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Figure 3. Finding the royal cubit, half a remen, and pi 22/7
(all measures in inches)


Developments

    • 1. A reverse image of 3.4.5 triangle ABC is created - it forms triangle JCB.
    • 2. BJ is extended to U.

Outcomes

    • 1. BU is 7 7/24 (7.291666 ...) inches, half a remen, that is, ten remen digits. BU is 1/1000th of what later became known as the Greek/Roman stade (607 23/36 British imperial feet or 600 Greek feet or 625 Roman feet. A remen digit measures 35/48 (0.7291666 ...) inch.
    • 2. LN is 6.875 inches, one-third of an ancient Egyptian royal cubit of 20.625 inches. KT is also 6.875 inches. The 3.4.5 proportion triangle KTF has a perimeter of 20.625 inches, the royal cubit. Note that KF is on the same line as the remen described in Figure 2.
    • 3. KL is 1.09375 inches and KM 2.1875 inches. LN is 6.875 inches and, as stated, one-third of a royal cubit. The quotient of LN 6.875 divided by KM 2.1875 is 22/7. This is arguably the most remarkable manifestation of the proportion ever found in a geometric configuration considering its relationship to the measures being unfolded here. Note that the intersection of BJ with AC establishes L and thereby KM and LN.


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