Reading 1.2 - Class 1/11/12

Salut mes amants des maths!

Today, we talked a bit about the region of Mesopotamia ("[land] between rivers" in Ancient Greek) which is a "toponym for the area of the Tigris–Euphrates river system, largely corresponding to modern-day Iraq, northeastern Syria, southeastern Turkey and southwestern Iran."

Map showing the extent of Mesopotamia

(Note: The following information is taken both from lecture and section 1.2.1 from the book since they both go hand in hand)

The subtopic highlighted with respect to Mesopotamia is the civilization of Babylonians and there own interaction with mathematics. By 1700 BCE, Hammurapi, the ruler of Babylon, had expanded his rule to much of Mesopotamia, instituting a legal system that would help regulate developing empire. 

The Babylonians also left behind a significant amount of documentation of their exploration and use of mathematics. Unlike the Egyptians, their archaeological remains consisted of written upon clay tablets. They also had different systems of numbers, but the standardized system used by scribes for calculations in the "Old Babylonian" period was organized in a base-60 place value system together with a grouping system based on 10 to represent numbers up to 59. They used a vertical stylus stroke on a clay tablet to represent 1 and a titled stroke to represent 10. Grouping of such strokes gave them combinations that formed the other numbers. Below is an example of how their numerals were written. 

For numbers that are greater than 60, a place value system was used as well. The Babylonians used "places" rather than symbols to represent powers of 60, representing the number of powers to be counted by the digit in each place. 

Above is an example of the number 3964 written in Babylonian numerals.

 In addition, such clay tablets portray values belonging to organized multiplication tables in addition to the approaches they took to geometric concepts such as the volume of certain solids and the Pythagorean Theorem, specifically the calculation of pythagorean triples. With respect to geometry, Bablyonians showed clever implementation of geometric tools to solve quadratic equations and systems of equations. Moreover, they used a unique problem solving method called false position to solve linear equations.

Well, that's all for today. Until next time!
Bisous!

-MB