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Topic: Berlin Papyrus
Replies: 6   Last Post: May 25, 2010 1:58 PM

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Milo Gardner

Posts: 1,105
Registered: 12/3/04
Berlin Papyrus
Posted: Mar 30, 2010 6:36 PM
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The Berlin Papyrus was partly decoded and published in 1862, a year before the British Museum received the RMP and the EMLR from the estate of Henry Rhind.

The Berlin Papyrus contains two second degree equations, each associated with x and y stated in a proportional relationship.

x^2 + y^2 = 100

and,

x^2 + y^2 = 400

A clear understanding of the scribal solution was published in 1900 by H. Schack-Schackenberg within a pesu problem discussed in RMP 69 and Ahmes' pesu proportional solutions solved in RMP 69-78, all scaled the number of hekats of grain needed to produce n loaves of bread.

In RMP 69 3 + 1/2 hekats of grain produced 80 loaves of bread.

The scribal solution is discussed on Planetmath per:

http://planetmath.org/encyclopedia/BerlinPapyrusAndSecondDegreeEquations.html

and Wikipedia per:

http://en.wikipedia.org/wiki/Berlin_Papyrus

The RMP 69 solution, connected to the Berlin Papyrus, is discussed on Planetmath per:

http://planetmath.org/encyclopedia/RMP69AndTheBerlinPaprusProportionMethod.html

The standard 1920s scholars Peet, Chace, et al, followed by Gillings 1970, Robins-Shute 1987 and Clagett 1999 failed to stress Schack-Schackenberg's common proportional solution to both problems, each for a different personal reason.

After 2000 a new path to reading 2/n tables and unit fraction arithmetic arrived on the scene, fully accepting Schack-Schackenberg's solution with no reservations.



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