This post was originally shorter. I added the following because I thought I had noted it before but apparently I hadn't. And to be honest I am too lazy to reread all the posts to see if I said it. It concerns something I discovered when I wrote a program using the numbers between 1 and 1000 to find the closest fractional approximation of Pi. I was curious if there was one closer than 432/275 that would have been in the range the Giza builders might have used. It turns out there was and if they had wanted to express Pi only it would have been better and easier. The values are 355 and 113. 355 / 113 gives you Pi to the 6th decimal. 3.141592. Which if they had built the pyramid only 355 MesoCubits on a side or roughly 621 feet, 621.25 to be exact and 113 MesoCubits high or 197.75 feet they would have, even with some weathering as we see today, probably preserved a record of Pi at least to 5 decimals or the entire 6. It certainly would have been easier to build. This tells me that the Giza Pyramid had more purpose than just demonstrating their knowledge of Pi. Their need to use the number 432 while presenting a much greater construction challenge also allowed them to insert an incredible amount of knowledge and to display their cleverness as you will see below.
Below is the original content of this post.
While messing around with my Giza Pyramid calculations the other day the following came to me.
Subtracting height of 275 from a side length of 432 in MesoCubits you get 157 which is half Pi or at least an approximation. If you do this with feet you get 756 - 481 which is weirdly enough 275 but is not easily translated as a permutation of Pi. Also when you divide 432 by 275 you get 1.5709. If the numbers were off slightly either way as in the following 4 mutations you would get.
431 - 275 = 156 multiplying by 2 = 312
433 - 275 = 158 " " = 316
431 / 275 = 1.567272 " " = 3.134
433 / 275 = 1.5745 " " = 3.149
From that set we see that a change in base length by 1 MesoCubit takes us further from Pi.
For the heck of it we will examine changing the height.
432 - 274 = 158 ==> 316
432 - 276 = 156 ==> 312
432 / 274 = 1.5766 ==> 3.153
432 / 276 = 1.5652 ==> 3.1304
Now changing both to one higher cubit or one lower cubit
433 - 276 = 157 ==> 314
433 / 276 = 1.5688 ==> 3.1376
431 - 274 = 157 ==> 314
431 / 274 = ~ 1.573 ==> 3.145
As we can see using 432 MesoCubits for the base and 275 MesoCubits for the height gives us the closest approximation of Pi or Tau depending upon which side of the Tau/Pi fence you are on. Although I use Pi when writing, because most people were taught Pi, I prefer Tau. Tau, as I have explained earlier, is a more organically derived number. But I digress.
432 / 275 = 1.5709 with 09 repeating which turns to a Pi value of 3.141818181818.... and Tau of 6.28363636...
This puts Pyramid Pi off of "true Pi" by just .0003 or 3/10,000ths. A very precise ratio. The ratio we are taught in school of 22 / 7 translates forward into 3.1428 where we see that the error occurs at the 1,000ths place thus showing that the 432 / 275 is a much better fraction to use.
Is a higher precision possible with fractions alone? Probably but the "perfection" or "symmetry" of using 432 and 275 are exquisite. 432 - 275 instantly gives you a very good "sign" that the builders are contemplating Pi. And yes if they were contemplating Tau and we are meant to divide the 4 sides together, which is 12 cubed, and divide that by the height we would get a good number for Tau. We cannot however find the same magic when we subtract 275 from 1728 we get 1453. Which may or may not mean something. It is a prime number. The 231st prime number. Lets play around with that while I'm thinking about it. If you recall from an earlier post I discovered that the 12th prime number was 37 which when multiplied equaled another favorite number of mine 444. Point being you never know where you will end up playing with primes.
1453 x 231 = 335,643. Which means nothing to me.
1453 + 231 = 1684. Which also means nothing to me.
1453 / 231 = 6.29004. Which rings no bells at the moment either.
1453 - 231 = 1,222. I like the repeating 2s but still nothing.
We will put those off to the side for awhile and see if anything turns up in the future.
In an earlier post on the Giza Pyramid I theorized that further evidence that the builders intended the structure to demonstrate their knowledge and perhaps in a "farfetched" possibility a message in the form of knowledge or fore knowledge that we might find other constants in the numbers. The number for Precession of the Equinoxes is there as I show in the calculations. Also a very close approximation of Phi which I showed comes up in all Pi Pyramids. While watching a show hosted by Brian Cox, the actor not the Physicist, an idea I had played with before came to me. That idea was to take the circle you can make on the outside of the base of the Great Pyramid and subtract its circumference from the circle you can create inside the base. Previously I was on the right track but since my notes are scattered here and yon I didn't see that I had arrived at the same conclusion. The speed of light might be built into the numbers of the pyramid. Here are the calculations.
Now recall or realize that it is not necessary to produce the exact number to show that you are trying to portray that number. If I write the number 31415926 or the number 3.1415926 or present either to you as the product of solving a problem such as the volume of a cube or sphere, which would be cool, then I am obviously trying to demonstrate Pi. Where the decimal point turns up isn't relevant unless you are very picky. And even though it is my suspicion that the builders were very mathematically advanced and could give us several decimal places they were also smart enough to realize that as few as four digits are enough to demonstrate a point.
The values for the Speed of Light in Metric and American are 299,792,458 meters per second and 186,282 miles per second respectively. We would want to find the MesoCubit equivalent which I did once before but I don't recall if I put it in this blog. In case I didn't here it is. Simply take the metric number and divide by the metric number for the MesoCubit or 299,792,458 (meters) and divide by .5334 (meters) which is a MesoCubit. You get 562,040,603 MesoCubits per second. If you do the calculation as I did once before and saw again in the video on youtube you make a circle on the outside of the base of the pyramid. This would give you a diameter for the circle of 432 times the square root of 2 which is 1.414. Multiplied you get 610.94... multiply that times Pi and you get a circle of 1,919.3238. To get the inner circle the diameter would be the length of the base by itself. This gives a circle of 432 x Pi or 1357.1668. When we subtract the two we get roughly 562157.... Without trimming or rounding following the calculation straight through you get 562,157,393. If you trim down to whole numbers while doing the calculations you get 56206..... The point here being as I have said before. If you are intent on producing a particular result it is possible to play with the numbers to get what you want. More decimals or fewer can sometimes do the trick.
I'm skeptical that this is a representation of the speed of light. If we work the calculation out in English Measurements we get 186,226 which is pretty good. In metric we get roughly 299,703,005.
All of which take us to the 4th digit in the sequence before the value goes off significantly. Is 4 correct digits enough to say the Speed of Light is being shown here? I'm not convinced. At least I'm not convinced this is what is being shown by the Pyramid. However if you notice that no matter what measuring system is used we get close to the Speed of Light in that system of measure. This tells me more about two circles bounded by a square than it does about this particular pyramid. Although the size of the pyramid does matter in arriving at these close approximations. I decided to explore the equation itself and see what this tells us.
Using MesoCubits the equation goes as follows; 432 x Sqr(2) x Pi - 432 x Pi or 562.05.... * using 3.141 as the value for Pi. If we eliminate the things that are redundant in the equation which is the number 432 we get Sqr(2) x Pi - Pi = 1.301. We can use this as a constant for any circumstance of a circle outside a square and a circle inside the square. Then all you need to do is plug in the values in what ever system of measure you are using. We can even run the equation backward to try and find the size Pyramid base you would need to get a closer match to the value for the Speed of Light in that measuring system.
First lets test our constant. MC 432 x 1.301 = 562.032. Metric 230.4 x 1.301 = 299.7504 English 756 x 1.301 = 983.556 (which is feet not miles) we must divide by 5280 to get miles. or .186279
So if we reverse engineer the problem. 562,040,603 MesoCubits per second divided by 1.301 = 432,006,612. Spin that around and you get 432.006 MesoCubits would have given us a value very very close to the number for the Speed of Light in Meso Cubits. If we imagined that given wear and tear on the structure that it was actually built at 432.006 Meso Cubits and used that to recalculate Pi we would get 432.006 / 275 = 3.1418618....virtually unchanged.
We can conclude from this that the calculation could have been there. The first 4 numbers are correct and to have gotten 6 numbers correct would have taken a high rate of precision. If the Pyramids base was 1 cubit shorter the answer would have been 431 x 1.301 = 560.....Off after only 3 digits. So to stick with my theory about Whole Numbers being sacred or preferred at least and the value of Pi or Tau being very important to this pyramid along with the Precession of the Equinoxes as well as the factorial of 9! Which is derived from the perimeter times the number of layers which is 210, it may have been a bonus to get close to the value of the Speed of Light. Although I haven't given up on the idea that there may be something intrinsic between the the value of Pi, Square root of 2, and the speed of light. It's a thought that has come back to me time and time again over the decades.
Perhaps even more interesting however, the pyramid and it's builders intentions aside, is how does this particular size of pyramid, regardless of the measuring system used, come so close to the speed of light in all systems? Was light used to lay it out? Is 432 somehow related to the speed of light along with the equation formed by putting two circles inside and outside of a square where the diameter of one is the hypotenuse of the square and the diameter of the other is the side? Which leads you to realize that perhaps the Speed of Light, or at least how we measure it, is related to the Square Root of 2 and the number 1.301? Is it somehow related to the size of the MesoCubit which is 533.4mm? Or is it just dumb luck that this particular size of a base produces a number that close to light?
More likely it has solely to do with this size of a base. So did the constant 1.301 formed from (Sqr(2) x Pi) - Pi mean something to the builders? To answer these questions, some of which are sophomoric I admit, we need to find out why 432 itself is so special and is there a natural corollary to the 533.4mm Meso Cubit in nature. Which is 21 inches incidentally.
To recap I have shown the interesting fact that subtracting the height from a side in what I am calling the MesoCubit System produces a 3 digit half value of Pi. Dividing a side by the height produces the same number to 3 digits. Subtracting the circumference of a circle that rests just inside the base from one that rests just outside the base comes close to producing the MesoCubit value for the speed of light. This is also true in the Metric and English measuring systems which seems very odd on the surface isn't really that big of a surprise. The value is linked to this particular length regardless of the system being used to measure it. And we also saw that 432 / 275 for a multitude of reasons is a better fraction for getting a good approximation of Pi than the classical 22 / 7.
I will be working on the idea that the base length is possibly some segment of the speed of light. Also it is worth noting that the notion of the time interval known as the second is artificial. A pure human construct. The builders of the pyramid regardless of their level of sophistication probably had their own notions of time. Could they have encoded this into the pyramid as well? If so perhaps this might change the precision of the speed of light calculation. For example if their measure of a time interval close to that of a second is less than ours then the number we found 562,040,603 (MesoCubits conversion from Metric speed of light) compared to the number derived from the circles, 562,157,393 a difference of 116,790 or .0207% off which is pretty good. But if their measurement of the time interval that is roughly a second but not a second is different in just the right way we might see a greater amount of precision.
Would they have discovered the periodicity of pendulums as we did and used perhaps a MesoCubit as their pendulum length? You can do the calculation for such a pendulum using the equation 2 x Pi x the Square root of Length of the pendulum over Gravity. Or you can use the calculator you can find online. Just type in a length. Using a length of 533.4mm and a gravity constant of 9.80665 m/s2 I got 1.466 seconds. So a MesoCubit Second is significantly longer than a regular second. If we put that back into our calculations by dividing the 562,040,603 by 1.466 we get 383,436,077 so no luck there. Unless a different measurement was used. The next question is how long of a pendulum would you need to produce the "correct second". You can work the equation a different way and put in time and figure out the length that way. Of course this was done for us when the standard second was decided. An interesting read all by itself.
More relationships seem to be appearing in the calculation plus many side chain thoughts as I call them. I think my next task will be to build a model of the pyramid of different materials and see what effects may occur. I will post the results, and perhaps a video on YouTube, if I find anything interesting.
That's it for now.
P.S. Note that the equation for periodicity of a pendulum uses Tau even though it is expressed as 2 x Pi.
Another P.S. - I didnt feel it necessary to make a whole new post for this "discovery" so I just edited this post. I used a different value for g in my pendulum equations. Instead of 9.8m/s2 I used the more precise 9.81m/s and got a period of 1.48 seconds. I will rework the Speed of Light calculations using that number or half that number. Also while playing with other ratios I happened to divide the height of 275 by layers, 210, and multiplied that times Pi. I got a very close match to the side length from corner to peak. I don't know if it means anything yet but I worked the numbers with other Pi Pyramid models and this doesn't work unless it is a method for deciding how many layers to use. I will study that angle and get back to you.
