Re: Strange Maths (was Re: Why not 13 months?)
13 Jul 1995 14:41:54 GMT
In article <firstname.lastname@example.org>, email@example.com says...
>In article <firstname.lastname@example.org>, Whittet@shore.net (Whittet) wrote:
>> or 5^2 + 6^2 + 7^2 + 8^2 +9^2 + 10^2 / 7^2 + 8^2
>Which doesn't quite equal pi.
>Watch out, folks, here come those Pyramid Inches :-)
Since you consider yourself knowledgeable in this area, perhaps you would care to
tell us what the actual measurement of the base of the great pyramid was in inches,
and why it is relevant to the discussion?
Perhaps this was suggested because, as I recall, I had said something to the effect that
100 x 365.24 x 24 x 60 x 60 / 24902.72727 x 5280 x 12 x 2 = 1
just above the relation you cite above.
The relation between the two is of course the work of a brilliant mathematician
named John Taylor, who was in his fifties when Howard-Vyse returned from Egypt.
Taylor was puzzled by why the builders of the pyramid had chosen an angle like
51 degrees 50 minutes, instead of 60 degrees at which to construct its slope.
You might *think about this in terms of how you would instruct workmen to course
the stones so the overlaying casing could be carved at a consistent angle*.
If I were designing this building, I would want most of my stones to be about the same
dimensions, certainly I would like the height of the stones in any given row to be
consistent. Obviously if stones are used of different heights in different rows, any
stones left over from one row can't be easily reused in the next.
The stones should also be about the same width and length so they align with each other
in a pavement for each course. If the gaps between them are too large or the surface of
any given course too far out of level, the structure would be weakened.
We can observe from the stones remaining with the casing removed That the outside rows
allign neatly. If they were they layed in a u shaped pattern from the outside in toward
the center it would work, but the perimeter of each course would have to be calculated
before the work was begun.
Whew, it just struck me how much really careful work that would have taken. You should
see what modern architects have to go through just to make sure the casework they order
fits in the freight elevator.
Please excuse my architectural digression ! Anyway... back to Taylor...
He set about drawing and redrawing every ferature of the pyramid on the basis of the
measurements reported by Howard-Vyse.
"Analyzing Herodotus' report of what the Egyptian priests had told him about the surface
of each face of the pyramid, Taylor concluded that they had been designed to be equal in
area to the Pyramids height. If so, this meant *the building was of a particular, if not
unique geometric construction; no other pyramid has these proportions.*"
"Taylor then discovered that if he divided the perimeter of the pyramid by twice its
height it gave him a quotient of 3.144, remarkably close to the value of Pi which is
computed at 3.14159+. In other words *the height of the pyramid appeared to be in
relation to the perimeter of its base as the radius of a circle is to its circumference*."
"This seemed to Taylor far too extraordinary to attribute to chance and he deduced
that the Pyramid must have been specifically intended by its builders to incorporate
the incommensurable value of PI"
Existing Egyptian mathematical papyri and leather rolls such as those from which
Milo Gardiner has worked out algorithms for unit fractions don't show any evidence of
such early sophistication, and indeed arguably not even some 500 years after the
pyramid was built.
"Searching for a reason for such a Pi proportion in the Pyramid, Taylor concluded that
the perimeter might have been intended to represent the surface of the Earth at the
equator, while the height represented the distance from the earths center to the pole."
"Perhaps Jomard had been right: perhaps the ancient designers had measured the length
of a geographical degree, multiplied it by 360 degrees for the circumference of the
globe, and by the Pi relation had deduced the polar radius of the Earth, immortalizing
their knowledge by making the circumference to scale with the perimeter and the radius
to scale with the height of the pyramid."
The equitorial circumference of 24,902.72727 mi divided by 360 degrees equals
69.1742 mi, or 365240 ft.
"To Taylor the inference was clear: The ancient Egyptians must have had a series of
measurements based on the true spherical dimensions of the planet, which used as a
unit which was within a thousandth part of being equal to a British inch."
Another way to put this is that the number of days in a millenia divided by the
the length of a degree, gives the number of feet in a mile, a standard of measure
which is clearly derived from the proportion of the two observed constants.
"Fired by what he considered a stunning discovery, Taylor launched into a monumental
study of the cubits, feet, spans, inches and stadia, not only of the ancient Egyptians,
but of the Babylonians, Hebrews, Greeks and Romans."
"He found that all kinds of cubits had been used in the past, some of which appeared
to have mathematical relations to each other. He also analyzed the ancient measures
of cubic capacity along with the modern gallons, firkins, kilderkins, hogdheads, butts,
barrels, gills, pecks, faggots and chaldrons"
"Taylor was amazed to find that the cubic capacity of the granite coffer was almost
precisely four times what the British farmer still used as a standard measure for grain,
the quarter, or eight bushels."
>From all his studies Taylor concluded that the proportions of the pyramid had
definitely been intended to incorporate geometric and astronomical laws simply
and easily expressed."
For the next hundred years a considerable portion of Egyptian Archaeology
was focused on just how close to 760' 11" each side of the Great Pyramids
base actually was.
760' 11" x 12 x 4 = 36524"
So as to determine the variance in the English inch from the actual measures
used in antiquity.
>=== James Petts ===