146 Views

Download Presentation
## The Ishango Bone

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**When, where, who and what??**• The Ishango bone is a bone tool dating from about 18 000 to 20 000 B.C. • Upper Paleolithic (a.k.a Late StoneAge), about 40 000 – 10 000 B.C. • Homo Sapiens , hunter-gathers, bow and arrow, cave painting, and tool specialization • Interesting note: Africa = Stone Age Europe = Upper Paleolithic**Background**• It is the fibula of a baboon with a sharp piece of quartz fixed at one end. • It is 10cm long. • Contains a series of notches carved in groups on three rows running the length of the bone. • Was it a writing tool, a “primitive” mathematical tool, an astronomical tool, or something different?**Found in 1960 in the then Belgian Congo, now the border**between Uganda and The Democratic Republic of the Congo. • Believed to be used by the Lake Edward Ishango fishing population.**Interestingly enough, the Ishango Bone currently sits in the**Royal Belgium Institute of Natural Science.**The markings on rows (a) and (b) each add to 60.**• Row (b) contains the prime numbers between 10 and 20. • Row (a) is quite consistent with a numeration system based on 10, since the notches are grouped as 20 + 1, 20 - 1, 10 + 1, and 10 - 1. • Finally, row (c) seems to illustrate for the method of duplication (multiplication by 2)**BUT ...Alexander Marshack (an American Paleolithic**archaeologist) concluded the Ishango was used as a lunar calendar.Claudia Zaslavsky (an American ethnomathematician) concluded the creator of the Ishango was in fact a woman, who used the bone to track her menstrual cycle.**The Yoruba people currently number over 15-30**million.According to their legends they came from Upper Egypt and settled what is now Nigeria, Togo, and the Republic of Benin between 600 and 1000A.D.**One of the most peculiar number scales in existence.It is a**base 20 system, many examples of which are found in western Africa.It is unusual because it relies on subtraction to a great degree.**The numbers from one to ten are represented with specific**terms:1. okan2. eji3. eta4. erin5. arunEtc.**Numbers higher than 10 are represented using addition and**subtraction termsFor example:11, 12, 13 and 14 would be represented as:10 + 1 or ookan laa10 + 2 or eeji laa 10 + 3 10 + 4**Then the numbers 15 to 20 are represented using**subtraction:20 – 5 or eedogan20 – 4 or eerin din logan20 – 320 – 220 – 1**Basically, you can add up to 4 to make a number. Anything**over 5 must be subtracted. I.e.: 14 = 10 + 4 so you are adding. 15 = 20 – 5 so you are subtracting. Adding -------------------------- 5--------------------------- SubtractingLet’s try this together:22 = 36 =**Answers:22 = 20 + 2 36 = (20 x 2) – 4Can you do it? Try**to represent the number on your table in the Yoruba system.