Allen Klinger, © 10/25/2004

Even mathematics' simplest aspects involve symbols, abbreviation and conventions. These may form an awkward barrier to understanding. Even more important, the conventions aren't always the best way to indicate the idea involved. A Western convention and the Asian (Vietnamese) equivalent, for tallying one through five (Compare Methods), shows the latter as quickly recognizable and advantageous.

Because a cultural context of some early quantitative issue may differ radically from our current understanding, students are asked to learn things that foreclose an option. That is true of partition, especially in the case of fair apportioning. For instance, dividing nine loaves of bread fairly among ten people can be solved in two ways. Our approach today involves nine nine-tenth, one-tenth partitions. That seems to be a fair way but it isn't how ancient Egyptians would have done it. In their view, to give equal portions to all ten people involved one needs to account for people in a real situation, something at the heart of a different numerical partitioning method. (The nine receiving nine-tenths a loaf would likely be envied by the tenth person who receives nine one-tenth loaf crusts.) [More at Unit Fractions, Fractional Blocks.]

Book References

Temple, Robert, The Genius of China, New York: Simon and Schuster, 1986.

Neugebauer, O., The Exact Sciences in Antiquity, New York: Dover, 1957, 1969.

Gillings, Richard J., Mathematics in the Time of the Pharaohs, Cambridge, MA: The MIT Press, 1972; NY: Dover Publications, Inc., 1982, ISBN 0-486-24315-X.

Ascher, Marcia and Ascher, Robert, Mathematics of the Incas: Code of the Quipu, Dover, 1997, ISBN 0486295540.

Joseph, George Gheverghese, The Crest of the Peacock - Non-European Roots of Mathematics, London UK: I.B. Tauris & Co. Ltd Publishers, 1991.

Ascher, Marcia, Ethnomathematics, A Multicultural View of Mathematical Ideas, Pacific Grove, CA: Brooks/Cole Publishing Company, Wadsworth, Inc., Belmont, CA, 1991, ISBN 0-534-14880-8.

Selin, Helaine, ed., Mathematics Across Cultures - The History of Non-Western Mathematics, Dordrecht, The Netherlands: Kluwer Academic Publishers, 2000, ISBN 0-7923-6481-3.

Bronowski, J., The Ascent of Man, Boston MA: Little Brown, 1973.

Osen, Lynn M., Women in Mathematics, ISBN 0-262-15014-X, Cambridge MA: The MIT Press, 1974.
10/25/04 Version
©2003 Allen Klinger