### Origins of Tamils?[Where are Tamil people from?]PART :26

[ Compiled by: Kandiah Thillaivinayagalingam]-WITH ENGLISH SUMMARY

"sumerian mathematics"

"Numbers and letters are the two discerning eyes, For all mankind to make the best of life"-Kural 392

Do you like mathematics? No matter what your answer may be, you are not alone.Mathematics is a challenging subject. Its basic concepts began to emerge when the world's very first civilization took root in Mesopotamia more than 5,000 years ago.Today we use numbers for showing prices,telling time,marking addresses,using the telephone,identifying cars and knowing the different players of a sports team.Although today most of the world uses the same decimal number system with Arabic numerals,there are several other numbers systems that have been used over the past hundreds of years.The Sumerians were one of the first to use numerals or signs to represent numbers.six signs were created.With closer inspection,it can be seen that there are really only two symbols[Wedge & circle],but they are combined and resized to make the other signs The number system was both decimal or base 10, and sexgesimal or base 60. To create numbers other than the six shown above, the symbols would be combined.For example, to create the number 73, one large wedge, one small circle, and three small wedges [1+1+1] would be used.The largest unit always appeared on the left . This Sumerian's number system used the main base 60 and the auxiliary base 10.It was passed down to the ancient Babylonians, and it is still used — in a modified form — for measuring time, angles, and geographic coordinates.For example, have you ever wondered why an hour has 60 minutes and a minute has 60 seconds? Have you ever thought about why a full circle has 360 degrees?  As a matter of fact, sumerian number system still plays a critical role in our everyday life.

Given our own deci-centric society this choice of 60 may at first seem very strange, but it was actually extremely natural and functional. Because 60 has so many factors, the Sumerians were able to handle many division problems with ease: fractions of one unit of measure were often whole amounts of another. It's exactly why we still divide an hour into 60 minutes, a circle into 360 degrees and so on.The number 60, a superior highly composite number, has twelve factors, namely {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified.60 is the smallest number that is divisible by every number from 1 to 6; Later,At some point, around 2000BC, Mesopotamian people  adopted this system but modified it so that it became positional (like ours).When we write numbers,in our decimal system the place of each symbol matters a lot.For example,In 278, the 2 is worth 200, the 7 is worth 70, and only the 8 is worth just that, 8.Here the place value is based on the number ten.So in 278, the 2 is worth 2 x 10 x 10 , and the 7 is worth 7x 10 & 8 is worth just 8.So, for every position a digit moves to the left, it is increased by a power of 10.This way of notation is for the Arabic numerals. But since both the Sumerians and the Babylonians used a sexagesimal system,as based on sixty,like our seconds, minutes and hours, each of their digits would be increased by a power of 60 as it moved along to the left. For example,4892 in decimal system is worth in sumerian system as:

Sixty lots of 60x60      Sixty lots of 60      Sixties     Units
(60x60x60)                 (60x60)                 (60)          (1)    x 60 x 60            10 x 60      23
=                       3600                  600           23
=               4223

This reduced the system to only two distinct symbols,the wine glass-like symbol[ is the sumerian number 1, and the horizontal A symbol [ ]is the sumerian number 10  and the position a sign occur within a number changes its quanity, just like "1" in the number "100" is different from the "1" in the number "10,000" in our modern system.This units digits were in base ten (Y, YY, YYY, YYYY, ... YYYYYYYYY) &  tens digits were in base six (<, <<, <<<, <<<<, <<<<<) meaning (10, 20, 30, 40, 50)these unit symbol ( ) and a ten symbol ( ) which were combined in a similar way to the familiar system of Roman< numerals (e.g. 23 would be shown as ). Thus,  represents 60 plus 23, or 83.The Mesopotamian people used this new positional notation in exactly the same manner in the decimal system.So, they had a ones place, a 60s place, a 60 x 60 = 3600s place, and so on.For example,Just as, (in the decimal system), 2 can be 2 or 20 or 200, depending on the digits place, so could a Sumerian 2 mean 2, or 120 (2 x 60), and so on, depending on the place.The 360 degree circle, the foot and its 12 inches, and the "dozen" as a unit, are but a few examples of the vestiges of Sumerian Mathematics, still evident in our daily lives. PART :27 தொடரும்/WILL FOLLOW