A scientific paper on magnetite crystal at http://www.pnas.org/content/98/5/2164.full?ck=nck notes that this crystal is a prime candidate for analysis of early life on Mars from meteor evidence. Diagram of magnetite shape is at http://www.pnas.org/content/98/5/2164.full?ck=nck

Magnetite has a cubic crystal structure of an octahedron made of two pyramids base-to-base. What I am wondering is how close the shape of magnetite is to the shape of the Great Pyramid, which has slope of ~51.8667 degrees.

The interesting thing about this slope angle is that it means the great pyramid shape is precisely designed so the octahedron axis = perimeter/pi

It makes me wonder if this is a naturally stable crystal ratio that is also shared by magnetite. Does anyone know?

This ratio means the great pyramid can be seen as an architectural Squaring of the Circle. If we consider the distance from the capstone point to the corresponding octahedron subterranean point below the pyramid as equivalent to the diameter of a circle, and the pyramid perimeter as equivalent to the circumference of the circle, the angle of the pyramid slope means the relation between the top and bottom points of the cubic crystal shape is equal to perimeter divided by pi with error of about 0.02%, from the data I have seen. I like to imagine this point at the base of this octahedron underground below the Great Pyramid is the location of the Emerald Tablets of Thoth. Octahedron crystal is found naturally in magnetite http://en.wikipedia.org/wiki/Magnetite Magnetite is the most magnetic of all the naturally occurring minerals on Earth, and these magnetic properties led to lodestone being used as an early form of magnetic compass. Information on the octahedron is at http://en.wikipedia.org/wiki/Octahedral

Robert Tulip

Some more info at the source.

The Circle/π relationships could be the result of using a unit radius/diameter wheel for measuring lengths by rolling it. So the π could have got incorporated without the engineers knowing the value. Of Course this does not prove that they didn't know the value. IMHO it would be trivial for them to figure it out.

__________________
"They reasoned that an object situated at the center and related equally to the extremes in every direction can have no impulse to move in any specific direction. In fact, they compared the situation of such an object with that of a man violently but equally hungry and thirsty, standing at the same distance from food and drink and unable to decide in which direction to move." - Aristotle

Magnetite crystals are isometric. The octahedron form of an isometric crystal has equilateral triangles as faces. If my trigonometry is correct, the 'slope' works out to be 54.74 degrees.

the what?

__________________
All Moderation in Purple
To report a post (even this one) to the moderation team, click the reporting icon in the upper-right corner of the post:
─────────────────────────────────────────────
◄Rules For Posting To This Board ► ◄Forum FAQs ► ◄ Conspiracy Theory Advice ► ◄ Alternate Theory Advice ►

But will it sharpen my razor blades?

__________________
Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

Many thanks all, the wiki golden ratio material shows how this perimeter pi derivation is controversial. The Emerald Tablets of Thoth are a document which Sir Isaac Newton translated into English. Newton's version gives this document as the source of the hermetic idea 'as above so below'. The pyramid builders revered Thoth as the founder of astronomy. I am simply intrigued by the possibility that, having apparently incorporated the perimeter/pi ratio in the slope to the capstone, they followed this through by preparing the foundations of the construction to form an octahedron, with the pyramid above reflected in a pyramid below ground, but I have no evidence for this. A claimed history of the emerald tablets is at http://www.alchemylab.com/hyper_history.htm

The pyramid is built on bedrock. There is, however, an unfinished subterranean chamber that roughly mirrors the layout of the King's chamber above.

link to Wikipedia picture

__________________
If they can get you asking the wrong questions, they don't have to worry about the answers.

Someone used a calculator?

__________________
All Moderation in Purple
To report a post (even this one) to the moderation team, click the reporting icon in the upper-right corner of the post:
─────────────────────────────────────────────
◄Rules For Posting To This Board ► ◄Forum FAQs ► ◄ Conspiracy Theory Advice ► ◄ Alternate Theory Advice ►

Sorry, I used ~51.8667 as an easier way to type 51° 52'. As a1call noted, this slope angle is extremely close to the "golden" (φ Phi based) pyramid inclination of 51° 50' and the Pi-based pyramid inclination of 51° 51'. Looking at http://www.guardians.net/egypt/gp1.htm which has good official diagrams of the passageways in the Great Pyramid, as Warren says the subterranean passage is shown in the bedrock, so this idea of an imaginary upside down pyramid is almost certainly without foundation. And yet, it seems to have a symbolic presence, for example in this picture of thoth balancing interlinked pyramids on his palm, which admittedly is more like a Star of David than an octahedron and comes from a modern woo site not from an ancient source. Ah well, Newton found some of this stuff interesting.

But it does not have the slope angle of a magnetite crystal, which was the subject of the OP?

Well as usual with this Numerology related stuff it's close enough

__________________
All Moderation in Purple
To report a post (even this one) to the moderation team, click the reporting icon in the upper-right corner of the post:
─────────────────────────────────────────────
◄Rules For Posting To This Board ► ◄Forum FAQs ► ◄ Conspiracy Theory Advice ► ◄ Alternate Theory Advice ►

Ok, to summarise

1. The crystal shape of magnetite is isometric, and is close to but not exactly two connected Great Pyramid shapes.
2. The GP height of perimeter/2 pi (with error 0.02%) means an imaginary GP octahedron in the shape of crystal magnetite has height of perimeter/pi
3. We do not know if the Egyptians used this ratio on purpose or by accident
4. Evidence from the bedrock beneath the pyramid suggests presence of anything at a supposed subterranean capstone 'as above so below' is purely fanciful

Many thanks for assistance in clarifying this material.

Robert Tulip

Interlinked tetrahedra, not pyramids. Geometrically it's a stellated octahedron.
For some reason the pretty visual aspects of the geometry of polyhedra is attractive to new-age woos.

__________________
‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

Two points, Henrik:

First, the general term 'pyramid' includes tetrahedron. So, Robert is correct in describing the object as interlinked pyramids. Although, why the isometric magnetite crystal was invoked to compare to this object, I can't understand.

Second, I believe a stellated octahedron requires the two tetrahedra to 'interlink' to the point where the vertices are described by a cube. In other words, that object Thoth is holding is not interlinked enough to be a stellated tetrahedron.

Thanks Geonuc, that was my intent, and I do apologise for my imprecision. I have been looking at information on the Platonic Solids. The dihedral angle of the octahedron is 109.47°, confirming your earlier comment 'if my trigonometry is correct, the 'slope' works out to be 54.74 degrees' and illustrating how magnetite forms a platonic solid. Of course the octahedron based on the great pyramid is compressed slightly at top and bottom by comparison. The connection is that in Egyptian mythology Thoth was reputed to have a role in designing the pyramids, and his Emerald Tablets are the source of the idea that the microcosm is a reflection of the macrocosm, an idea which is conveyed in symbolic form in the stellated octahedron. To tell the truth, I am not aware of any Egyptian use of the octahedron, nor of this two/three dimensional representation like the Star of David.
Are you sure? It looks like there are eight small tetrahedrons around a central octahedron, so the shape seems to be made of nine platonic solids, but maybe my eyes are playing tricks. It would be easy to build one to put on my Christmas tree.
Thanks CM, that takes me back thirty years! Checked this out here and here. What I was wondering, tangentially, is whether the isometric shape of magnetite causes it to be magnetic. If so, we could imagine all sorts of resonant vibrations from an octahedron based on the GP. As I recall, the Von Danikin/Geller/whoever spookiness was at the pyramid focus point of the King's Chamber, whereas I am wondering about the relation between the end points of an octahedron.

ETA
A friend has sent me the following comments

Why not?
it looks just like this, only from a different angle and perhaps with some perspective. The upper parts of some triangles seem to be over-exposed and not visible in the bright background.

The implied 3d object seems to fit the bill and would correspond to a cube.

__________________
"They reasoned that an object situated at the center and related equally to the extremes in every direction can have no impulse to move in any specific direction. In fact, they compared the situation of such an object with that of a man violently but equally hungry and thirsty, standing at the same distance from food and drink and unable to decide in which direction to move." - Aristotle

Not sure what you mean by an implied object, but it seems to me that the Thoth object isn't quite interlinked enough. I could be wrong - the image is not real clear.

Not really.

By implied 3D object I mean the the 3D object that one would represent by the given 2D image.

What do you mean by "quite interlinked enough?

Do you mean the two equal tetrahedrons don't quite reach far enough into each other? To me it seems that they do (ie the edge of one passes through the edge of the other).

__________________
"They reasoned that an object situated at the center and related equally to the extremes in every direction can have no impulse to move in any specific direction. In fact, they compared the situation of such an object with that of a man violently but equally hungry and thirsty, standing at the same distance from food and drink and unable to decide in which direction to move." - Aristotle

Yes, that's what I mean. If the Thoth object is as you say, then Henrik's observation is valid and I am wrong.

I can only see a slight distance on the left-edges-crossing point and not at any other (of the 3 visible crossing points). I don't know who has drawn the image or how, but I would attribute this to artist's error/inaccuracy. I assume the original image is a hand drawing.

__________________
"They reasoned that an object situated at the center and related equally to the extremes in every direction can have no impulse to move in any specific direction. In fact, they compared the situation of such an object with that of a man violently but equally hungry and thirsty, standing at the same distance from food and drink and unable to decide in which direction to move." - Aristotle

Looking at the Thoth image again I concede to geonuc that it does look like one of the tetrahedra is slightly smaller than the other making my description of it as a stellated octahedron wrong.

I also agree that a tetrahedron is a pyramid when using geometrical terminology, but since the topic under discussion was Egyptian pyramids and wooisms related to them I used the common use shorthand in which pyramid only means the special case with a nearly square nearly horizontal base with the apex directly above the center of the base.

__________________
‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.