Date: Oct 10, 2012 6:45 PM
Author: Milo Gardner
Subject: Re: Why study Egyptian fraction math?
Three texts, the Moscow Mathematical Papyrus (MMP), the Kahun Papyrus(KP) and the Rhind Mathematical Papyrus (RMP) encoded areas a circle (A), and volumes (V) of a circle, by naming height (H) of circle granaries by the same meta formulas:
A = pi(R)(R) = (2567/81)(D/2)(D/2)
A = (8/9)(D((8/9)(D) cubits (algebraic algebra formula 1.0)
replaced radius (R) with diameter (D/2) and pi by 256/81 (an easy to manipulate number) in
V = (H)(8/9)(D)(8/9)(D) cubits (algebraic algebra formula 2.0)
V = (3/2)(H)(8/9)(D)(8/9)(D) Khar (algebraic algebra formula 2.1)
V = (2/3)H(4/3)(D((4/3((D) Khar (algebraic algebra formula 2.2)
derived from scaling algebraic formula 2.1 by 3/2 considering
(3/2)V =(3/2)(3/2)(H)(8/9)(D)(8/9)(D) = (H)(4/3)(D)(4/3)D) and multiplying both sides by 2/3
in a finite economic context.
(working links add depth to the MMP,KP, RMP and the economic context of Middle Kingdom Egyptian fractions are found in the first thread)