||46-49; 243-245; 249-253
|Counting with words; bases
|Alphabetic numbers, mysticism,
|History of modern-day numbers
Book codes: AC=Africa Counts; MMC=Multicultural Math Classroom;
CP=Crest of the Peacock; UHN=Universal History of Numbers
Assignment #1. (final
list--due Thursday, September 20th)
The Api counting system. The Api people of New Hebrides
have the following words for the numbers 1-18:
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 19-24.
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.
Sumerian and Babylonian 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:
and find the results.
10% of 2,300
1% of 2,300
Write the following as Egyptian fractions, using the unit fraction method.
Write 7/16 as an eye-of-Horus fraction.
Write 218,012 in Sumerian numbers.
Write 218,012 in pre-Seleucid Babylonian numbers (i.e. with
Write 218,012 in Seleucid Babylonian numbers.
Give four possible interpretations of TTTTT << TTTTTT
by the pre-Seleucid Babylonians.
Write 180 4/15 in Seleucid Babylonian numbers.
Convert : << TTTT into Indo-Arabic numbers (the
``:'' stands for the place-holder).
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
You will not be responsible for eye-of-Horus fractions or the Sumerian
convert integers from Egyptian hieroglyphics to present-day numbers and
convert fractions from Egyptian hieroglyphics (using the unit fraction
method) to present-day numbers and vice versa.
convert integers and fractions from Babylonian numbers (with or without
a placeholder) to present-day numbers and vice versa. Be aware that
if you are using pre-Seleucid numbers there will be multiple interpretations.
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 multiple-choice questions based on lectures and readings.
To help you focus, here are some key concepts we have discussed or will
You should be familiar with each concept and able to give an example for
finger counting system
additive number system
positional or place-value system
Hall / Department of Math and Computer Science / St. Joseph's University
Images are from the MacTutor
History of Mathematics Archive (used by permission).