Re: Strange Maths (was Re: Why not 13 months?)
Whittet (Whittet@shore.net)
24 Jul 1995 19:02:02 GMT
In article <3v09hb$bbj@sunsystem5.informatik.tu-muenchen.de>, paysan@informatik.tu-muenchen.de
says...
>
>
>In article <3um8n0$98o@shore.shore.net>, Whittet@shore.net (Whittet) writes:
>>First the Pyramid has a slope of 51d51' which makes it far from easy to const
>ruct
>>casually.
>
>Well, that's 14 above and 11 aside (thus 51.8427734126309 deg or
>5151'34"). Nothing special problematic to construct, and quite OK for
>statics.
I like that ratio also, but the Egyptians only worked in unit fractions.
Now we could covert it to a unit fraction using their algorithm which
Milo Gardiner dates to about 2,000 BC or we could use a rise of an Egyptian
cubit and a run of a greek foot with a ratio of 1:1, but either is a bit of
a cheat.
>>Secondly its Apothem, or sloped side is equal to a stadium (600 Greek feet)
>>1/600th of a degree (1/360) of the Earths circumference.
>
>Didn't the greek by a number of not accumulating errors got to a good
>approximation of the earth's circumference (about 600 statium a degree,
>where the "about" turned out to be quite good)?
The Greek Eratosthenes used the Egyptian data from measurements which align
with a reasonable accuracy only at a period considerably before his time.
>
>>Third, that degree has 365240 English feet in it. How can that be a coinciden
>ce?
>
>Does it? Assuming 40'000 km (and 2.54cm/"), I get 364537 feets/degree. Or I
>get 43'139 km, but I doubt that the earth is really that flat.
Your 40,000 km is not quite accurate, though the meter was supposed to be a
geocommensurate system. The actual circumference of the Earth at the Equator is
24902.727... miles.
"The 1988 Information please Almanac", Houghton Mifflin, Boston, p 343
Doesn't the circumference of the earth change according to
things like its coeficient of expansion, tidal attraction, plate techtonics,
and polar meander ? Of course, but Geographers and surveyors have established
some standards whaich allow us to give a number according to the "Universal
Transverse Mercator Systems which is generally based on the Clarke Spheroid of 1866."
>From "Surveying" Eighth Edition,
Francis H Moffitt, Harry Bouchard, Harper & Row, New York, 1987
>
>>Fourth the circumference of the pyramid at its base has 36524 English inches
>in it
>
>Who's? Cheops' alias Khef'ren?
Yes, Cheops' No, not alias Khef'ren.
There are three main and also more than a dozen smaller pyramids at Giza.
The one refered to as the Great Pyramid is that of Kufu or Cheops. A second
is attributred to his sucessor Kephren and the third to Mykerinos.
Cheops' is AFAIK about 140m height, so the
>14/11 ratio leads to 34644 inches around, ok, that's +- some percent, but
>exactly 36524? There's a lot of material missing on the sides and on the top
>of Cheops' pyramid.
The height in meters is 147.65 aprox.
When Jomard measured it he got 144 m for the height, 230.902 m for the base,
and an angle of 51d 19' 14" by trig, but the base had not been completely cleared.
The French surveyors Coutelle and Le Pere got 51d 51' and a base length of 763.62 feet.
its perpendicular height was calculated by them to be 147.9 m above the center of the base,
but Howard Vyse measured 764 feet for the base.
Taylor used these measurements from Howard Vyse's expedition for his calculations.
Smyth obtained 51d 49' and Sir John Herschel got 51d 52'14.3" Smythe chose to take
the mean of these observations for his calculations.
The base sockets and a few of the casing stones at the lowest level have been preserved.
>
>>Fifth the ratio of its height to the circumference of its base is the same as
> the
>>ratio of the radius of the earth to its circumference.
>
>Well, pi, but was this really intentional? Former piramids had a different
>slope, but had problems with statics.
I think the major intended correlations are Pi, the stadium, as a measure of the
earths circumference, and the length of a year incorporated in the perimeter of
the base.
All this really tells us, is that there is a reason that there are twice as
many seconds in a century as inches in the circumference of the earth, and
that the reason is that the Egyptians used the inch, the foot the mile and
the second as well as the artaba, the cubit, the palm, the hand and the finger
as geo-commensurate standards of measure millenia before the meter was invented.
>
>--
>Bernd Paysan
Steve
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