Readings.
Topic 
Book 
Pages 
Tallies 
AC 
1720; 9397 
Finger counting 
AC 
4649; 243245; 249253 
Counting with words; bases 
MMC
AC
CP 
6371
3951; 204209
4146 
Egyptian hieroglyphics 
UHN
CP
MMC 
162168
5763
7580 
Babylonian numbers 
CP
MMC 
91102
8082 
Alphabetic numbers, mysticism,
and chronograms 
MMC 
867
handout
on chronograms 
History of modernday numbers 
CP 
239243 
Book codes: AC=Africa Counts; MMC=Multicultural Math Classroom;
CP=Crest of the Peacock; UHN=Universal History of Numbers
Assignment #1. (final
listdue Thursday, September 20th)
The Api counting system. The Api people of New Hebrides
have the following words for the numbers 118:
1 
tai 
10 
lualuna 
2 
lua 
11 
lualuna tai 
3 
tolu 
12 
lualuna lua 
4 
vari 
13 
lualuna tolu 
5 
luna 
14 
lualuna vari 
6 
otai 
15 
toluluna 
7 
olua 
16 
toluluna tai 
8 
otolu 
17 
toluluna lua 
9 
ovari 
18 
toluluna tolu 
Based on this information,

What number (or numbers) is the base of the Api system?

What is the literal translation of toluluna lua?

Write the Api words for the numbers 1924.

What do you think might be the words for 25? 26? 34?
55? 125? 153? There are several answers that make sense.
Justify your answers by translating them literally into English.
Egyptian numbers.

Write 765,839 in Egyptian hieroglyphics. Refer to Ifrah,
p. 166 to see the standard grouping of symbols.

Write 2,300 in Egyptian hieroglyphics. Explain how an
Egyptian scribe could easily compute the following:

10% of 2,300

1% of 2,300
and find the results.

Write the following as Egyptian fractions, using the unit fraction method.

4/5

3/7

7/11

Write 7/16 as an eyeofHorus fraction.
Sumerian and Babylonian numbers.

Write 218,012 in Sumerian numbers.

Write 218,012 in preSeleucid Babylonian numbers (i.e. with
no placeholder).

Write 218,012 in Seleucid Babylonian numbers.

Give four possible interpretations of TTTTT << TTTTTT
by the preSeleucid Babylonians.

Write 180 4/15 in Seleucid Babylonian numbers.

Convert : << TTTT into IndoArabic numbers (the
``:'' stands for the placeholder).
Sample Test Questions.
You may bring a 5x7 index card with any notes you wish on it.
The test will be about 30 minutes long.

Several questions will be similar to homework questions. In particular,
you should be able to

convert integers from Egyptian hieroglyphics to presentday numbers and
vice versa.

convert fractions from Egyptian hieroglyphics (using the unit fraction
method) to presentday numbers and vice versa.

convert integers and fractions from Babylonian numbers (with or without
a placeholder) to presentday numbers and vice versa. Be aware that
if you are using preSeleucid numbers there will be multiple interpretations.
You will not be responsible for eyeofHorus fractions or the Sumerian
system. :)

There will be some questions on a language you haven't seen before, similar
to question 1 on the homework. You will be asked to determine the
base or bases of the system, and write down a few words for numbers.

There will be a few multiplechoice questions based on lectures and readings.
To help you focus, here are some key concepts we have discussed or will
discuss:

tally

onetoone correspondence

finger counting system

base

additive number system

unit fraction

positional or placevalue system

placeholder

alphabetic system

chronogram
You should be familiar with each concept and able to give an example for
each.
Web Resources.
Multicultural Mathematics
home page.
Images are from the MacTutor
History of Mathematics Archive (used by permission).
Rachel W.
Hall / Department of Math and Computer Science / St. Joseph's University
/ rhall@sju.edu