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Berlin Papyrus
Posted:
Mar 30, 2010 6:36 PM


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. SchackSchackenberg within a pesu problem discussed in RMP 69 and Ahmes' pesu proportional solutions solved in RMP 6978, 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, RobinsShute 1987 and Clagett 1999 failed to stress SchackSchackenberg'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 SchackSchackenberg's solution with no reservations.



