## Sunday, August 23, 2009

### The Royal Cubit & Foot of the Fourth Dynasty

A significant event in the history of Ancient Egypt was the unification of Upper and Lower Egypt. This was accomplished by focussing on similarities rather than differences. The subsequent events show what happens if two people work with each other instead of against each other. The central administration of the Old Kingdom resulted in a new class of scribes and a general advance in society over previous times.

But our main focus is the royal foot (remen) whose use can be seen in the design of the pyramids of the Old Kingdom. Let's take a look at the Great Pyramid of Giza whose original dimensions are estimated to have a base of 230.5 m and a height of 146.6 m. What does this tell us? Well, the ratio of the base to the height is 1.57231 which doesn't say much by itself but we can look at its continued fraction.

Ignoring the sequence after 1,1,1,2 tells us that the ratio is nearly equal to 8/5 while ignoring that after 1,1,1,2,1 suggests a ratio of 11/7. Comparing these multiples of the royal foot and cubit with the dimensions of the pyramid gives the following information,

which shows that one gets a best fit for 11/7 with a scale factor of 40 cubits or 70 feet. This implies that in Khufu's time,

1 royal foot = 299.35 mm

1 royal cubit = 523.86 mm

which is very close to the values for the cubit stick from the 18th Dynasty.

An interesting coincidence is that,

11/7 = 1.5714

π/2 = 1.5708

π/2 is the arc of a circle corresponding to 90°.