Mark Heaton Wrote:
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> The design of the Grand Gallery provides an
> explanation of how to square the circle for the pi
> approximation 22/7.
>
> Marking off twice the diameter of a circle on the
> floor of the Grand Gallery of the Great Pyramid
> would result in a vertical rise corresponding to
> the precise side length of the circle’s equal
> area square. It is, of course, impossible to
> square the circle exactly, but this proposition
> requires a theoretical slope of precisely 26.30
> degrees, or 26.31 degrees for the Pi approximation
> 22/7.
>
> Smyth determined the angle of the slope as a
> weighted average of approximately 26.29 degrees
> (26 degrees 17 minutes 37 seconds). A build angle
> would be within 0.05 degrees of the intended angle
> for a positive error of 1 part in 1000 on the rise
> and a negative error of 1 part in 1000 on the run,
> or vice versa, and the proposed model is
> approximately 0.02 less than the theoretical
> angle.
>
> Petrie measured offsets from a mean axis of 26.275
> degrees (26 degrees 16 minutes 30 seconds), or
> approximately 0.035 degrees less than the
> theoretical slope. A simple 1 in 2 slope would
> require an angle of precisely 26.565 degrees which
> is 0.255 degrees steeper than the theoretical
> slope, so this may have been the intended slope
> but only if the build standard was low.
>
> The diameter of the Pyramid’s Equal Area Circle
> is 280 cubits. The theoretical slope to square the
> circle for the Pi approximation 22/7 is defined
> exactly by a right angled triangle with a long
> side of 15 cubits and a hypotenuse equal to the
> square root of 280 multiplied a cubit (approx
> 16.73 cubits). Remarkably, the gallery’s
> vertical height above its entrance may be regarded
> as the diameter of a 1/sr280 scale model of the
> Pyramid’s Equal Area Circle.
>
> Smyth’s first three measurements of the vertical
> height near the entrance, as taken on the inclined
> floor rather than the broken section, were 344.2
> inches, 343.7 inches and 346.0 inches. The mean of
> 344.6 inches (approx 8.753 metres) is 0.6 inches
> (approx 15 mm) less than the theoretical vertical
> height of sr280 cubits. Applying Smyth’s
> determination of the average slope of the gallery
> to the vertical height yields a perpendicular
> height of 308.9 inches (approx 7.846 metres) which
> is 0.55 inches (approx 14 mm) less than the
> theoretical perpendicular height of 15 cubits, as
> calculated for a cubit of 20.63 inches (524 mm).
> The Grand Gallery was built perpendicular to the
> slope.
>
> The model circle with a diameter of sr280 cubits
> is equal to a square with a side length of 2 x
> sr55 cubits and an area of 220 square cubits. This
> means the Pyramid’s Equal Area Circle with a
> diameter of 280 cubits has an area 280 times
> greater than the model circle:
>
> Area of triangular cross-section of pyramid = 1/2
> x 440 x 280 = 61,600 square cubits
> Pyramid’s Equal Area Circle = 280 x 220 square
> cubits = 61,600 square cubits
> 22/7 x 140 cubits (radius) x 140 cubits (radius) =
> 61,600 square cubits
>
> This model provides an explanation for the unusual
> soaring height of the Grand Gallery, as assessed
> at the entrance near the north end wall, so
> squaring the area of a circle for the Pi
> approximation 22/7 is naturally applicable to the
> Pyramid’s Equal Area Circle:
> Side length of equal square = [sr55/sr280] x (2 x
> diameter of 280) = sr55 x sr280 x 2 cubits
> Area of pyramid’s equal area square = 55 x 280 x
> 4 square cubits = 61,600 square cubits
>
> Applying this model to a circle with a diameter of
> 70 digits yields an area of 3850 square digits.
> The volume of the sphere latent in the dimensions
> of the sarcophagus would then be 2/3 x 70 digits x
> 3850 cubic digits which is exactly equal to the
> volume of a sphere with a diameter of 70 digits as
> calculated for the Pi approximation 22/7.
>
> Mark

and why would someone - and if - a big if - had the AE continued on who would have gone into the pyramid and
'Marking off twice the diameter of a circle on the floor of the Grand Gallery of the Great Pyramid'?