From: jfb@draco.macsch.com (John Baskette)
Subject: Re: The Great Pyramid of Giza
Organization: MacNeal-Schwendler Corp.
Date: Mon, 23 Nov 92 20:43:49 GMT

In article <1992Nov21.091202.14495@netcom.com> bosak@netcom.com (Jon Bosak) writes:

>John Baskette (in an otherwise excellent summary of the facts
>regarding pyramid measurements):
>
>JB> The pi ratio in the pyramid is derived from the ratio of the 
>JB> pyramid baseline divided by the height.  The average baseline 
>JB> is 9,068.8.  Divide this by the height (5776 +- 7 inches) and you
>JB> get 1.5701.  This value times two is 3.1402.  A better approximation
>JB> of pi is obtained using the angle of the slope of the faces of the 
>JB> pyramid.  The angle for the north slope according to Petrie is 
>JB> 51 deg. 50 min. 40 sec. +- 1 min. 5 sec.  The same ratios in a 
>JB> pyramid with this angle yield a value of 3.1427+-0.002.  
>JB> 
>JB> Petrie believed this feature was accidental.  The Egyptians, he
>JB> said, chose to build the pyramid using a sloping angle that
>JB> was 11 at the base and 7 at the height.  11/7 is 1.5714.  Times
>JB> that by two and you get 3.1429 which is just about exactly
>JB> the angle of the sloping stones.
>
>I don't get the impression that Petrie believed this relationship
>based on pi was accidental at all.  In _Pyramids and Temples of Gizeh_
>he says:
>
>    For the whole form the pi proportion (height is the radius of a
>    circle = circumference of Pyramid) has been very generally
>    accepted of late years, and is a relation strongly confirmed by
>    the presence of the numbers 7 and 22 in the number of cubits in
>    height and base respectively; 7:22 being one of the best known
>    approximations to pi.  With these numbers (or some slight
>    fractional correction on the 22) the designer adopted 7 of a
>    length of 20 double cubits for the height; and 22 of this length
>    for the half-circuit.  The profile used for the work being thus
>    14 rise on 11 base.
>
>If you know some other place where Petrie explicitly recanted this
>theory, I would like to hear of it.  As far as I know, he found the
>explanation based on pi to be among the most likely ones.  It is true
>that the value of 22/7 for pi (or 11/14 for pi/4) is traditionally
>attributed to Archimedes, but it seems highly unlikely that this value
>had not been discovered previously by the Egyptians, from whom the
>Greeks directly inherited several standards of weight and length.

I think that Jon is correct about Petrie's thinking and that my statement
about "accidental" is not correct and is based on my misreading of the 
text. Note that my explanation of the construction profile which was an
attempt to simplify what Petrie said is not essentially different.

I referenced a copy of _Pyramids and Temples of Gizeh_ when presenting
data to refute the claims about the base circuits encoding the days
in a year idea and other data.  Note also that the facts do show that
the pi value used, even if it was intentionally incorporated into the 
design of the Pyramid by the ancient Egyptians, is not the extremely 
accurate value unmatched until modern times as claimed by Pyrmidologists. 

John
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