Precession Math Found At Giza
I have been giving this Giza Complex thing some thought. I tried to put myself into the shoes of the builders of the pyramid complex at Giza. I am going to admit up front, I haven't spent a lot of time studying this and have only read one book completely on the subject my entire life. I took Ancient Egyptology in college but I don't remember the class much. If you pardon the joke it was rather dry like the Egyptian desert. My professor was elderly and didn't seem much interested in doing much more than teaching the text. We never heard anything about the mathematics of the pyramids.
The numbers I am using, such as the 756 feet for the Cheops/Khufu pyramid is a pretty well accepted number. I found that number online and in most the books I have found on the subject. 481 to 481.4 is the range I have found on the height. I see no reason I can't use 481.25. It is well within the range. Not that it matters much. If the builders intended to show Pi the difference between using 481 or 481.25 or 481.4 is minimal. It doesn't change the precision of the Pi number derived by much but it does allow the builders to use whole numbers in their construction. Something I find likely. And if this is indeed an attempt to demonstrate a knowledge of Pi then of the 3 choices 481.25 gives an accuracy to the 4th decimal place of 2/10,000ths.
I am sticking with the possibility that the cubit used is the Mesopotamian Cubit but I also found that in a list on the internet. Usually these cubits are found by measuring an ancient structure where the builders used glyphs to give the measurements. A modern measurement divided by the glyph numbers provides a conversion for the cubit being used. Cubit has become a generic term used for anything not measured in meters or feet. The assumption being that all ancient builders were imprecise and worked at the whims of the ruler.
This is the problem with archaeology up to a few years ago until the arrival of thinkers like Graham Hancock, Robert Bauval, Robert Schoch, and others who weren't satisfied with the bigoted and slanted grave robbers and coattail chasers who built the imperfect and not at all well reasoned foundations of pyramid archaeology. Men who thought dynamite was a tool and removing the gold and precious items along with the artifacts and corpses to their sponsoring countries was an acceptable practice. One lie was built upon another. One assumption built upon another assumption until the entire field is inscrutable.
It takes a special amount of racial bias to not see the fact that at the time the pyramids were discovered that the level of precision and craftsmanship involve in the pyramids was beyond their own engineers. The idea that "darkies" could have mathematics and skills far more advanced than the much over rated Greek society and the subsequent Anglo domination of the world must have been painful to say the least.
I don't necessarily believe the builders of the Giza Complex were sending a message of some future catastrophic event but they were sending a message whether intended or not. The Khufu pyramid is the key. It appears to be the oldest but the most intact with the most accurate and "stable" measurements. The entire complex is obviously laid out to match the constellation Orion which in that time was known as Osiris. They are obviously aligned with geographic North. Not sort of but dead on. It is speculation I admit that if you take the complex as a copy of Orion and match it to the night sky and you see that the angle doesn't match even though the layout matches. But by using the phenomenon of precession, the wobble of the earths axis over a time span of 25,920 years you can make that map on the ground match the one in the sky but you have to run the precession clock back to 10,500BC.
I say dead on but that isn't exactly true and that may be a good thing. It is 3 minutes of a degree off of True North. I am probably not the first to think of this but let's say for a moment that it was originally dead on aligned with true north. If the difference now is a function of Continental Drift and we can find a good measurement for that drift we could date the actual building of the pyramid to at least an epoch or even to a century. In fact this could establish once and for all a good approximate date for the structure. If we find that it takes longer than 4500 years to move 3 minutes of a degree off true north then we have an even better argument for its age being greater than the current mainstream accepted age.
I dismiss the idea that the structures were meant as a tomb since the same people who had to break into an upper chamber to supposedly find a "quarry mark" also never found a body. Perhaps they didn't have one handy to stick in it. Ultimately it doesn't really matter. The math that is revealed in the layout and the tools that must have been used to achieve it contradicts pretty much everything else in Egyptian grave robbing, er....uh I mean archaeology. The mathematics is there and it doesn't matter who the latest face is for Giza research is. Math is math. It is a lot easier to fake a quarry mark than to haul in a corpse or change the building itself. In the words of Donald Rumsfeld,and one of my favorite expressions, "It is what it is".
There are examples of clay tablets from Sumer that date to at least 4500 years ago. Here is an image of one of those tablets. Unless you have some agenda it is obvious you are looking at a sun centered solar system with planets around it. Not only round but intentionally cut in spherical relief. If you accept that, you also see that not all the representations of planets are the same size. And if you know the story behind the tablet you know that in Sumerian "mythology" the Sumerians believed that at one time there were more planets and that in fact the Earth was formed from the collision of two planets which formed the asteroid belt in the process which is exactly the modern theory of the formation of the Earth/Moon system and the asteroid belt.
What the exact story this tablet is meant to convey is anyone's guess but that doesn't really matter. You have as recently or as long ago, take your pick, as 4500 years a civilization that knew more than the sophisticated science and culture of most of the Western world up to the 1600s.
The ancestors of these people may be the builders of the pyramids.
These monuments to the society that built them are indeed a brag. A display of knowledge. A billboard that says "Hey look at what we accomplished". They are meant to be deciphered They are meant to be studied. But I have to admit, by my own logic, that if the builders meant to tell us something about some future event and weren't just showing off, then where are pictures that give us some clue as to "what is coming" if that is the intent of the structure?
Here is the logic. They builders build the pyramid complex and use the constellation of Orion to give us a date. 10,500 BC. Are we then supposed to find a number that corresponds to a certain number of years from that date, and we are supposed to know that something is going to happen around that time? If this were true I would suspect the people who could carve granite with such fine detail could have given us a picture. A picture inside the pyramids with a pictogram of a comet hurtling toward earth. A set of lines and figures that clearly tell us something. Anything. Volcanoes going off. The sun going out. And so forth. But as I said there isn't even a name in them other than what some guy wanting to prove his theory scrawled while no one was looking.
Whatever the purpose for building these structures it was not to communicate a story unless the builders were so wise as to know what kind of people might find their message. People who have their own beliefs and like Pharaohs were known to do in the later dynasties destroy the work and the name of those in the previous dynasty. Perhaps they sat around and one guy said "If we are going to build this thing and something happens to our people and they cannot guard it or even remember what it is for let's not be like Pharaoh Bob and put so much BS on the walls they will feel compelled to chisel it off. Let's put none. If we put none then there won't be anything to offend anyone and they will probably let it stand." And then another one of the ancient wise men said "Yes I see but someone may come along and wish to claim it as theirs and put their names and their deeds on the walls. So we should build it in such a way that the entire thing has to be mostly destroyed to destroy its meaning. We put the message in the math."
So if these structures weren't meant to deify a pharaoh as they obviously were not then what was their purpose?
Their ultimate purpose I cannot guess. Why does a culture spend decades building such magnificent feats of engineering? In a time when lifespans were short how do you keep the same people working on the same thing and with the same level of skill? What is so important that not only did the designers but the actual people who built it kept at it for so long? What did they want us to know? Could it be as simple as cultural pride? Could it be the ancient equivalence of the American and Soviet space race? Could it be the same as the Arch in St. Louis or the Empire State Building in New York or the Washington Monument in DC? Is it just a sign saying "Hey we are awesome. Look what we know?" Is it that simple?
We may never know the answer to that but there are some questions we can answer just by looking at it.
One thing we know is that the ancient Egyptians or Mesopotamians or maybe even Atlantians or whoever they were were capable of moving massive loads up the height of a modern high rise apartment building without cranes. As I said before. The Great Pyramid alone has 2.5 million blocks weighing on average 2 tons each, some as heavy as 70 tons, into position with a great deal of skill and precision. That precision was matched by the people who cut the stones as well. The designers and planners were of the highest caliber. The math alone says that for this one single structure to be built in 20 years would take a stone being cut miles away, transported, and laid every few minutes. Seems pretty unlikely.
But let's put that aside for the moment. We know they were capable of such feats of engineering because the structures are there. The skills or the pride in the work seems to have waned after the largest one was built until we find ourselves at the smallest of the 3 with a much different building style and what would seem to be a much easier task.
I am tempted to go into a long discussion about the possibilities but I would be no better equipped to discern the true intent of the builders than those who have pretended before me. As I said I can't see it as a message of impending doom given the total absence of something like hieroglyphics to tell me what I am supposed to be watching out for. If the world is going to be in trouble I would expect at least one wall of "Watch Out For The Big Sky Rock" or something like that. I could even imagine that they were "purists" and the buildings were built for their gods. Maybe those gods were spiritual or aliens as some think. Maybe for the Pharaoh to put his name on it would be blasphemy or arrogance. That is possible. Without a lot more study I can't say.
But I can tell you what the math tells me. As I said at the beginning the numbers were found on the internet and when I give it some thought I don't see how even going to the library and finding several years and generations of books on the subject would help me since you can't trust anything written by tomb robbers. So what's a guy to do? Just work with what you got until you find something better I suppose.
Below you will find my last run of a program I wrote to compare the three largest pyramids on the Giza Plateau. The categories are self explanatory. I will admit up front I had to "find" a number for the Menkaure Pyramid that fit my theory of the Mesopotamian Cubit of 533.4 mm. But also the first two numbers are well accepted numbers for the bases of Khufu and Khafre. This 533.4 mm isn't as obscure as you might think. It actually turns out to be a ratio and in the world of math and counting natural things in general ratios are good solid numbers. For instance it doesn't matter what language you speak when you are counting days of the year. There will still be 365 and roughly 1/4th which is why we have leap years. If you find a list of numbers and it has certain numbers in it and one of them is 365 1/4th then you know you are talking about days in a year. If you find 29 or there abouts then you are looking at days for the moon to make a complete orbit around the earth.
The 533.4 mm is also 21 inches and when you are measuring the base of the Great Pyramid in feet and you give it some thought then 21 inches is 1.75 feet exactly. Or you could put it another way. 7/4ths of a foot. However the meter is based on natural measurements and if you believe the builders of the pyramids to have been more advanced than we have been led to believe the idea that they would stumble across the exact same definition for meter or that their ratios would come out similar then it is not that farfetched. The meter was originally defined as 1/10,000,000 of 1/4th the distance around the Earth from equator to North Pole. A quadrant. Other suggestions such as the length of a pendulum that swung with a periodicity of 2 seconds was also discussed but since gravity is slightly different depending upon where you stand on earth the former was chosen. The current meter turns out to be off by .2 mm or 1/5th of a millimeter from the calculated distance which frankly isn't bad given the Earth is 40,000 km in circumference. So let's break that down. 1/4th = 10,000km. Can't use that to make a measuring stick so you have to go smaller. Lets reduce it to 1 km. That is another 1/10,000. But 1 km is still pretty big. Let's go down another 1/1,000th. That gives you something about 39 inches long. Which is a fairly handy measurement. That's 1,000 x 10,000 or 10,000,000.
10 millionths is a pretty good number to use. If you wanted to build monuments that showed your knowledge of things and you actually knew the same thing back then that we knew in the 1800s which is when the meter was defined you would, if you think about it, have to go all the way to 10 millions of a 1/4th of the Earth to get a useful measuring stick. Not too short not too long. If you stopped at 9 millionths you are left with a measuring stick of 1.11 meters which isn't too bad but why not just keep the numbers easy. Counting by 10s is easy. Incidentally if you divide the 40,000km just by 9,000,000 you get 4.44444444.......A mistake I made while originally doing the calculation. If you have read my other posts you would know why that is funny. Also in case you are wondering the length of a pendulum with a period of 2 seconds for the swing in both directions is .994 meters or 994mm. And to to show you how these ideas build on each other this is how the time interval in grandfather clocks was determined by Clements based on Huygen's who suggested the length as the meter. The second of which has a probe named after him. But the 1/10,000,000th of 1/4th became the standard and now that standard is measured both by a metal bar and a certain wavelength of a gas. A spectral line actually from Krypton gas atomic number 36. That standard is red cadmium spectral line (1 m = 1,553,164.13 wavelengths).
It is not unimaginable that these people had this knowledge or at least it won't be after I finish. Not of Krypton gas, that is pretty much arbitrary, but of the distance from the equator to the pole. This measurement of 533.4 doesn't have to be handed down from Mesopotamia either. It could be a coincidence I stumbled onto by chance. If you play with mathematics and ratios long enough you find that sometimes you run off on a wild goose chase because you see a familiar number and then it turns out that it was there naturally. Take for instance finding a very close approximation of the Golden Ratio in the areas of the pyramid. You can see that in the data I have presented in previous blogs and later in this entry. Knowing that it is easy to be fooled I ran some more numbers. Remember we are dealing with a pyramid based on an approximation of Pi. An approximation so close that it is off by only 2 - 5 parts in 10,000. Which is pretty good. So I made up some false data and ran it through my program. I created theoretical Pi Pyramids with the same amount of precision and since the program figures out all the other numbers it shows that the Golden Ratio will appear in any Pi Pyramid.
But I also noticed something else. The builders were trying to show a bunch of things at one time. It is hard to stuff lot's of relationships into a single structure. You have to pick what you think is most important and go with that. What numbers are you trying to show? How can you get the most bang for the buck? Is is sheer coincidence that you get the Golden Ratio in a Pi Pyramid? Possibly. But one of the ways to derive the Golden Ratio is to use square numbers and draw a figure such as the one below.
I haven't gone deep enough into that part of the math to see why a Pi Pyramid produces in 3 dimensions what this produces in 2 but I intend to. The point is that it is a geometric construct using more or less simple numbers. It is not that big of a surprise that it produces something similar. And it may be the builders way of pointing us from circles and squares and special numbers in 2 dimensions into higher dimensions. Which I can imagine 3 but what if the pyramid demonstrates the transition from 3 to 4 to 5 or more? And did the builders believe time was one of those dimensions. Which incidentally I do not. I don't believe time is actually changeable. Only the perception of time. But that's another story.
Sometimes when you are working out the mathematics of something you wind up having to work backwards. Let's say you wanted to represent a number such as the distance around the Earth in a Pi Pyramid using modern measurement standards. You have to find somewhere in the dimensions to put the number 40,075. Since you are constructing a Pi Pyramid to show off Pi or perhaps it is a Golden Ratio Pyramid and you get one or the other just by "luck" so it's a twofer either way you go. You could even work it out so that you get the best "happy" medium between the two. You can play with the numbers so that your base and height produce two numbers, Pi and GR, so that both have the best possible precision in say the 3rd decimal place. In some cases you may not be able to show anything better or you might have the latitude to do something really cool like be off by exactly the same in both. I am not saying that is the case here but the possibilities exist. So you want to express 40,075 in your Pi Pyramid so you start with what you know. Divide 40,075 by Pi/2 which is roughly 25,512.53 Now you decide how you want to put that into the math of the pyramid so just to make it easy we put it into the area of the base so you just square root 25,512.53 and you come up with 159.725. This is just an example of how to build a number into something. Using Pi to find your length to square root gives you the Pi ratio, the Golden Ratio, and your message which is 40,075 which will be the area of the base. If a side is 159.725 squared you will get 40,075 back out.
Here is the problem though. You can't be sure the person doing the measuring will be measuring things the way you do. Your 159.725 is in your unit of measure so how do you make sure they come up with the same thing? You could leave a yard stick etched in the wall. But as far as I know they didn't.
I could drone on for some time. I have been playing the "Building A Mystery" game for awhile now. That's how I went from Space Alien believer back to skeptic. It's like the Bible. You read it enough times and you start to see the flaws. That is how I have come to the positions I have on certain things. If you want to build a mystery you give the answers so your "believer" will follow them. This is "pointing". But apparently the builders weren't interested in pointing anyone in any specific direction or probably it would be more correct to say they had the presence of mind to make sure that you had to figure out the whole thing to get any of it. It is like I was saying before. You see the number 365.242 and you know you are talking about days. You see the number 1.61803 or there abouts and you know you are talking about Golden Ratio. You see the number 3.141 and you know you are talking about Pi and circles.
How do you build your structure to convey your point and make sure someone a couple thousand years later can get it? The Pi relationship is easy. No matter how you measure, feet, meters, cubits, whatever it will pop up. And since it is a Pi Pyramid the Golden Ratio will pop up. Those two are easy. Now you have to play with the numbers to fit the rest of your message in. There are even better numbers you could use for Pi and give the searcher 5 decimals of Pi and send a stronger message "Hey We Know Pi". But Pi isn't the big big message. So if Pi isn't your big message then you must be willing to give up something. In the above example if I wanted to put 40,075 in the message I would have adjust the height to match the base to keep my numbers. But if my message is bigger than Pi, Phi, and the 40,075 then I am going to have to give it a lot of thought how to jam everything into a structure that one conveys my message and two can actually be built. It looks like the builders went to a lot of trouble to get the dimensions they got. That's why even after I show you what else I have found I know it has to go deeper because you can get these numbers easier than building something 481 feet tall.
And here is why I think the Giza Complex is constructed to show a specific set of numbers and why I probably just got lucky that the meter is a naturally produced length of measurement. I got lucky that the Mesopotamian Cubit I read online was 533.4 mm. It turns out that this is a ratio. 533.4 is 21 inches which is 1.75 feet or 7/4ths. I think the true number is the 7/4ths. The fact that when you convert 533.4 using the approximations for millimeters into inches is either just luck or because it is naturally based I don't know but here is that math. 533.4mm/25.4mm = 21. 21/12 = 1.75. 1.75 = 7/4. I don't know what this means in the context of the pyramid yet but I will tell you what this serendipity has produced.
Here is a methodology note. I like to convert to millimeters because it is such a small unit of measure. If I don't know the exact length of something if I reduce the increments to a very small known length of measure then however far off I am isn't going to be as far off as if I used inches or feet. I say that just to explain why I use millimeters.
If you read my last post you know I converted the 756 feet of the Great Pyramid Base to the MesoCubit. I can skip the millimeter conversion and just divide 756 by 1.75 which is 432. I do the same thing to the height. I will admit here that I chose 481.25 which falls between the two heights I have found of 481 and 481.4 and even a 481.28. I chose it for a reason because when I use it my Pi ratio gets better and I get an even number of 275. So I end up with 432 for the base and 275 exactly for the height. We can assume that the builders would have done the same thing. Using even numbers. For the moment this is the only way I can see getting two exactly even sets of numbers for the two largest pyramid bases. Here is a kicker. When you find a widely accepted 717.5 foot base for the Khafre Pyramid you find this converts to exactly 410 but the Khafre Pyramid is either not meant to be a Pi Pyramid or the building and designing got sloppy by that time. A number I have seen more often is 706 feet for Khafre. I am exploring that as well because you get even fractions with it and a fraction that keeps showing up. Fractions dealing with 7ths. If the base of the Khafre Pyramid is indeed 706, which to be honest comes up more times than I have found 717.5, then what you get is 403 and 3/7ths exactly when you convert to MesoCubits.
This is kind of odd since Archimedes' famous rendition of Pi was achieved using geometry and fractions (not decimals) and the fraction he used was 7ths. Starting with the Hexagon and making polygons with more sides to increase the perimeter of his polygon to get them into the arc of a circle he wound up coming to a very good approximation of Pi. Between 3 1/7th and 3 10/71ths. Or between 3.1428 and 3.1408.
I have a suspicion the builders may have done something similar so I will be researching that aspect of it as well. In several runs of my program and using some of the height and base measurements, I have found online, the decimal portion of the numbers, in mesocubits, are portions of 7ths. I will blog this later though. I am going to stop posting these intermediate findings until I find something of interest. When I come back with another Pyramid Post I want to have something really good for you. Feel free to take anything you find interesting and run with it. Like I said in earlier posts. If you find anything just give me some credit.
But I was able to find measurements that fit my needs. I am telling you this up front. I wanted to find these other numbers for the other two pyramids but my numbers for the Great Pyramid are well accepted numbers. The 756 for Cheops/Khufu is very very good.
If I carry this over to the Menkaure Pyramid the numbers I have found for its estimated base and height allow me to produce another even number of 203 for the base. I am telling you this to make a point. The numbers fit well within the parameters.
So what was I looking for? Now remember I did not invent the Mesopotamian Cubit. I found it in a cubit list and I tried the entire list on the base number of the Cheops Pyramid. Also the Mesocubit is a good fraction when going from feet to meters and the meter is a naturally derived standard of measure. The error over a quarter the circumference of the Earth being divided by an even 10 million and this being called a meter can be found by anyone who can measure the earth and the precision is 2/10s of a millimeter. Meaning that if ancient people could measure the earth and used a value of 10 millionths and this was a "method" of measuring then the fact that their numbers and the English and Metric numbers fit together is not that astonishing. It would be like 3 people having the same length of street to divide into easy to use measuring units. Not too long not too short. If the people are smart enough to use easy to remember numbers like 100ths or 1000ths they are going to come up with the same thing or similar units.
And now for the BIG FINISH. If I displayed to you in even numbers the number 25,920 and you now being an expert on this area of astronomy you can tell me Hey! That's precession! These people knew about precession. Now look at the clever way they did it and also the hard way they did it and why I think there is more to look at.
Short lesson on Precession. The Earth wobbles on its axis. The earth
still spins around the same invisible point but if it had a big stick
poking out the top the end of that stick would mark out a complete
circle over a time period of 25,920. That's 1 degree of motion over 72
years. 360 x 72 = 25,920.
Astronomers and astrologers
know the numbers of precession well. A scholar of ancient texts that
also knows astronomy knows instantly when they are looking at a culture
that if they see these numbers they are looking at a culture that had
three things. A long history of watching and charting the movement of
the sky, a sophisticate knowledge of mathematics, and a knowledge of the
true shape and movement of the planet they were standing on.
So what did I find?
So here we go. Out of curiosity I used the equation for the volume of a pyramid. I had exhausted the 2 dimensional space and was looking for a reason to write more into my program. The equation for the volume of a pyramid is the same as that for a cone. Area of base times height times 1/3rd. When you work that calculation with the feet converted to MesoCubits, which I may start calling, LuckoCubits, you get the number, 17,107,200. I didn't see anything interesting in that number but knowing that I am looking for "hidden messages" I just randomly divided some numbers I know into it. The base perimeter is 1728 or 12 cubed so I put that in. Answer was 9900. Volume/base perimeter equals 9900. An even number. I don't know if it means anything. It could be a "round robin" number. Something that would be produced just by the mathematics. I will let you know. So I eventually got to 25,920 and the number 660 popped up. So the number for precession is inside the volume equation! The volume is 660 times Precession!
So Precession is in the numbers! This one single object holds Pi, Golden Ratio, and Precession.
So before I post the data let me recap and tell you where I am going from here. I am going to explore the numbers produced by the precession numbers. 660 and 9900 and so on. I am going to explore the use of fractions such as the Mesocubit being just 7/4ths and the 7ths that keep popping up in my calculations. Khafre's tomb at 706 feet being 304 3/7ths. I am considering posting some of the programs I have written and letting other people take a crack at some of their favorite numbers. One reason for the different measurements on the outside is due to people taking the limestone casings for their own use and defacement and weathering but the measurements on the inside are better preserved. There is a lot more math inside there to look at. If my so called Mesocubit exists I should find it represented in there. So I will need good data for the inner passages and chambers.
I am going to pull back and look this over more carefully. Probably use some trig and figure out based on the inclination and the base lengths what the true measurements should be and see if they fit with the books and the online findings.
I am going to follow the Graham Hancock and Robert Bauval research and start with a date of 10,500 BC and see if it is the case that the numbers point to years then are they pointing to any year that would be of importance to us. 10,500BC is where the Orion/Osiris model on the ground points us. If I do find a year calculation this is the point where the builders are saying the clock starts. Maybe they are pointing, like the Mayans, to where the clock stops. Actually the Mayan calendar doesn't stop it just says a new age starts. Again that is another story.
Finding the Continental drift rate and putting this together with the 3 minutes of a degree of error in the North/South Alignment may give us the time it was built. Not the time it points to but when the builders built it. Like setting a watch to a certain time then breaking it.
The only hope for an image of what might be coming, if that is what this is supposed to be pointing us to, is that hidden somewhere in the pyramid and in the math are the directions to a room or some scrolls with pictures and writing on them describing the event. Otherwise the best we can hope for from the math alone is a year date and that with the numbers of precession showing up that perhaps we need to be looking at the sky. That's about the best we can do.
Here is that data. I have made several runs of this changing the numbers. I will just post a page of those too, here in a few days but anymore extensive work on this subject will be awhile in coming. Take note of the base area divided by precession on the Khufu pyramid. 7.2, this corresponds to 1/10th of a degree during precession. Something to follow perhaps.
Khufu base 756 feet
Khufu height 481.25 feet
Khafre base 717.5 feet
Khafre height 478.3 feet
Menkaure base 355.25 feet
Menkaure height 216 feet
Base 432.00000 Base 410.00000 Base 203.00000
Height 275.00000 Height 273.31429 Height 123.42857
Perimeter 1728.00000 Perimeter 1640.00000 Perimeter 812.00000
Hypotenuse 610.94026 Hypotenuse 579.82756 Hypotenuse 287.08535
Corner 411.01946 Corner 398.43531 Corner 189.31221
Face Height 349.68700 Face Height 341.65143 Face Height 159.80257
Face Area 302129.57051 Face Area 280154.17159 Face Area 64879.84452
Base Area 186624.00000 Base Area 168100.00000 Base Area 41209.00000
Total Area 488753.57051 Total Area 448254.17159 Total Area 106088.84452
Ratio Face/Total 0.618163 Ratio Face/Total 0.624990 Ratio Face/Total 0.611561
Ratio Base/Total 0.381837 Ratio Base/Total 0.375010 Ratio Base/Total 0.388439
Ratio Total/Face 1.617695 Ratio Total/Face 1.600027 Ratio Total/Face 1.635159
Ratio Total/Base 2.618921 Ratio Total/Base 2.666592 Ratio Total/Base 2.574410
Ratio Base/Face 0.617695 Ratio Base/Face 0.600027 Ratio Base/Face 0.635159
Ratio Face/Base 1.618921 Ratio Face/Base 1.666592 Ratio Face/Base 1.574410
Total Length Lines 3372.0779 Total Length Lines 3233.7413 Total Length Lines 1569.2488
Volume equals 17107200.000 Volume equals 15314710.476 Volume equals 1695456.000
Volume/Precession 660.000000 Volume/Precession 590.845312 Volume/Precession 65.411111
Base/Height x 2 3.141818 Base/Height x 2 3.000209 Base/Height x 2 3.289352
Pyramid Pi - Pi 0.000226 Pyramid Pi - Pi -0.141384 Pyramid Pi - Pi 0.147759
hypotenuse/height 2.22160 hypotenuse/height 2.12147 hypotenuse/height 2.32592
Height/hypotenuse 0.45013 Height/hypotenuse 0.47137 Height/hypotenuse 0.42994
Height/corner 0.66907 Height/corner 0.68597 Height/corner 0.65198
corner/Height 1.49462 corner/Height 1.45779 corner/Height 1.53378
volume/660 25920.0000 volume/660 23204.1068 volume/660 2568.8727
base/660 282.7636 base/660 254.6970 base/660 62.4379
corner/660 0.6228 corner/660 0.6037 corner/660 0.2868
hypotenuse/660 0.9257 hypotenuse/660 0.8785 hypotenuse/660 0.4350
perimeter/660 2.6182 perimeter/660 2.4848 perimeter/660 1.2303
basearea/precession 7.2000 basearea/precession 6.4853 basearea/precession 1.5899
facearea/precession 11.6562 facearea/precession 10.8084 facearea/precession 2.5031
totalarea/precession 18.8562 totalarea/precession 17.2938 totalarea/precession 4.0929
*note that we pulled the 660 out of the volume by dividing volume by Precession. When we divide the perimeter by that 660 we get Phi squared again which is the same as the ratio of the base area divided into the total area. This is probably that "round robin" phenomenon but I will look closer.
Enjoy
