Number Systems

Suggestions

1. Focus on one or two numbers systems or one characteristic of number systems in several different systems.
2. The idea of different bases (ours is base 10) can be a helpful organizing idea.

Resources

• Books on reserve in the library:
  • Chapter 2: The counter culture from "Pi in the Sky: counting, thinking, and being" by John D. Barrow.
  • Ifrah, Georges, The universal history of numbers : from prehistory to the invention of the computer, 2000.
  • Ifrah, Georges, From one to zero: a universal history of numbers, 1985.
  • Zaslavsky, Claudia, Africa counts : number and pattern in African culture, 1979.
  • Zaslavsky, Claudia, The multicultural math classroom : bringing in the world , 1996.
  • Menninger, Karl, Number words and number symbols; a cultural history of numbers, 1969.
  • Lumpkin, Beatrice,Algebra activities from many cultures, 1997.
  • Bazin, Maurice, Math and science across cultures: activities and investigations from the Exploratorium, 2002.
• Links to Information on Number Systems (from MathForum)
• Development of Counting Systems (from online module/course at U. of Wolverhampton)
• Different ways to count (brief summary)
• More links about number systems
• Number Systems of the World, particularly interesting:
  • Hindi (no apparent pattern, just memorize words for 1-100),
  • Alamblak (only has words for 1, 2, 5, and 20 and so every other number is described as a combination of them),
  • Ainu (only 15 native speakers),
  • Tzotzil (base 20, vegesimal, for numbers bigger than 100)
  • Danish (has fractions)
• Pitjantjatjara
  Lesson Plan with more about Pitjantjatjara
• Ipili (body counting, base 14) (the first sentence is a bit colloquial, but the author has first hand knowledge of the Ipili) Page down to November 21 or search in text for "teseradecimal".
• 1-10 in over 4500 languages
(not as helpful as previous links)
• History of Math at St. Andrews (has information on Babylonian, Egyptian, Greek, Indian, Arabic, and Mayan numerals)
• Quipu
  • What is a khipu?
  • Quipu (Link to How to make your own)
  • The Quipu (references to a few articles)
• Mayan mathematics (includes java applet)
• More Abacus (applet)
• About the Abacus

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Last modified: 4/30/03