08-01-2017, 11:50 PM
(This post was last modified: 08-02-2017, 05:03 AM by Ancient Vizier.)

I'm trying to table up more of the data from George Andrews - as scarce as any reliable measurements seem to be, the wealth of data the available papers by Andrews is simply too valuable to pass up - but it's literally weeks worth of clerical work trying to condense all those 40 page reports into one page data tables.

Meanwhile, I've run into several points that still sort of confuse me, which is another incentive to try to get an even broader overview of ancient American arithmetic... I think I've made numerous arguments in favor of ancient Mesoamericans having been rather fond of Yoda's "Alternate Pi" 1.177245771 in addition to the Pi ratio itself, as well has having possibly given examples of how the ancients liked to "mix-and-match" creatively, so we might want to expect numbers that can be made using Pi with Alternate Pi, not the least of which is the primary figure for the calendar year itself

1.177245771 x Pi = 3.698426663 = 1/2 Squared Yoda Megalithic Yard = 7.396853327 / 2

1.177245771 x (Pi^2) = 11.61895004 (sqrt of 135, which may have been important just for being part of this series)

1.177245771 x (Pi^3) = 365.020081 / 10

Likewise, we can divide Alternate Pi by Pi

1.177245771 / Pi = 3.747289674 = (4 / 1.067438159) x 10^n = (1.040913798 x 360) / 10^n = 14.989158700 / 4

So we are already back to my proposal that we might see some of these "shaved" numbers in practice, such as 14.989158700 instead of 15, in some metrological applications like this (and half of this figure, 14.989158700 / 2 = 7.494579343, is at this hour still trying to get itself declared to be a number intentionally built into Tikal's temples)

1.177245771 / (Pi^2) = 1.1927993500 / 10^n

And that's one of the things that still confuses me - it still seems hard sometimes to tell in a given instance whether they meant this, or perhaps 1.184352528 = (12 x (Pi^2)) / 10, which has managed to make something of a name for itself in these procedings, or perhaps something else. (At a tolerance of about 2/100 of a foot, sometimes the intended figure in the target range could even be 1.177245771 itself).

Next question, did the ancients find a lot of usefulness in dividing Alternate Pi by another power of Pi, or have we about run out of good combinations of Pi and Alternate Pi here?

1.177245771 / (Pi^3) = 3.796798252 and THAT, is the primary figure suggested here to represent the Venus Cycle, divided by 10^n

37967.98252 / 2 = 18983.99126 representing 18980 (days)

So 1.1927993500 may indeed fall within the spectrum of useful items, we might expect to see a certain amount of it accordingly, (the bulk of the equations in this post thus far appear to be written into the Aztec Sun Stone when measured in modern feet) and we may have increased or at least better organized our insights into any ancient fondness for Alternate Pi 1.177245771 given some of the things can be built of just it and the Pi ratio.

Not sure what it means yet but I've seen a number of occasions when trying to figure out what the ancients might use to represent the number 19, which does not itself actually belong to this system of numbers, where the equation comes out suggesting that 18.98399126 could have been used to represent 19.

Another curio turns up often enough in the proceedings, and there's a small amount of backstory I might add. A curious notation, "Stone Pi" often turns up in my notes. This started back when I thought that 2.920160646 might be the "Grid Point" of Stonehenge - a proposal that's now gone into the waste basket, but the numbers remain. So, "Stone Pi" is shorthand for

(Formerly Stonehenge "Grid Point") 2.920160646 x Pi = 9.173955233

And at this point, the history of the number 9.173955233 might include that after undoubtedly testing more equations than I even care to think about, Yoda decided that 917.3955239 was the "Grid Latitude" of the Kulkulan Pyramid at Chichen Itza. As often, Yoda may be making these numbers out of numbers found in real life at the respective sites rather than just making them up out of map data, so they continue to promise to mean something independently of concerns about global "Grid" positioning.

2.920160646 x (Pi^2) = 28.82083036, which may have been already found in the Tizoc Stone

2.920160646 / (Pi^2) = 29.58741331 (360 / 1.216733603), which may be the primary ancient figure for representing the Lunar Synodic Period.

9.173955233 x 2 = 18.34791047

And that's one that I think I seem to see a lot in working with ancient American monument data (I've forgotten all the details but I know in the past I had some discussion with Michael L. Morton about the possible usefulness of the square of this number)

18.34791047^2 = 336.6458185

These days we are aware of the possibility that 259.7575763 may have been a highly favored way for the ancients to express the very sacred calendrical number, 260 - so it probably catches our attention with sufficient ease that

(1 / (1.177245771^2)) x 10) = 7.215488230 (as proposed to occur at Rio Bec), and

7.215488230 x 360 = 259.7575763

259.7575763 x 360^2 = 33664.58188 / 10^n

So 336.6458185 could have been valuable to the ancients, just for having been made out of some rather obvious ingredients, if it will better prove its usefulness in practice.

But obviously in an arithmetic system that, at least at Giza, seems to have elementary circular geometry as its lowest level (i.e., 360 / Radian 57.29577951 = 2 Pi),

18.23781305 = Radian 57.29577951 / Pi

Is both obviously very important, but is also easily confused with 18.34791047, and similar confusion (at least for me) still exists surrounding any given example whether what LOOKS like the Double Radian 57.29577951 x 2 = 114.5915590 could turn out to mean 114.8380617, which is a reciprocal of the door height at Tikal Temple II (1 / 8.707914303 = 114.8380617 / 10^n), or even some other third possibility. Some instances of values in this range could turn out to be 1.141489711 or even 11.4148971 feet without exceeding a reasonable tolerance for error (1 / 1.141489711 = primary figure for Hours in a Year / 10^n = 365.020081 x 24) / 10^n).

There are more that may call for some careful thought - I see a good number of things that look like (72 Pi) / 100 = 2.261946711, and we may have reason to believe that 72 was an important symbol of Venus and its path through the heavens, but 225 / Pi^2 = 2.279726632 or 224.88373803 / (Pi^2) = 2.27807985 are also ways of mixing numerical Venus symbols with the Pi ratio in simple combinations. It's really up to whether a particular number makes good sense in a particular application, and whether or not we actually have the data needed to clarify some of these situations (worse, I've gathered enough photographs to know how often the top and bottom widths of ancient "temple" doors seem to be two different figures where I only have a single width figure in the data).

I have an awful lot of data on ancient American door widths where unlike with Tikal, all I can do is suggest a few possibilities because I just don't have the data on their heights to be more certain. On the other hand, I should have enough data that I'd better be able to make something out of it.

(BTW, here is my link for Andrews' data if anyone else is interested in archiving it or working with it).

https://repositories.lib.utexas.edu/brow...+1918-2000

Meanwhile, I've run into several points that still sort of confuse me, which is another incentive to try to get an even broader overview of ancient American arithmetic... I think I've made numerous arguments in favor of ancient Mesoamericans having been rather fond of Yoda's "Alternate Pi" 1.177245771 in addition to the Pi ratio itself, as well has having possibly given examples of how the ancients liked to "mix-and-match" creatively, so we might want to expect numbers that can be made using Pi with Alternate Pi, not the least of which is the primary figure for the calendar year itself

1.177245771 x Pi = 3.698426663 = 1/2 Squared Yoda Megalithic Yard = 7.396853327 / 2

1.177245771 x (Pi^2) = 11.61895004 (sqrt of 135, which may have been important just for being part of this series)

1.177245771 x (Pi^3) = 365.020081 / 10

Likewise, we can divide Alternate Pi by Pi

1.177245771 / Pi = 3.747289674 = (4 / 1.067438159) x 10^n = (1.040913798 x 360) / 10^n = 14.989158700 / 4

So we are already back to my proposal that we might see some of these "shaved" numbers in practice, such as 14.989158700 instead of 15, in some metrological applications like this (and half of this figure, 14.989158700 / 2 = 7.494579343, is at this hour still trying to get itself declared to be a number intentionally built into Tikal's temples)

1.177245771 / (Pi^2) = 1.1927993500 / 10^n

And that's one of the things that still confuses me - it still seems hard sometimes to tell in a given instance whether they meant this, or perhaps 1.184352528 = (12 x (Pi^2)) / 10, which has managed to make something of a name for itself in these procedings, or perhaps something else. (At a tolerance of about 2/100 of a foot, sometimes the intended figure in the target range could even be 1.177245771 itself).

Next question, did the ancients find a lot of usefulness in dividing Alternate Pi by another power of Pi, or have we about run out of good combinations of Pi and Alternate Pi here?

1.177245771 / (Pi^3) = 3.796798252 and THAT, is the primary figure suggested here to represent the Venus Cycle, divided by 10^n

37967.98252 / 2 = 18983.99126 representing 18980 (days)

So 1.1927993500 may indeed fall within the spectrum of useful items, we might expect to see a certain amount of it accordingly, (the bulk of the equations in this post thus far appear to be written into the Aztec Sun Stone when measured in modern feet) and we may have increased or at least better organized our insights into any ancient fondness for Alternate Pi 1.177245771 given some of the things can be built of just it and the Pi ratio.

Not sure what it means yet but I've seen a number of occasions when trying to figure out what the ancients might use to represent the number 19, which does not itself actually belong to this system of numbers, where the equation comes out suggesting that 18.98399126 could have been used to represent 19.

Another curio turns up often enough in the proceedings, and there's a small amount of backstory I might add. A curious notation, "Stone Pi" often turns up in my notes. This started back when I thought that 2.920160646 might be the "Grid Point" of Stonehenge - a proposal that's now gone into the waste basket, but the numbers remain. So, "Stone Pi" is shorthand for

(Formerly Stonehenge "Grid Point") 2.920160646 x Pi = 9.173955233

And at this point, the history of the number 9.173955233 might include that after undoubtedly testing more equations than I even care to think about, Yoda decided that 917.3955239 was the "Grid Latitude" of the Kulkulan Pyramid at Chichen Itza. As often, Yoda may be making these numbers out of numbers found in real life at the respective sites rather than just making them up out of map data, so they continue to promise to mean something independently of concerns about global "Grid" positioning.

2.920160646 x (Pi^2) = 28.82083036, which may have been already found in the Tizoc Stone

2.920160646 / (Pi^2) = 29.58741331 (360 / 1.216733603), which may be the primary ancient figure for representing the Lunar Synodic Period.

9.173955233 x 2 = 18.34791047

And that's one that I think I seem to see a lot in working with ancient American monument data (I've forgotten all the details but I know in the past I had some discussion with Michael L. Morton about the possible usefulness of the square of this number)

18.34791047^2 = 336.6458185

These days we are aware of the possibility that 259.7575763 may have been a highly favored way for the ancients to express the very sacred calendrical number, 260 - so it probably catches our attention with sufficient ease that

(1 / (1.177245771^2)) x 10) = 7.215488230 (as proposed to occur at Rio Bec), and

7.215488230 x 360 = 259.7575763

259.7575763 x 360^2 = 33664.58188 / 10^n

So 336.6458185 could have been valuable to the ancients, just for having been made out of some rather obvious ingredients, if it will better prove its usefulness in practice.

But obviously in an arithmetic system that, at least at Giza, seems to have elementary circular geometry as its lowest level (i.e., 360 / Radian 57.29577951 = 2 Pi),

18.23781305 = Radian 57.29577951 / Pi

Is both obviously very important, but is also easily confused with 18.34791047, and similar confusion (at least for me) still exists surrounding any given example whether what LOOKS like the Double Radian 57.29577951 x 2 = 114.5915590 could turn out to mean 114.8380617, which is a reciprocal of the door height at Tikal Temple II (1 / 8.707914303 = 114.8380617 / 10^n), or even some other third possibility. Some instances of values in this range could turn out to be 1.141489711 or even 11.4148971 feet without exceeding a reasonable tolerance for error (1 / 1.141489711 = primary figure for Hours in a Year / 10^n = 365.020081 x 24) / 10^n).

There are more that may call for some careful thought - I see a good number of things that look like (72 Pi) / 100 = 2.261946711, and we may have reason to believe that 72 was an important symbol of Venus and its path through the heavens, but 225 / Pi^2 = 2.279726632 or 224.88373803 / (Pi^2) = 2.27807985 are also ways of mixing numerical Venus symbols with the Pi ratio in simple combinations. It's really up to whether a particular number makes good sense in a particular application, and whether or not we actually have the data needed to clarify some of these situations (worse, I've gathered enough photographs to know how often the top and bottom widths of ancient "temple" doors seem to be two different figures where I only have a single width figure in the data).

I have an awful lot of data on ancient American door widths where unlike with Tikal, all I can do is suggest a few possibilities because I just don't have the data on their heights to be more certain. On the other hand, I should have enough data that I'd better be able to make something out of it.

(BTW, here is my link for Andrews' data if anyone else is interested in archiving it or working with it).

https://repositories.lib.utexas.edu/brow...+1918-2000

"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911