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Egyptian Mathematical Leather Roll


The Egyptian Mathematical Leather Roll (EMLR), dates to the Middle Kingdom, and was purchased in Egypt in 1858 by Henry Rhind, near the time when the Rhind papyrus was purchased. While the Rhind papyrus dates to 1650 BC, no specific date has been determined for the EMLR. Both the EMLR and the Rhind papyrus have been in the British Museum since 1864, donated by the estate of Henry Rhind. The EMLR was not unrolled until 1927.

It consists of 26 unit fraction series each of which is an expression of a rational number of the form 1/p or 1/(pq) into an Egyptian fraction. Five methods were listed to generally convert any 1/p or 1/(pq) to a concise and exact unit fraction series. Four methods have been confirmed as being additive, with three of them being identities and the fourth based on a remainder (Boyer and Merzbacher 1991).

For the last 75 years, only the first four methods have been stressed as fairly representing the central theme in the EMLR. However, in 2002, a connection to the Rhind papyrus 2/(pq) series rule was published, so there is also a fifth method using the rule

 1/(pq)=1/A×A/(pq)
(1)

for A=5, 7, 25, as used implicitly in four of the EMLR's 26 series.

As an example of method five consider 1/8=1/A×A/8.

1/8=1/(25)×(25)/8
(2)
=1/5×(25)/(40)
(3)
=1/5×(3/5+1/(40))
(4)
=1/5×(1/5+2/5+1/(40)),
(5)
=1/5×(1/5+1/3+1/(15)+1/(40))
(6)
=1/(25)+1/(15)+1/(75)+1/(200),
(7)

as listed in the EMLR.

The Rhind papyrus considered A=(p+1), showing that the EMLR was a student test results paper, teaching the student to use several less optimal values for A when learning to convert 1/p and 1/(pq), as a foundation to learning 2/p and 2/(pq) conversion methods.


See also

Akhmim Wooden Tablet, Egyptian Fraction, Rhind Papyrus, Unit Fraction

This entry contributed by Milo Gardner

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References

Boyer, C. B. and Merzbacher, U. C. A History of Mathematics, 2nd ed. New York: Wiley, 1991.Gardner, M. "The Egyptian Mathematical Leather Roll, Attested Short Term and Long Term." In History of the Mathematical Sciences (Ed. I. Grattan-Guiness and B. S. Yadav). Hindustan Book Agency, pp. 119-134, 2002.Gillings, R. Mathematics in the Time of the Pharaohs. Boston, MA: MIT Press, pp. 89-103, 1972.Glanville, S. R. K. "The Mathematical Leather Roll in the British Museum." J. Egyptian Arch. 13, 232-238, 1927.

Cite this as:

Gardner, Milo. "Egyptian Mathematical Leather Roll." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/EgyptianMathematicalLeatherRoll.html

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