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Terry,
Can you really conclude from the
information below that the Egyptians really used feet and inches. We know
that the Egyptians used the cubit, a unit of length equal to the distance from
the elbow to the tip of the finger. So, why wouldn't they use other
measurements taken from body parts? The foot is a part of the body and so
is the inch, it being the length of the thumb from the tip to the
knuckle.
In order to keep numbers and math simple
and also the fact that most innumerate and illiterate people could not count
past 20, units were devised so that the relationship between one unit and the
next was less than 20. You will see this even in modern times when
referring to non-SI unit systems. I'm sure they would have broken the 480
feet into something smaller and simpler.
The main problem with trying to convert
metric units back to stone age units, is the true value of the stone age
units are unknown. I might interpret from you statements below that
you would have a believe that even if the Egyptians did use a system of feet and
inches, they are the exact same feet and inches used in the US today. But,
can they be? It is a fact that until the metric system came into
existence, the only thing common between units in various countries is the unit
name. A foot, an inch,a pound, etc. varied in value from country to
country, town to town and even person to person. So, what is the real true
length of any of the non-SI units still in existence?
Because of these varied values of the
stone age units, it is possible to come up with any conversion factor.
Thus the foot/metre could just as well been 0.3047967, as this will make the
146.302 417 m become exactly 480 feet. And again, that 480 feet would be
the "foot" used at that time by the person using it. A foot used by
someone else in a different time and place would be different, even if only by a
small amount.
Comments?
The inch connection
A very interesting thing happens when the heights from above are changed from
meters to feet and inches. The old conversion formula is:
Length in Meters / .30479974 = Length in Feet
First the average height:
146.302417/.30479974 = 479.9952159
= 479 feet 11 and
15.08/16 inches
Then the rest of them:
| North |
479 feet 11 and 15.09/16 inches |
| East |
479 feet 11 and 14.89/16 inches |
| South |
479 feet 11 and 15.15/16 inches |
| West |
479 feet 11 and 15.18/16
inches |
So this best set indicates that the height of the Pyramid is one
sixteenth of a inch less than 480 feet. The first of those most interesting
features.
I did not believe this result at first. I ended up rechecking the
calculations and trying three other variations of the "error of fit" equation
(equation 3). For me in the end, it came down to one of the following two
conclusions:
1. The data from table one is a hoax perpetrated by J.H. Cole or
2. The
Egyptian used feet and inches.
On a trip to Washington D.C. I went to the Congressional Library to try and
investigate both of the above. All I could find about J.H. Cole's survey was
that he was criticized because his data on the north side mark (115.090 +
115.161) did not match the data for the north base (230.253).
And on the foot, I found a lot of authors claimed it was a very ancient
unit of measurement but none were really sure of how ancient it was or where it
really had come from (but most agreed that the foot of today was derived from
the British Imperial Yard). So none of this is conclusive. It was only after
studying the unit fractions of the "best set that I started to lean toward
conclusion 2.
Since the Egyptians did not use the
Arabic numeric system, how did they represent their equations and numbers in
written form? Did they use the solidus to represent division or some other
symbol? Did the Egyptians use the base 10 numeric system or some other
base?
Can you enlighten me on
this?
Egyptian fractions
The early Egyptians had a different way of handling fractions and ratios.
Whenever a fraction was involved in a math problem, they would convert it into a
sum of fractions, all with a numerator of one. Here are some examples:
| 2/7 = 1/4 + 1/28 |
| 2/97 = 1/56 + 1/679 + 1/776 |
| 2/99 = 1/66 + 1/198 |
| 23/40 = 1/2 + 1/14 + 1/280 |
The first three are from documents written about 1700 B.C. These are
conversion examples starting with the integer fractions. I'll take another
approach, using the survey data and guesses about the height to form ratios,
then converting the ratios to the nearest equivalent Egyptian fraction.
The procedure used for converting is essentially the same as the one provided
by J.J. Sylvester, a British mathematician (1814-1897).
John
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