Origins of Tamils?[Where are Tamil people from?] PART :29

Compiled by: Kandiah Thillaivinayagalingam]-

[Babylonian Yale tablet YBC 7289 showing the sexagesimal number1;24,51,10 approximating √2] 

Thus,the square root of 2, the length of the diagonal of a unit square,was approximated by the Babylonians of the Old Babylonian Period (1900 BC – 1650 BC) as

It has on it a diagram of a square with 30 on one side, the diagonals are drawn in and near the centre is written 1,24,51,10 and 42,25,35. These numbers are written in sumerian/Babylonian numerals to base 60.Now the sumerian/Babylonian numbers are always ambiguous and no indication occurs as to where the integer part ends and the fractional part begins. Assuming that the first number is 1; 24,51,10 then converting this to a decimal gives 1.414212963 while √2 = 1.414213562. Calculating 30 × [ 1;24,51,10 ] gives 42;25,35 which is the second number. The diagonal of a square of side 30 is found by multiplying 30 by the approximation to √2.

[Babylonian tablet numbered 322[Plimpton 322]]

The tablet numbered 322 has four columns with 15 rows. The last column is the simplest to understand for it gives the row number and so contains 1, 2, 3, ... , 15. In every row the square of the number c in column 3 minus the square of the number b in column 2 is a perfect square, say h. c² - b² = h^2, So the table  is a list of Pythagorean integer triples.

Have you ever studied Pythogaras theorem? It was discovered by Pythogoras who lived during 569–475 BC. Thats what our books and we say...Then, what about this below poem by a Tamil Poet called Pothayanar ?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! ie This method employs finding hypotneuse without using square root!!!

Hypotenuse = 7/8 * Longer Side + 1/2 * Shorter side.Say,Hypotenuse  = C,Length  = L,wide = W,  Then C = 7/8 x L + 1/2 x W

ஓடும் நீளம் தனை ஒரேஎட்டுக்

கூறு ஆக்கி கூறிலே ஒன்றைத்

தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால்

வருவது கர்ணம் தானே.

This poem is said to be written by Tamil poet bothayanar.

Explanation:seven eigth of largest side[a] added with half of smallest side[b] 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 [You may get approximate answer with out application of squre root) An easy method for pythagorous theorem by bothaiyanaar:

c=(a-a/8)+(b/ 2),where a>b. b>a is not possible. If possible that object may not stand very longer period.(it is against the nature.]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 (a=4,b=3),[6:8:10] and 5:12:13 (a=12,b=5)... 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!!!!

As we shall see above,Mesopotomian mathematics is quite impressive.However,like the ancient Egyptians,the mesopotomians never gave what we would call "PROOFS" for their results.The first people to do so were the Greeks. 

Any way,With their advanced knowledge in numerals, people in Mesopotamia were excellent mathematicians. When applied to their daily life, they developed formulas to calculate weights, areas, volumes, and wages. Students from that time needed to study mathematics at school, too. They had to learn how to do addition, subtraction, multiplication, division, and fractions. During the reign of Hammurabi (1792 B.C. - 1750 B.C.) of the 1st dynasty of Babylon, there were even specific laws addressing issues such as interests and loans. Because of those codified rules, we know that people in Mesopotamia were the ones who established the world's first banking system. Without mastering mathematics, that would be entirely impossible!

PART :30 WILL FOLLOW in next week