நூல்அறி புலவர் நுண்ணிதின் கயிறுஇட்டு தேஎம் கொண்டு, தெய்வம் நோக்கி‘ பெரும்பெயர் மன்னர்க்கு ஒப்ப மனைவகுத்து" 

In the history of mathamatics, tamils had great achievements. The below verses/poems indicates that they knew how to calculate area of circles even before pythagorouss & others. This was stated in a text called Kakkai Paadiniam[காக்கைப்பாடினியம்”]  of pre christian era by female poet Kakkai Paadiniar[காக்கைப்பாடினியார்].In this text she explained the area of a circle in a poem.

Image result for properties of circle
வட்டத்தரை(1/2 * perimeter)] கொண்டு விட்டத்தரை(1/2 * dia) தாக்க[to multiply] சட்டெனத் தோன்றும் குழி[Area]
[This means area of circle is (1/2 * dia) *(1/2 * perimeter)].These poems of Kakkai Paadiniar are available in Kanakkathikaram as poems 46 & 49.
Explanation:வட்டத்தரை     =  Circumference of circle / 2 = 2πr/2 =  πr

விட்டத்தரை     =Diameter/ 2     = 2r/2  =   r
குழி (Area)    =Half of circumference of circle X Half of diameter  ( தாக்க=to multiply)
∴Area of circle    =    πr  x  r    =   πr² 
Also Poem 50 explain how to calculate circumference of a circle.


Pythagoras was a famous Greek philosopher and Great Mathematician in 495 BC. Pythagoras has been discovered a theorem in Geometry called after his name as”Pythagoras Theorem”. In his theorem he established the relationship between the Hypotenuse and the other two sides adjacent to the right angle. Though this theorem now bears his name it was previously formulated and used by Indians and the Babylonians.According to this theorem The Square of the hypotenuse is equal to the sum of the squares of the other to sides.But before his period, The Tamil people in India followed a easy way to calculate the lengths of the sides with out taking Square roots. The Tamil Poet Bothaiyanar [போதையனார்] mentioned this method in his below Tamil verses.The highlight of this formula is that it gives a method to calculate hypotenuse using linear equation instead of the non-linear one given by Pythagoras! 

"ஓடும் நீளம் தனை ஒரேஎட்டுக்
கூறு ஆக்கி கூறிலே ஒன்றைத்
தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால்
வருவது கர்ணம் தானே."

This method employs finding hypotneuse without using square root!!!

Hypotenuse = 7/8 * Longer Side + 1/2 * Shorter side.that is ,seven eigth of largest side[L] added with half of smallest side[W] will give  Hypotenuse [C] .ie The formula is hyp = (adj - (adj/8)) + (opp/2),where  the adjacent side is always longer than the opposite side .An easy method for pythagorous theorem by bothaiyanaar:c=(L-L/8)+(W/ 2),where L>W. or we may say:largest value be deducted by its 1/8 and half of the smallest value added to it.Please note it is not always correct.

It works for 3:4:5 (Where,W or b=3,L or a=4,),[6:8:10] and 5:12:13 ... but, not for 9:40:41... So, it can not be generalised as a theorem .There are so many restrictions,but may give approximate answer.The issue is not about the correctness of this formula... The issue is that he(Bothaiyanar) was atleast tried to establish a formula!!.Though this applies for restricted usage,It does not take away any credit from this great man!! In those days,this formula is used to calculate a perfect slope to move heavy objects easily to the height, (example::Tanjai periya kovil gopuram). So the formulae is always meant for length is greater than height. If you want a steep slope value to be found (eg length < height) Just invert the triangle to have the height is less than length. In a poem of such a short verse not everything will be explained.

0 comments:

Post a comment