Ishango Bone: a 20000 years old african mathematical document !!!

Ancient Math Tools

Ancient Times

The oldest known objects used to keep representation of numbers were bones with notches carved into them. The oldest bone was discovered in Lebombo Mountains of Swaziland (South Africa). It is believed that this bone is since 35,000 BC. This bone has 29 notches on it and is believed it was used as a calendar. That is because people in this area use sticks calendars until now.

Ishango bone appears to show much more than tally system. The notches on the first row and second row each have sum of 60. The second row contains prime numbers between 10 and 20. Furthermore, the last row seems to show a method of duplication like that used later in Egyptian multiplication. In some literature the bone has described as a lunar calendar.

A second Ishango bone is revealed this year in Belgium as mentioned before. This bone has also curved notches made on it. Dr. Huylebrouck from university of Brussels has written about it in Dutch. But information in English about this bone is hardly found.

Egyptians

Ancient Egyptians have written numbers and symbols in pyramids, graves, caves, stones and papyrus. They had their own system of numbers. Egyptian mathematics is connected to their gods like Horus, Sesheta and Toth.

An important document of Egyptians is Rhind (Ahmes) papyrus (1650 BC). Rhind is discovered in a small building near the temple of Ramses in Thebes. A Scottish rich man called Rhind has bought this document during his visit to Egypt in the period between June 1855 and July 1856. The document is now owned by the British museum and it is kept now in this museum. Rhind papyrus is about 40 cm in width and 513 cm in length. It is fragmented in 14 pieces .

Sumerians and Babylonian

Sumerians and Babylonian built great civilizations in areas now called Iraq and Syria. Babylonian civilization has started around 3000 BC. Both civilizations had written mathematical symbols in clay.

One of the most famous of all tablets made by Babylonians is the Plimpton 322. This can be found in appendix A. An old surviving document from the period of Babylonians is Salamis tablet. It was used by the Babylonians and it was discovered on the Greece island of Salamis.

The Abacus

In ancient history Greeks has used Babylonians’ Salamis tablet as a counting board. They gave the name Abacus which is derived from Abax (means table). The middle times of Abacus are between 300 BC and 500 AD when the Romanians have used the so called Roman hand-Abacus.

The modern Abacus was made in china circa 1200 AD. The Chinese Abacus is made of 13 columns with 2 beads on top and 5 beads bellow. There is a beam which separates the upper beads from the lower ones. Beads can slide up and down on vertical rods. Probably the Chinese abacus has been made during the Song Dynasty (960-1297).

The Chinese Abacus is the most widely used Abacus now. There are other examples of Abacus like Japanese Korean and Russian Abacus.


Ishango bone

Description of the bone

Ishango bone is discovered by the Belgian archeologist Jean de Heinzelin de Braucourt in 1957. The place Ishango is now in the Democratic Republic of Congo near the border with Uganda. It is in a shore of Edward Lake, one of the sources of the river Nile. The bone has been taken to Belgium and now is one of the attractive objects in The Belgian Museum of Science in Brussels.

A second Ishango bone is revealed in a conference in Brussels, Begium, in februari this year. This bone also has curved notches on it, but they have different arrangement than the first one.

The Democratic Republic of the Congo, also had been called Belgian Congo and Zaire, is one of largest countries by area on the African continent. It is located in the central African region. It borders the Central African Republic and Sudan on the north, Uganda, Rwanda, Burundi on the east, Zambia and Angola on the south, the Republic of the Congo on the west, and is separated from Tanzania by Lake Tanganyika on the east.

The bone dates back to 22,000 BC. It is one of the oldest mathematical objects in the world. Some writers consider the document as a table of prime numbers. Others consider it as a lunar calendar. The dispute about the nature of this bone is still going on. Katz wrote in his book that “the notches represent count of certain period of the moon ”.

Arabic Forum