One of its injunctions is the familiar an eye for an eye and a tooth for a tooth. Hammurabi is now known for his code of law, The Hammurabi Code which was very logical but also very harsh. One dynasty, the Amorite dynasty, achieved its greatest might under the rule of Hammurabi (circa B.C.E.). Many groups of invaders battled for control in the region for about three thousand years. The geography of the land made cities of the river plain open to blatant attack from many groups. 5 From what we do know, a series of invasions and sporadic warfare served to awaken and stimulate the culture. However, there are so many tablets that the task is still far from complete. It wasn t until 1846 that the deciphering code was broken, which then allowed the translation process to begin. There are many tablets that have been discovered with writings from this time period, but translation is slow and a relatively recent process. Knowledge about their political and cultural history is somewhat limited 4 but is growing. To build tools (and weapons), they used copper smelting and bronze smelting techniques. Besides writing, they utilized other forms of technology such as wheeled vehicles, boats, plows, weaving, and brick towers known as ziggurats. 3 The cities had extensive irrigation systems, codes of law, postal services, and an administrative bureaucracy. ) Cities, writings, and metallurgy were necessary to form this civilization. The Greeks were originally those who called it Mesopotamia, which means, land between the rivers.
This is the area from Baghdad south to the Persian Gulf. Background & Historical Information 1 The Babylonian civilization was made up of people who lived in the alluvial plain between the Tigris and Euphrates rivers. We will also look at some of their algebraic techniques, particularly for solving quadratic equations. We will need to come up with new methods of operations for multiplication and division, as the Babylonians did not give us as much information on how they did their calculations as the Egyptians did. As we did with the Egyptians, we will explore the symbols for their numbers, their base system, and their basic methods of doing arithmetic.
In this reading, I will use the terms interchangeably, despite the fact that they are not the same. However, Babylon was only a small part of Mesopotamia. While this is its official, scholarly title, it is often referred to as Babylon. 1 History of Math for the Liberal Arts CHAPTER Babylonian Mathematics Lawrence Morales Seattle Central Community College MAT107 Chapter 3, Lawrence Morales, 001 Ģ Table of Contents Part 1: Introduction to Babylonian Numbers.4 Background & Historical Information.4 Early Mathematical Development.5 The Babylonian Writing System and Scribal Schools.5 Babylonian Number Symbols.7 Part : The Sexagesimal System.8 The Sexagesimal System as Used by the Babylonians.8 Difficulties With Babylonian Numbers.10 Babylonian Fractions.11 Going the Other Direction.14 Why Base 60?.18 Part 3: Babylonian Arithmetic.19 Addition.19 A Primer on Multiplication.1 The Babylonian Multiplication Table.8 Babylonian Multiplication with Tables.30 Babylonian Multiplication on Tablets.34 Babylonian Division.34 Division on Babylonian Tablets.37 Part 4: Babylonian Root Approximations.38 Babylonians and Square Roots.38 An Alternate Method of Estimating Roots.41 Plimpton Part 5: Babylonian Algebra.44 Systems of Equations.44 Babylonian Quadratics.50 General Approaches to Quadratics.54 Part 6: Homework Problems.57 Conversions.57 A Babylonian Translation Problem.57 MAT107 Chapter 3, Lawrence Morales, 001 Pageģ Multiplication.58 Division.58 Tablet Problems.58 Root Approximations.59 The Alternate Method of Estimating Roots.60 The Babylonians and Pythagorean Triples.60 A Famous Babylonian Tablet.61 Babylonian Algebra Systems of Equations.61 Babylonian Algebra Solving Quadratic Equations.6 Practice and Application of the Quadratic Equation.63 New Quadratic Equations.63 Yet Another Quadratic Formula.64 Real Babylonian Algebra Problems From Tablets.65 Writing.66 Appendix: Blank Gelosia Grids.67 Specific Gelosia Grids.71 Part 6: Endnotes.73 MAT107 Chapter 3, Lawrence Morales, 001 Ĥ Part 1: Introduction to Babylonian Numbers The next civilization that we will explore in this course is ancient Mesopotamia.
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