Analyzing Historical Number Systems



Math 12 Project: Analyzing Historical Number Systems

Introduction

In this paper we will be discussing and analyzing historical number systems. The two systems that will be analyzed will be from Chinese stick, Egyptian, Babylonian, Mayan, Thai, and Roman. We will be comparing Babylonian and Egyptian Numerical system.

Discussion and Analysis

Babylonian Number System

The Babylonian numbering system is a system of representation of numbers in cuneiform script. This system first appeared around 1800-1900 a. C. Also credited as the first positional numbering system, i.e. in which the value of a digit particularly depends on both its value and its position in the number being represented. This was an extremely important, because, before the place-value system technicians were forced to use unique symbols to represent each power of a base (ten, hundred, thousand, and so on), becoming even more basic calculations unwieldy.

Although his system clearly had a decimal system preferred internal use 60 as the second smallest unit instead of 100 as we do today, more appropriately considered a mixed system of bases 10 and 60. A large value to be based on sixty is the number results in a smaller numeral and also can be divided without remainder by two, three, four, five, six, thus also ten, fifteen, twenty, and thirty . Only two symbols used in a variety of combinations were used to denote the numbers 59. A space was left to indicate a zero (third century BC.), But later devised a sign to represent an empty place.

The most commonly adopted is that 60, a composite of many factors (the numbers before and after the series would be 12 to 120), was chosen as the base because of its factorization 2 × 2 × 3 × 5, which does divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. In fact, it is the smallest integer divisible by all integers from 1 to 6. Integers and fractions were represented in the same way: the point integer and fractional separator was not written, it was clear from the context.

For example, the number 53 in Babylonian numbering is represented using five times the symbol for 10 and 3 times the symbol for 1, as seen in the picture above.

Plimpton 322: clay tablet dated approximately between 1900 and 1600 a. C. reveals that the Babylonians discovered a method for finding Pythagorean triples, ie sets of three integers such that the square of one of them is the sum of the squares of the other two. By the Pythagorean Theorem, a triangle whose sides are proportional to the three a Pythagorean triple is a right triangle. Right triangles with sides proportional to the simplest Pythagorean triples in turn frequently in Babylonian texts problem, but if this pill had not come to light which would have had no reason to suspect that a general method capable of generating a number Unlimited different Pythagorean triples known a millennium and a half before Euclid.

Mayan Numbers

The Mayans were sedentary person was located geographically in the ...