I cannot claim to have any real understanding of what this phrase means, but I was wondering whether you all would agree with the meaning as it's put here:
The Pharaoh's stairway to the Heavens. This is a simulated view looking north. The pole star is in the center of all of the rings. Each band or layer of the pyramid represented five degrees of the dome of the sky (with the exception of the base layer due to other considerations). The circular pathways of the stars intersect with the pyramid as they rotate in the sky and become infused into the quadrangular tiers of the structure. This provides an insight into the esoteric meaning of 'squaring the circle': the circle is celestial and the square is terrestrial.

The picture that this is the caption for is the last one here:
http://www.crystalinks.com/steppyr.html
Thanks, Jo, for a very interesting site!

Dunno bout no esoteric meaning. Its exoteric meaning is perty easy to splain.

Each band or layer of the pyramid represented five degrees of the dome of the sky

this (5º) is a common 'celestial' increment-- a full moon is about 5º of the 'arc' of the sky (which from horizon to horizion is about 180º)--its a handy 'measurement' to know, since your 'thumb' held at arms lenght is just about the right size to 'cover the moon'.. so you can use a 'rule of thumb' to measure celestial distances.. useful when a news article says 'planet X can be seen 20º to the south of the moon at 9PM' --as they are want to do.. knowing the 'size of the moon is 5º, its easy to figure out 20º, or any other odd number, not precicely, but close enough.

"Squaring the circle" refers to the problem of taking a given circle and constructing a square with the same area. One was probably limited to just using a straight-edge and compass.

The site you gave was using this as a play on words, as the curved lines of the orbits about the north star blend into the ends of the lines marking each layer of the step pyramid (the base of a pyramid being a square).

There are three issues with the claim:

1. It's not all that miraculous that the ancients would know what North is.

2. Precession. The earth doesn't just rotate on its axis. It wobbles. The wobbling has a long period, but over time the north star changes. Unless the step pyramid is mounted on a swivel, it's not likely that the picture looks so obvious as what the portray. (I think the ancient egyptians considered alpha draconis - and not Polaris - as the North Star.)

3. The concentrentric circles they draw to illustrate their point just happens to be through stars whose "orbits" take them into the edges. Considering the number of stars in the night sky - particularly in those ages before urban light pollution - it would have been much more impressive had they noted that those "orbits" were absent of stars.



k

The area of a circle is pi times the diamer. Pi is a number that starts 3.141.......... and has been computed out to over a hundred thousand places. So there is no possible square root of such a number. So it is impossible to find the area of a circle given as the square of a number.

I cannot help being skeptical of some of the theories about the intentions of the builders of the pyramids. I was much more interested in a book I read about eight years ago, by a French authority on geopolymers, of which Portland cement is an example, that the blocks of the Great Pyramid were not cut out of stone, but were cast in place using crushed limestone. I could find nothing improbable in his arguments.

http://www.raygirvan.co.uk/apoth/though11.htm

out of print - First edition: The Pyramids, An Enigma Solved
by Joseph Davidovits and Margie Morris
ISBN 0-87052-559-X Hippocrene Books, New York 1988
ISBN 0-88029-555-4 Dorset Press, New York 1990)

Interesting site. Don't think I've ever heard anyone suggest the blocks were concrete. This is really remarkable if there's evidence to confirm it.

"The area of a circle is pi times the diamer."
Minor misremembering. That's the circumference. The area is pi*r^2. PI's a transcendental number (i.e., it's not the solution of any polynomial equation with integer coefficients).


k

I've been reading a book by Margaret Visser "The Geometry of Love" in which she delves into the historic, artistic and symbolic and entymological background and significance of every item, including architectural elements, of a small church founded in the 7th century, outside the walls of Rome. The octagon was a very symbolic shape for the people of that time period as it combined the square, representing the physical and earthly ( 4 directions, 4 elements etc) with the circle representing heaven (eternal, unending, perfect.)
The book is very detailed but not dry as you might expect.

Area of circle - another senile moment.

Dr. Bill and Keith, here's a link that supports that theory:
http://www.geopolymer.org/archaeo.html. If you click on (Are Pyramids made out of concrete?), near the bottom, you are invited to view a documentary in RealPlayer format verifying this.

I think this is great. I love it when ages-old questions are figured out in a completely different way from what everyone was expecting.
I know, I know, it's still just a theory...

Area of circle - another senile moment.


hahaha....not at all, or if so, I have dozens of them every day.

With great affection,
k