## Number Systems for Ancient Cultures Lays Foundation for Computers

Not all technology integration requires a computer. When including more computer science topics into the curriculum, do not overlook the importance of history.

When educators consider technology integration they think it is a requirement for more computer usage. It is, however, possible to include more technology education in the curriculum through an understanding of how numbers are represented in different cultures. Through an understanding of historical number systems, students gain a more complete understanding of how math and history relate to the computer.

No matter their age, many students are fascinated by other cultures. When teaching history, it is common to include exposure to the life styles of people who lived during that time. Many historical cultures also had their own number systems, a familiar example being Roman Numerals. Exposing students to different number styles when young gives an opportunity to strengthen their current math skills while preparing them to understand the number systems used by computers.

### Number Systems Based on Tens

One option involves ancient Egypt. Egyptian numbers were represented by pictographs. Each picture represented a power of ten and multiples were shown by repeating the symbol. For example, “1” represented the ones, “n” the tens and “9” the hundreds. 111111 nnn 9” is 6×1 + 3×10 + 1×100 or 136. Students can also figure out the modern number by the placement of the pictographs and how many of each is available. Addition and subtraction problems that reinforce borrowing and grouping strategies can then be introduced with the pictographs.

The Babylonians had a pictorial number system similar in construction to the Egyptians. It led to much confusion due to its lack of a symbol for zero and because its rules for positioning the values were not strictly followed. They did, however, have the ability to represent fractions. This number system can also be introduced in a simple fashion to children, especially the fractions, but math problems could prove difficult.

The Greeks had a graphical number system, called the Ionic system, in use around the 5th century BC. It contained more symbols for numbers, specifically an individual symbol for values of one through nine. It was created from the 24 letters of the Greek alphabet and three ancient Phoenician letters. As with the Egyptian number system, the Greek system is good for addition and subtraction exercise. In addition, it also provides convenient symbols for multiplication.

The Chinese number system combines the best of the Egyptian and Greek numerals. Though it is arguably as old as the other two systems, records for the Chinese system are difficult to obtain prior to around 220 BC. Each number is written vertically and has symbols not only for 1-9 but also multiples of 10.

### Other Number Bases

The Mayan Indians of Central America developed a number system with a base of 20. It provided grouping techniques based on dots and bars. Unlike the other systems that were created for accounting, it was designed for use in their calendar, which had 20 days in 18 months with five extra holidays. This caused it to not truly be based on 20, because the third position in its notation becomes 18×20 instead of 20×20. However, it is still a good number system to introduce to middle school or older students because of its use of a base other than 10.

The binary number system can be introduced with the history of India or the Industrial Revolution. Its invention is attributed to Pingola, an Indian mathematician from around the 3rd century AD. His use of only two digits per position contributed to Leibniz’s development of logic as a mathematical concept in the early 1700s. Leibniz’s work then allowed George Boole to develop his Boolean algebra in 1854. It is on this work that computer processing is based.