Historical Quest:
We mentioned that the Egyptians wrote their fractions
as sums of unit fractions. Show that every positive fraction
less than 1 can be written as a sum of unit fractions.
References:
Bernhardt Wohlgemuth, "Egyptian Fractions," Journal
of Recreational Math, Vol. 5, No. 1 (1972), pp. 55-58.
The
Egyptians had a very elaborate and well developed system
for working with fractions. Write a paper on Egyptian
fractions.
References:
George Berzsenyi, "Egyptian Fractions," Quantum,
November/December 1994,
p. 45. Follow up comment in The College Mathematics Journal,
March 1995, p. 165.
Richard Gillings, Mathematics in the Time of the
Pharaohs (New York: Dover Publications, 1982).
Spencer Hurd, "Egyptian Fractions: Ahmes to Fibonacci
to Today," Mathematics Teacher, October 1991, pp.
561-568.
