Unit 1: Number Systems August 27- September 17 Babylonian mathematics & the Pythagorean theorem

 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.

• Several questions will be similar to homework questions.  In particular, you should be able to
• convert integers from Egyptian hieroglyphics to present-day numbers and vice versa.
• 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.
You will not be responsible for eye-of-Horus 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 multiple-choice questions based on lectures and readings.  To help you focus, here are some key concepts we have discussed or will discuss:
• tally
• one-to-one correspondence
• finger counting system
• base
• unit fraction
• positional or place-value system
• placeholder
• alphabetic system
• chronogram
You should be familiar with each concept and able to give an example for each.

Web Resources.

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