Angles
Surface
Volume
Equilateral Pyramid top
You can also produce an octahedron by connecting the centres of the squares of a cube by lines. Cube and octahedron are dual.
If you give the original data a=232.7m and h=146.6m, the edges are s=220.4m, the base 5.4150 ha, the lateral faces 8.7120 ha, the lateral surface 14.13 ha, the volume 2646000 m³ and the angle of inclination 51.6°. The volume is illustrated. If you let a stone block be
a cube with the edge 1m, you can form a line 2500km long. This is nearly
the
distance London - Athens.
Both equations result in the second ratio h':(a/2)=1/2*[1+sqr(5)]. This is the golden ratio phi = =1.6180... . 2
3
You can often see a sky with
five-cornered stars on a blue background in tombs.
4
After the annual flood of the Nile
the fields were measured by 3-4-5-strings with knots.
5
The position of the Great
Pyramid is remarkable, especially as you can look far into the Nile delta,
if the smog of Cairo permits.
6
Summary: It is certain, that the ancient Egyptians chose the measurements of the pyramid in order to make it safe and nice. Who knows? Perhaps mysterious laws are hidden in the
pyramids.
On the other hand: Numbers are patient... as we say
in Germany.
Stop ;-) ! This was a scientific joke. The yearning for esotericism, which arose at that time, should be satirized. - The famous journalist of "Scientific American" Martin Gardner wrote this article.
M²=a^4 + 4a²h² V=1/3*a²h There are ten cases:
2) Given:
a,s. Search: h,V,M.
3) Given:
h,s. Search: a,V,M.
4) Given:
a,V. Search: h,s,M.
5) Given: h,V. Search: a,s,M.
6) Given: s,V.
Search: h,a,M
7) Given: a,M.
Search: s,h,V.
8) Given: h,M.
Search: s,a,V.
9) Given: s,M.
Search: h,a,V.
10) Given: M,V.
Search: a,h,s.
An Example:
(Give M,V):
Which shape has a pyramid, which has the same volume and the same lateral faces as the Great Pyramid of Gise? Solution: You derive the equation
h³ - (M²/12/V)*h² + (3/4)*V = 0.
This isn't a new contribution to the pyramid research.
This only is fun.
You find this pyramid in the following way. You lay a yellow triangle (3) inside the given pyramid, and introduce the square side x and the height y. The volume is V=1/3*x²y. With the help of the equation h:(h-y) = a:x you get V(x)=1/3*hx²-1/3*h/a*x³. You get x=2/3*a and further y=1/3*h by V'(x)=0.
German Christian Tietze/Rico Hecht
Frank Dörnenburg
Ingrid Huber (Hubsi's Lehrer Homepage)
Wikipedia
English Andrew Bayuk (Guardian's CyberJourney To Egypt)
Eric W. Weisstein (MathWorld)
FERCO
Kevin Matthews and Artifice, Inc. (greatbuildings.com)
Lee Krystek
Tim Hunkler
Wikipedia
(6) "Gibt es ein Geheimnis der Pyramiden?" Two TV reports from the series "Querschnitt" by Hoimar von Ditfurth, ZDF (29.03.1976 und 05.04.1976, repeated in 1991) In these two TV reports Hoimar von Ditfurth reacted
to Erich von Däniken's bestseller "Erinnerungen an die Zukunft" with
the speculation: "The pyramids were built with the help of extraterrestrial
beings".
The report said: "The ancient Egypts already had the
abilities
to build the pyramids."
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