Unit 1:
Number Systems

August 27-
September 17


Babylonian mathematics & the Pythagorean theorem


Readings.
 

Topic Book Pages
Tallies AC 17-20;  93-97
Finger counting AC 46-49;  243-245;  249-253
Counting with words; bases MMC
AC
CP
63-71
39-51; 204-209
41-46
Egyptian hieroglyphics UHN
CP
MMC
162-168
57-63
75-80
Babylonian numbers CP
MMC
91-102
80-82
Alphabetic numbers, mysticism, 
and chronograms
MMC 86-7
handout on chronograms
History of modern-day numbers CP 239-243

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:
 

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,
    1. What number (or numbers) is the base of the Api system?
    2. What is the literal translation of toluluna lua?
    3. Write the Api words for the numbers 19-24.
    4. 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.
    1. Write  765,839  in Egyptian hieroglyphics.  Refer to Ifrah, p. 166 to see the standard grouping of symbols.
    2. Write  2,300  in Egyptian hieroglyphics.  Explain how an Egyptian scribe could easily compute the following:
      1. 10% of 2,300
      2. 1% of 2,300
      and find the results.
    3. Write the following as Egyptian fractions, using the unit fraction method.
      1. 4/5
      2. 3/7
      3. 7/11
    4. Write 7/16 as an eye-of-Horus fraction.
Sumerian and Babylonian numbers.
    1. Write  218,012  in Sumerian numbers.
    2. Write  218,012  in pre-Seleucid Babylonian numbers (i.e. with no placeholder).
    3. Write  218,012  in Seleucid Babylonian numbers.
    4. Give four possible interpretations of  TTTTT  << TTTTTT  by the pre-Seleucid Babylonians.
    5. Write  180  4/15   in Seleucid Babylonian numbers.
    6. 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.



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