Mesopotamia

Reading: 1.2

Summary:
The Mesopotamia civilization contributed a large number of tablets that contained math problems, their solutions and mathematical tables. The Babylonians from Mesopotamia had used various systems of numbers over time, but generally they used based 60. They had placed value of 60, 60^2, 60^3, etc. Being in a different number system their representation of number are different then the present. For instance 90 would be 1,30 since (1x60^1)+(30x60^0) = 90. To represents decimals, the Babylonians used ";" instead of ".' and the place value would work in a similar process as mention above. Many of the tablets that were preserved were multiplication tables and scratch tablets. Since there were no any addition tablet some speculated that the scribes knew their addition well enough.

The Babylonians had an algorithm to find square roots. To find the square root of a number, N, they would:
1) Find the largest number, K, such that K^2 < N^2
2) Find b = N-K^2
3) Find c= (1/2)b(1/a)
4) N ^(1/2) =  K+c

For system of equations, the Babylonians also used false positions.

Q&A
1) Did the Babylonians have another method to find the square root of a number?
      Yes, having found your K, the the square root of your number N would be [ (N/k)+k ] / 2.

2) Using a different number system, did the Babylonians have a different concept of zero?
       Yes, they did not have an assigned symbol for zero in terms of "nothingness" like our present day zero.

3) What type of symbols did the Babylonians used for their numbers?

1. A triangle pointing downward represented 1's
2. A triangle laying on its side represented 10's

Unanswered Question:

1. Why did the Babylonians changed their number system numerous times? Was their an advantage one had over all the others?

Evaluation of reading:
Interesting: 7
Quality: 8
Complexity: 7