As usual, I will try to keep the history lesson brief. The Rio Bec Mayan archaeological site lent its name to a style of architecture that is though to have persisted some 500 years, from about 700-1200 AD. Rio Bec style architecture is noted for imposing pairs of towers featuring facades that imply pyramid temples. Some have noted a resemblance between the towers and the pyramid temples of Tikal, suggesting that Tikal’s lofty pyramid temples may have inspired them.
https://en.wikipedia.org/wiki/R%C3%ADo_Bec
Rio Bec, Group N, Structure 1. George F. Andrews
Being that what I think to be my successes in archaeological interpretation of ancient American architecture began at Tikal, and that I am quite taken with the imposing false towers of the Rio Bec style, I am much intrigued by the Rio Bec site. A number of attempts to interpret architecture at the site have suggested the application of very skilled and sometimes seemingly unorthodox calendar-related mathematics expressed in metrological terms.
One of the intriguing findings at Rio Bec was the possibility that several unusual approximations of the “Golden Ratio” Phi may be in evidence (see “Rio Bec Phi”); a less unorthodox finding was a suspected emphasis on the number 12 (Pi^2), which turned out to be the apparently link between the Half Venus Cycle and the Venus Orbital Period and has been used in my experimental calendar tables for that function ever since.
There were also hints of self-referential equations made out of the length, width, and height of some of the rooms of the structures. To my knowledge these have never been solved although several attempts were made and various insights were gained.
Unfortunately there is a limit to the data I have to work with. Thankfully George Andrews gathered a substantial amount of data on some of the structures at Rio Bec, but the quantity of data is considerably compromised by the dilapidated condition of a number of structures there. Thus I don’t always have the complete data sets for the rooms in these structures – length, width, height, vault height, etc – that I prefer to work with to help keep guesswork to a minimum.
Rio Bec, Group B, Structure 1. George F. Andrews
Rio Bec, Group F. Structure 17. George F. Andrews
Structure XVII of Rio Bec Group I is also known as the south building of Merwin’s Group F. Some of the data from Andrews gives us:
Room 1: length 8.54 m, width 2.74 m, height ~3.20 m, exterior door 1.65 m wide
Room 3: length 8.02 m, width 2.74 m, height 3.22 m, exterior door 1.75 m wide
Room 5: length 7.75 m, width 2.74 m, height ~3.20 m, exterior door 1.70 m wide
The heights are to the springline rather than to the top of the ceiling vaults. No data on the height of the vaults is available due to their collapse, and no data on Rooms 2, 4, and 6 is available due to their being filled with the debris at the time of Andrews’ visit.
Several of the first notable things we find are that for Room 1,
Length / height = 8.54 / 3.20 = 2.66875; 10.67438159 / 4 = 2.668595398
Height / width = 3.20 / 2.74 = 1.167883212; 1168.064258 / 2 = 584.0321292, Venus Synodic Period
As I’ve said before, it seems we can barely turn around in a Mayan structure without running into a Venus reference, a prevalence which seems to correspond to the significance of Venus in Mayan astronomy and mythology.
The measurements themselves that are involved in these ratios
8.54 m = 28.0183727 ft; 2.74 m = 8.989501312 ft; 3.20 m = 10.4968766 ft
As at Tikal, the recurring 2.75 m value is suggestive of 4 x Venus Orbital Period / 100 = (224.8373808 x 4) / 100 = 8.993495232, while 28.0183737 is somewhat suggestive of 224.8373808 / 8 = 28.10467260, but that much of simple fractions or simple multiples of the Venus Orbital Period almost seems needlessly redundant.
The 3.20 m = 10.4968766 ft value is curious. (Pi / 3) x 10 = 10.47197551 (3.1919 m), and with (Pi / 3) being thought to have been extremely prevalent in the mathematics of Tikal, and the Rio Bec style of architecture possibly having been inspired by Tikal’s pyramid temples, it would seem by far like the most reasonable guess.
However, when we begin to put the pieces together, we may find that this is not necessarily so. For Room 3,
Room 3: length 8.02 m, width 2.74 m, height 3.22 m, exterior door 1.75 m wide
8.02 / 2.74 = 2.927007299, looking rather like “The Real Mayan Annoyance” that I have mentioned on a number of occasions including very recently. Still mysterious, this number seems important to ancient calendar systems and formulas. It was referred to as annoying because of the possibility it might be too easily mistaken for Venus Synodic Period 584.0321292 days / 2 = 292.0160646. 2.926442327 is the “real” “Mayan Annoyance” because it seems to be at least the primary value among similar numbers with such functions, while other similar numbers of still unknown usefulness exist.
For the measures of Room 3 itself,
8.02 m = 26.31233596 ft; 2.74 m = 8.989501312 ft; 3.22 m = 10.56430446 ft.
26.31233596 looks a great deal like a useful way to incorporate the extremely important number 1.622311470 in the architecture, as its square.
1.622311470^2 x 10 = 26.31894506 (~8.022 m)
Indeed, it is true that 26.31894506 / (224.8373808 x 4 / 100 = 8.993495232) = 2.926442321, the “Real Mayan Annoyance”.
8.02 / 3.22 = 24906.8323 / 10000, very close to 24901.19742 / 10000 or 24903.44228 / 10000. Both of these equatorial circumference in miles figures and their appearance at Tikal and Chichen Itza have been discussed in the most recent posts.
3.22 / 2.74 = 1.175182482, suggesting that the architecture has also been fitted with the extremely important constant 1.177245771, also known as “Alternate Pi”; it is also suspected of being the primary intended value for the Megalithic Foot.
“Algebraically”, if 2.74 m = 8.993495232 and 3.22 m / 2.74 m = 1.177245771, 8.992495232 x 1.177245771 = 1.058755423, and if 8.02 m = 26.31894506, then 8.02 / 3.22 = 26.31894506 / 1.058755423 = 24858.38047 / 10000.
So we have a successful coherent equation involving the standard polar circumference in miles value of 24858.38047, rather than a reference to the equatorial circumference.
It’s somewhat suggestive of Tikal Temple V. As Munck pointed out, Temple V is the only one of the major pyramid temples to align north-south which may have a special meaning. When I took this to possibly signify a possible special relationship to the polar meridian/circumference, I soon discovered that 24858.38047 is highly responsive to the Venus Orbital Period A figure of 224.8373808, and remarkably, this includes exponential use of 224.8373808.
Here at Rio Bec, the VOP A figure 224.8373808 is seemingly already provided to show us the very same thing then, in the fairly obvious form of 224.8373808 x 4 / 100 = 8.993495232.
For Room 5, length 7.75 m, width 2.74 m, height ~3.20 m, exterior door 1.70 m wide.
7.75 m = 25.42650919, which resembles 216/10 x 1.177245771 = 25.42850865 or 30 / 1.177245771 = 25.48320898. (Curiously, the number 2542.850864 was part of Munck’s “geomathematical” scheme for Tikal, and we might consider what it would have taken this number mathematically to earn that prestigious honor).
7.75 / 2.74 = 2.828467153, which is suggestive of the reciprocal of the Lunar Year, probably the Lunar calendar year of about 354 days rather than the Lunar Year proper of.
If this is so, then we can try 1 / 353.9334578 = 1 / (572.9577951 / 1.618829140) = 2.825389852 with the presumed value of ~2.74 m, namely 8.993495232 ft.
At this about point, however, things still begin to get muddied. They have apparently done something unusual here, and it’s difficult to tell whether it would be an unusual form of the Venus Orbital Period – the standard form sreved us too well up until now to simply cast it aside – or an unusual form of the Lunar Year, or what exactly.
It may be possible that the Lunar Calendar Year in use was not the “A” value of 353.9334578. but the presumed “B” value of 353.6776513. This is 10^n x the reciprocal of 90 Pi, and appears to be the form of Lunar Year expressed by the 900 x Pi ft base perimeter of Chephren’s pyramid at Giza.
Let’s go back to Room 1 and consider a couple of things, and see if we can get better bearings.
Room 1: length 8.54 m, width 2.74 m, height ~3.20 m, exterior door 1.65 m wide
8.54 m = 28.0183727 ft; 2.74 m = 8.989501312 ft; 3.20 m = 10.4968766 ft
Length / height = 8.54 / 3.20 = 2.66875; 10.67438159 / 4 = 2.668595398
Height / width = 3.20 / 2.74 = 1.167883212; 1168.064258 / 2 = 584.0321292, Venus Synodic Period
If we continue to assume that 2.74 m = 8.993495232, if 3.20 m = 10 x (Pi/3) = 10.47197551 ft
10.47197551 / 8.993495232 = 1.16394403, rather than the target figure 1.168064258.
This is really where the first seed of doubt is cast whether we are really seeing 10 x (Pi / 3), as amazing as that sounds.
If 3.20 m = 10.47197551 and 8.54 / 3.20 = 10.67438159 / 4 = 2.668595398. 8.54 m would mean 10.47197551 x 2.668595398 = 27.9454654 rather than 28.0183727 – that much would be plausible enough, but are problems, including that 27.9454654 does not seem directly compatible with the 8.993495232 value that has recieved a number of votes of confidence.
What exactly have the ancient Maya gotten us into here?
To shorten an already long story, I did promise a new “Wonder Number” so I owe one to the reader. Although it is the result of an incomplete and inconclusive effort, one appears to have been found.
Whether or not in the long run it turns out to really have been part of this structure at Rio Bec, a number of mathematical probes used to try to sort this out have pointed to the existence of the number 1.049450222, similar to but different from (Pi / 3) = 1.047197551.
1.049450222 seems to have a curious way of potentially fitting into at least some of the proceedings for this ancient structure from Merwin’s group F at Rio Bec.
But why would they forsake the mighty (Pi / 3) for this?
Well, I have been known to wax outright poetic before about the architects of Rio Bec, how they seemed to show not only what seems like particular high proficiency in mathematics, but also something of a fondness for adopting forgotten numbers as if they were stray pets. I’ve done that much work with the site as to be able to get that distinct impression.
If 1.049450222 x 10 ft is indeed a part of the architecture of Rio Bec, (Pi / 3) = 1.047197551 was not forsaken; rather it’s (Pi / 3)^n that confirms the “Wonder number” status of 1.049450222 by forming important data chains from it.
If 1.049450222 x 10 ft was not part of the architecture of Rio Bec, it hardly seems to matter. It appears to be a genuine “Wonder Number” that to the best of my knowledge is previously unreported and previously unknown. There’s a lot left to learn about it, but I do believe there likely is an “iceberg” beneath what appears above the surface.
It appears to be a “Pi Number” (see my early post on “Pi Numbers” and “Square Root Numbers” https://pijedi.home.blog/2019/11/30/pi-numbers-and-square-root-numbers/) so we expect that either it or its reciprocal should resolve into a valid whole number by applying the Pi ratio.
Sure enough, (1 / 1.049450222) x (Pi^5) = 2916/10.
While reaching this conclusion, we gain what we need to know that
(Pi^3) / 1.049450222 = 29.54525712 = Morton’s Royal Cubit Squared x 10 = 1.718873385^2 x 10.
Using one of the handiest and most obvious mathematical probes, 360, we learn that
1.049450222 x 360 = 377.8020799, the “B” value for the Saturn Synodic Period and also 1/2 of the base length of the Great Pyramid.
Applying 1.177245771 as a potent mathematical probe, we learn that 1.049450222 can be conjugated from two very important numbers as (2 / 1.618829140) / 1.177245771 = 1.049450222, and that 1.177245771 continues to unlock data from 1.049450222 to at least 1.177245771^3.
Surprisingly 1.049450222 divided by 1.177245771 = 891.4453106, the projected perimeter value of the Stonehenge Aubrey Circle based on Thom’s lower estimate, which is a “fractional reciprocal” to the full-fledged “Aubrey Number” I often write about because the “Aubrey Number” seems to enjoy remarkable distribution throughout the ancient world, so there have been many reports of it in the past year.
As I said there is a great deal to learn about 1.049450222, but just finding out it exists, and recognizing that it IS a “Wonder Number”, surely represents already winning 2/3 of the battle.
With any luck we will be hearing more about this new “Wonder Number” 1.049450222 soon, which will hopefully include a clearer understanding of its place and function at Rio Bec besides simply representing a rich cache of stored mathematical data.
–Luke Piwalker
Luke Piwalker 