Ancient Numbering Systems

Running head: ANCIENT NUMBER SYSTEMS

Ancient Number Systems

College Mathematics

Ancient Number Systems

This paper will provide a brief overview of selected ancient numbering systems, including Egyptian, Greek, Babylonian, Indian, and Mayan. In particular, key areas of both differences and commonality will be explored, such as base system, concept of zero, and effects of medium and economy.

Base Systems

Our present-day numbering system is known as a base 10 system (need name?). The Romans and Hindu used a base 10 system as well, although it was very different from our system in that it was not positional.

The Mayans used a system based on 20. This is referred to as a vigesimal system. One might assume that this arose from the practice of counting on both fingers and toes, whereas a base 10 system presumes that fingers only were used for counting.

The Babylonian system was hexasegimal, meaning that it was based on 60. This concept carries forward today in the way we think of time (60 seconds in a minute, 60 minutes in an hours, etc.)

Concept of Zero

Most early numbering systems did not incorporate a concept of zero, which means that these were not "positional" systems. Only two cultures, the Mayan and the Hindu, developed these two concepts and used zero as a place holder.

The Babylonians

The Greeks

Ancient Greeks first used an acrophonic number system for purposes of counting and transacting business. Within this system, written symbols for the numbers came from the first letter of the number name. This alphabetical system was based on the position of the letters in the alphabet. At the time, the Greek alphabet consisted of 24 letters. Three older letters that were obsolete were used to round out the numbering system.

The Ancient Greek number system used a base of 10 as a decimal system. The reason for this was quite simple--we have ten fingers to count off of. Accent marks were used to denote that a number should be multiplied by 1000.

A chart depicting the Greek number system is below (www.wikipedia.org):

The Romans

The Indians

India created the first base 10 numbering system and the concept of positional numerology. (wikipedia.org, 2007) The Indian numerology system is commonly known as the Hindu-Arabic numeral system. It is believed that the number system first spread to Persia, where it was picked up by Arabs in a time of war. Sometime in the seventh century, the Indians added zero as a tenth positional digit.

The importance of the Indian numbering system can be summed up by the French mathematician Pierre Simon LaPlace. Pierre wrote, "It is India that gave us the ingenious method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity."

The Mayans

The Mayan civilization in the Central American region flourished from approximately 250-900 AD, although it actually arose from an earlier civilization dating back at least 2,000 years before that. Their numbering system was highly sophisticated, and they were probably the most advanced civilization in the world at that time in terms of mathematics.

Although the Mayan numbering system was based on 20, it was not a true base 20 system as we think of it. First, it used only three symbols (instead of 20). Next, it does not consistently follow the pattern of 20, changing in the third iteration,