**THE DISCOVERY OF A MATHEMATICAL DOCUMENT AT ISHANGO VILLAGE **

**AROUND LAKE EDWARD NEAR SEMULIKI RIVER.**

**THE ISHAGO BONE**: was discovered by Belgian archeologist in 1957 in a place called Ishango at a shore of Lake Edward near the border of D.R Congo and Uganda, part of the source of the river Nile.

The bone is 10 cm long dark brown object with a tally notches made on it and tabulated in three rows (columns). **A second Ishango** bone was also discovered by the same person.

A discussion about Ishango bone is still going on.

One group of researchers in Beligium thought that the bone has shown that ancient East and Central African people around Bunyoro during pre-historic time had knowledge of mathematics .

Other researchers have argued that the bone is just a historical document. It could be some sort of a calendar according to the second group of researchers

It proves that people around Eastern Zaire and western and Central Uganda, perhaps during or before the era of **Batembuzi rule,**used tools (instruments) for different mathematical and scientific purposes like counting, measuring and registering facts.

A study by international scientific researchers is apparently continuing to investigate how ancient people around this area of Africa have used tools for mathematical calculations and registrations.

We will concentrate mainly on the Ishango bone (tool / document) which was used **at 22,000 BC** (a date that is corrected many times by researchers).

History of this document is 22,000 BC. The historical position of this period is the one commonly known as the Stone Age. It is roughly coinciding with the period supposedly before the discovery of agriculture.

But how in that time there was sharp increase in the diversity of artifacts is a mystery. Also evidence from elsewhere in Africa like at **Blombos** cave in South Africa at that time bone artifacts and a kind first art appeared in the fossils in Africa.

**Recordings**

On the **Bone**,the first row shows a system of addition based on the number** ten**. The numbers in this row are:

**10+1, (10 * 2) + 1, (10 * 2) – 1, 10-1 **

This shows understanding of addition, subtraction and multiplication based on ten.

The second row starts with 3 notches. It is then doubled to become 6.

The same is done with the next number (4), which is doubled to become 8. The number 8 followed by 10 which halved to form 5. This is followed by 5 and 7. The operations give us evidence that people who have used this document have some understanding of multiplication and division by 2.

The last row is a** set of prime numbers** between 10 and 20. These numbers are 11, 13, 17 and 19. The numbers in this row as well as in the first row are odd number.

**The sum of the numbers in the first and the last rows is 60.** This can not be a coincidence.

The sum of the numbers in the last row in the middle is 48. This implies that all sums are multiple of 12.

From all these remarks some people suggest that this bone may have been used as an ancient **counting tool **or an** ancient ****calculator **or an** accounting ledger **document.

It may have been used to record data regarding live stock, lost number of solders, assets, etc.The bone reveals that African people at that time had an understanding of mathematics.

The technique of dividing and multiplying by 2 was used by old Egyptians in later times. This can lead to suggestions that Egyptians were largely influenced by their old African ancestors from around the source of the Nile (ancient Bunyoro region).

The second assumption is that Isahango bone is a **calendar**. But the fact that numbers in two rows have a sum of 60 is not a proof of this assumption.

Calendars were used in ancient times as widely known.

The Egyptians used a solar calendar. They knew that a year has 365 day and 12 months. Every month has 30 days. They reserved extra 5 days to complete year days to be 365 days.

**ISHANGO VILLAGE**

Is found near the confluence of river Semliki and lake Edward in what is now Eastern DRC ( formerly Zaire) Ishango in local surounding dialect which means swampy place or in kinyoro and kinyankole in western Uganda, the word means originally found place but also the term can be derived from * ekishanga *which means a swampy place.

**Semliki River** (sometimes **Semuliki**) is a major river in Central Africa. It flows northwards from Lake Edward in theDemocratic Republic of the Congo, across the Uganda border, through western Uganda in Bundibugyo District, near theSemuliki National Park.

It empties into Lake Albert in Uganda at 1.2225°N 30.5038889°E.

In places, the river has demarcated the border between Uganda and the DRC; its changing course sparked confusion in 2009 over the location of the boundary between the two countries.(wikipedia)

The structure and the techniques on the Ishango bone closely resembles the **LEBOMBO BONE **which is a similar ancient African document discovered in the Lebombo mountains located between South Africa and Swaziland in the 1970s *during excavations of Border Cave and dated about 35,000 B.C., *

*the Lebombo bone is marked with 29 clearly defined notches. This suggests it may have been used as a lunar phase counter, in which case African women may have been the first mathematicians, because keeping track of menstrual cycles requires a lunar calendar. *

*Certainly, the Lebombo bone resembles calendar sticks still used by the SAN people of Botswana and Namibia.*