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# Giza the Ancient Rubic cube

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posted on Dec, 23 2014 @ 06:46 AM
There has been threads on Ats before that analyze the Giza plateau dimensions with various ideas put forward about the nature of the measurements used in the pyramids geometrical layout in the plateau. This thread continues in that spirit, but will start first with a quick recognition of the survey performed on the Giza plateau by Sir Flinders Petrie's 1880–82.

This is arguably the most detailed survey ever taken.

www.ronaldbirdsall.com...

Sir Flinders Petrie's 1880–82 survey of the Giza plateau, which included the Great Pyramid of Khufu and the relatively unknown Trial Site, is probably the most detailed Egyptian study ever undertaken by a surveyor.
This is the original edition of 1883 which was sold out during the first few months and never reprinted. A highly abridged second edition, which summarized many of the tables into a few lines of text and omitted much of the technical work, appeared in early 1885.
Other surveys of lesser scope have been conducted on the Giza plateau, but Petrie's contribution stands head and shoulders above them all. His extensive measurements of the Great Pyramid, in particular, have become the standard of reference for virtually all studies of that amazing edifice.

The next diagram which can easily be found on the internet by googling "Giza measurements photos". It diagrammatically shows Petries measurements of the Giza plateau.

I looked at the diagram and decided to myself that if the measurements are not random, but have been selected with a meaningful intent then some form of encoded logic will exist. I thought in terms of an encoded logic, similar as found in a Rubics cube where there is an inherent order that hides in the random features of the lattice. Keep that in mind and look at the diagram below, which is a version of the diagram above but I have modified it with colours, because this will allow easier to follow the simple calculations beneath it.

Calc 1 >>>

1732 - 429.5 - 250 = 1052.5

Calc 2>>>

440 + 411 + 201.5 = 1052.5

Calc 3>>>

1417.5 - 353.5+ 201.5 -213 = 1052.5

To appreciate the relevance arriving at the same result from three different paths, consider that by just adjusting a single measurement in the Map causes the 3 way synergy of results not to be achieved. When I refer to different paths note that each separate calc uses its own different numbers from the Map, (except for last two equations where 201.5 appears twice).

And just as a final interesting and equally interest to note i also found that

1417.5 - 201.5 - 213 + 411 = 1414 which is representative of the square root 2 to three decimal points (e.g 1.414).

The value 1.414 which has mathematical relevance to the 45 degree triangle

and which has a mathematical brother to the

in that 1732 represents the square root 3 to 3 decimal pts (e.g 1.732) which has mathematical relevance to the 30/60 degree triangle
This thread is just to share some interesting patterns in the numbers which i know may interest some people who like reading threads on Giza and the Ancients.

In my view the numbers are telling me Petries survey data was spot on as i dont see the number outcomes happening as a coincidence.

My intent in this thread doesn't extend to supporting any particular theory (e.g Aliens or Anti grav etc) its only to appreciate how the though the ancients put into their designs, which never ceases to amaze and surprise me.

posted on Dec, 23 2014 @ 08:17 AM
Thank you!!

These Ancient and Great Complexes have always Intrigued me.

Several authors have repeated each other’s argument that there are major correspondences between the pyramids of Giza and those of Teotihuacan.

The Pyramid of the Sun is 225 m wide and 65 m high, constructed out of five successive layers of mud.
Its ascent is via 242 stairs. The floor plan is rather close to that of the Pyramid of Khufu at Giza.

The Pyramid of the Moon is much smaller, 42 m high and 150 m wide, yet its summit is as high as that of the Pyramid of the Sun, because it sits on the site’s highest point. This feature can also be seen in Giza, where Khufu and Khafra pyramid's reach an equal height, even though one is taller than the other.

The three pyramids at Giza and the three main structures of Teotihuacan in my studies represent the Belt of Orion.

Is intriguing that ancient man could calculate such accurate measurements of the heavens.

posted on Dec, 23 2014 @ 08:21 AM
An interesting theory it does like a Rubic cube.

posted on Dec, 23 2014 @ 04:38 PM
Thanks for sharing! I never thought of the Pyramids that way...hmmm...now you have me thinking.

posted on Dec, 23 2014 @ 05:31 PM
Again, the measurements are interesting if you fudge them enough and give them credit for more accuracy than they really had. Just how do you go about accurately measuring something that is mostly disintegrated? You guess. You fudge. And there's a tendency for people to fudge in the direction that helps confirm their pet theories.

Also, how do you know this dude's measurements were accurate? Do you just accept it? It would be pretty hard to verify.

posted on Dec, 23 2014 @ 07:06 PM
a reply to: AthlonSavage As above so below

posted on Dec, 23 2014 @ 07:07 PM

originally posted by: AthlonSavage

Calc 1 >>>

1732 - 429.5 - 250 = 1052.5

Calc 2>>>

440 + 411 + 201.5 = 1052.5

Calc 3>>>

1417.5 - 353.5+ 201.5 -213 = 1052.5

To appreciate the relevance arriving at the same result from three different paths, consider that by just adjusting a single measurement in the Map causes the 3 way synergy of results not to be achieved. When I refer to different paths note that each separate calc uses its own different numbers from the Map, (except for last two equations where 201.5 appears twice).

While I completely accept that there may well be greater mathematical significance in the pyramids than previously thought (though I recall seeing another survey that identified the layout as simply being determined by existing rock formations), and I laud you for putting the time and effort into this, I have serious issues with the calculations drawn from them.

Calc 1 is essentially just taking the gaps away from the overall width. The overall width is the combination of gaps and widths of the pyramids, therefore the end result is just the sum of the widths of the pyramids.

Calc 2 is doing exactly the same thing, it's just adding up the sum of the widths of the pyramids.

Although I've not actually tried it with other numbers, this pattern will hold true regardless of what width or gap is used.

Think of it this way: draw a line that is 100cm long; the first 60cm of the line is red and the last 40cm is blue.

Calc 1 = the overall length minus the length of the red line = 40cm.
Calc 2 = the length of the blue line = 40cm.

It's not a mystical correlation, it's just... well it just is. This is basically all you are doing with the first two calculations.

Except... you mention that Calc 3 is the key. It's this synergy which you identify as being of particular importance. Unfortunately, you seem to have picked the numbers to use with no actual identifiable pattern.

You've picked the distance from the top of the first pyramid to the top of the second pyramid, and the width of the first pyramid - but then the distance from the bottom of the second pyramid to the top of the third pyramid.

Why these numbers? It makes no sense, other than "they just happened to add up to the number I needed".

There may well be a very good reason for you choosing those numbers that adds more gravity to the point you are making. I just... don't see it. The first two calculations are meaningless in terms of a pattern because they should always come to the same values. The third calculation seems like nothing more than a coincidence (and a bit of a stretched one at that).

Apologies, I don't want to come across as debunking an otherwise interesting observation, I'm just not seeing anything beyond coincidence.

posted on Dec, 23 2014 @ 07:30 PM

I highly recommend you read Graham Hancock's Heavens Mirror is you haven't done so already. It is filled with mathematical analysis and relationships within Giza and many other ancient sites such as Ankgor Watt and also how they relate to each other in some respects with their positions on the planet as a whole. Great stuff.

posted on Dec, 23 2014 @ 07:47 PM
While agree that the numbers chosen are purely arbitray (what is the reason for subtracting the gaps, for example,) I just want to chime in to say that the Egyptians did understand both the square root of 2 and the square root of 3, though not numerically.

Both numbers can be thought of as constructed lengths. The square root of two is the length of the diagonal on a 1 by one square. The square root of 3 is the length of the base of a right triangle with one side measuring 1 and the hypotenuse (diagonal of the rectangle) measuring 2.

Since we know that the Egyptians expressed their lengths as whole number cubits (along with palms and fingers as partial cubits,) and we know they had standard cubit-sticks by which they measured these lengths, we can see that they would have known how to find the lengths (square roots) that are mentioned here.

Harte

posted on Dec, 23 2014 @ 09:27 PM

The root 3 = 1.732 and the cos of 30 degrees in the 30/60 deg triangle above is 0.866

Adding the red lengths in the south north direction 201.5 + 250 = 451.5

Adding the green lengths in the east west direction 201.5 + 213 = 414.5

Add these values togther is 451.5 + 414.5 = 866 which is representatibe of 0.866 to three decimal points

1732 divided in half is 866

edit on 23-12-2014 by AthlonSavage because: (no reason given)

posted on Dec, 24 2014 @ 02:32 AM

From www.evawaseerst.be... you can find a link there to the reference to precession.
Difficult to say of course after all those years and all erosion that must have been the case, but a number around 52 degrees seems to be a reference to precession. The number (or a number close to it) is related to the Giza pyramids. There should be no more doubt about that. That the number 52 comes forward here is no surprise.

edit on 24-12-2014 by zandra because: (no reason given)

posted on Dec, 24 2014 @ 06:34 AM
Petrie in his survey used the of 20.620 inches (0.52375 metres) for the eygtian royale cubit. A bit of dicussion on this can be found:

goodfelloweb.com...

The reason why I brought that up is because i will show how I think the Giza Plateau east west longitudinal direction) dimension 1417.5 may of been used effectively as a basic unit for mapping the circumference of earth.

First a few basic details of how the earths longitude is measured in nautical miles.

There are 360 degrees in the circumference of circle (earth). In a single degree there are 60 nautical miles.

Therefore the longitudinal circumference of earth is 21600 nautical miles at equator.

In 1 nautical mile there is 1852 metres which using the (0.52375 metres) converter gives 3536.03818 royal cubits

3536.03818 divided by 1417.5 by = (3536.03818 / 1417.5) = 2.494559

The 2.494559 represents the Giza Plateau east west longitudinal direction length 1417.5 divides into a single nautical mile theoretically 2.5 times. Bear with me and i will explain the significance of the rounding error later on. i.e. 2.494559 to 2.5.

The 2.5 x 21600 means there are 54000 lots of the giza 1417.5 length that will fill the circumference. Think of a scale on a rule that is circle shape and has 54000 graduations.

The round off causes the following error (2.5 x 21600) - (2.494559 x 21600 )=
54000 - 53882.4744 = 117.5256

The 117.5 to the ancientes represented up to 117.5 lots of 1417.5 distance of error variation in the earths theoretical circumferential longitude.

Where i am going with this is to demonstrate to you how they could of used this value practically for creating a system which can be used to convert between measurement scales, with the aim of doing this to measure arc movements of the sun using measurements to record displacement using a 24 hr time scale which is composed of 24 x 60 min = 1440 mins and 1440 x 6 = 86400 seconds.

Since 1 nautical mile is comprised of 2.5 lots of 1417.5 royale cubits

Then the theoretical variation 117.5 is made can vary as much up to the limit of 117.5 / 2.5 = 47 nautical miles
Therefore the 47 nautical mile is the distance tolerance variation I believe the builders of the Giza pyramids are using to male a theoretical calculation of earths circumference).

Now 47 nautical mile divided by longitudinal circumference of earth is 21600 nautical miles
= 47/21600 = 0.002175 a dimensionless fraction value

In a 24 hour time scale ( 1 full circumferential rotation of earth), there are 86400 seconds.
86400 seconds x 0.002175 = 188 (an exact value result no round off required)
188 seconds / 60 seconds = 3.13333 minutes

Therefore in 3.13333 minutes 47 nautical miles are progressed
In one minute 47/ 3.13333 = 15 nautical miles progressed per each minute passed on the 24 hr scale (1440/86400).

Working backwards now to verify result 15 nautical miles of x 1440 minute ( on the 24 hour scale) = 21600 nautical miles the longitudinal circumference of earth.

I believe this was the basis for Giza using 1417.5 length for the longitudinal east west direction.

posted on Dec, 24 2014 @ 01:46 PM

originally posted by: AthlonSavage

Where i am going with this is to demonstrate to you how they could of used this value practically for creating a system which can be used to convert between measurement scales, with the aim of doing this to measure arc movements of the sun using measurements to record displacement using a 24 hr time scale which is composed of 24 x 60 min = 1440 mins and 1440 x 6 = 86400 seconds.

Since 1 nautical mile is comprised of 2.5 lots of 1417.5 royale cubits

Then the theoretical variation 117.5 is made can vary as much up to the limit of 117.5 / 2.5 = 47 nautical miles
Therefore the 47 nautical mile is the distance tolerance variation I believe the builders of the Giza pyramids are using to male a theoretical calculation of earths circumference).

Now 47 nautical mile divided by longitudinal circumference of earth is 21600 nautical miles
= 47/21600 = 0.002175 a dimensionless fraction value

In a 24 hour time scale ( 1 full circumferential rotation of earth), there are 86400 seconds.
86400 seconds x 0.002175 = 188 (an exact value result no round off required)
188 seconds / 60 seconds = 3.13333 minutes

Therefore in 3.13333 minutes 47 nautical miles are progressed
In one minute 47/ 3.13333 = 15 nautical miles progressed per each minute passed on the 24 hr scale (1440/86400).

Working backwards now to verify result 15 nautical miles of x 1440 minute ( on the 24 hour scale) = 21600 nautical miles the longitudinal circumference of earth.

I believe this was the basis for Giza using 1417.5 length for the longitudinal east west direction.

Again, and my apologies for sounding rude, but I really don't follow the logic in what you are saying. I'm interested in the mathematics but I was never good with numbers, I would appreciate a little help in understanding this better.

The first part of the post is establishing that the width of the Giza site is 1/54000th of the circumference of the Earth. Fair enough, no problem with that.

The second part of the post raises more questions than it answers.

When you say "The round off causes the following error (2.5 x 21600) - (2.494559 x 21600 ) = 54000 - 53882.4744 = 117.5256. The 117.5 to the ancientes represented up to 117.5 lots of 1417.5 distance of error variation in the earths theoretical circumferential longitude", a question occurs to me. You have identified this number based on the rounding error between 2.49 and 2.5 - yet both of these numbers are derived from a conversion between cubits and the nautical mile, not to mention already needing to know the circumference of the Earth in the first place to arrive at these figures.

How could these figures be calculated by the original designers without knowledge of the nautical mile (use of the nautical mile raises a host of other questions as well) or the circumference of the Earth? Also, you appear to be suggesting that the designers were aware of the value 117.5, but where or how is this indicated in the site? Or have I misunderstood what you are saying?

If there was no way for the designers at the time to arrive at the value of 117.5, then every calculation that follows is interesting... but of no value in establishing any deliberate design for calculating the circumference of the planet. Your calculations seem to rely heavily on the end result already being known.

It's also worth pointing out that the earliest-known accurate measurement of the Earth's circumference was made by a second-rate mathematician with a sundial and a hole in the ground. The pyramids seem like a ridiculous tool to use for this kind of calculation and if their understanding of mathematics was profound enough to design for this purpose, they surely would have understood enough to realise there were infinitely easier ways of doing it.

posted on Dec, 24 2014 @ 06:36 PM
The Ancient Egyptians certainly were aware of the number 117.5.

As a length, they knew it as 117 cubits, three palms and 2 fingers.

Harte

posted on Dec, 24 2014 @ 07:07 PM

originally posted by: Harte
The Ancient Egyptians certainly were aware of the number 117.5.

As a length, they knew it as 117 cubits, three palms and 2 fingers.

Harte

...good point

But did they know that it represented a margin of error for calculating the circumference of the globe based on the width of the site? Because I suspect they didn't.

I'm trying to find the politest and most diplomatic way possible to suggest that the theory is an inverted pyramid of piffle, cut me some slack

posted on Dec, 24 2014 @ 07:13 PM

originally posted by: EvillerBob

originally posted by: Harte

The Ancient Egyptians certainly were aware of the number 117.5.

As a length, they knew it as 117 cubits, three palms and 2 fingers.

Harte

...good point

But did they know that it represented a margin of error for calculating the circumference of the globe based on the width of the site? Because I suspect they didn't.

I'm trying to find the politest and most diplomatic way possible to suggest that the theory is an inverted pyramid of piffle, cut me some slack

Relax, I saw what you were doing.

Just trying to cover for you.

You wouldn't want a fringer to call you on that, would you?

Harte

posted on Dec, 24 2014 @ 11:19 PM
Im speculating when i say that there may be a connection between the Giza and Bruce Cathies mathematics of the world grid.

Quote"
Originally, when Bruce was starting his research into the World Grid and harmonics, he plotted sightings of UFOs on a map of New Zealand. After he had plotted a lot of sightings, he noticed that he could draw a set of lines that would connect the sightings. These lines formed a grid pattern and by measuring, he found that the lines were 30′ apart. When I say 30′, I mean 30 minutes of arc or 30 nautical miles. "

www.worldgrid.net...

This is something i may look into further because the 15 nautical miles i showed with some maths having a relationship to 1417.5 and i also noticed in a curious check that Bruce cathies dimension of the world energy grid are formed in grid pattern with the lines 15 x 2 = 30 nautical miles apart.

posted on Dec, 25 2014 @ 03:14 AM
Now i am going to repeat the calculation i did for the east west longitudinal direction dimension 1417.5 but use 1732 instead and see what result in nautical miles pops out as the result in the lattitudinal Noth South direction.

First a few basic details of how the earths longitude is measured in nautical miles.

There are 360 degrees in the circumference of circle (earth). In a single degree there are 60 nautical miles.

Therefore the longitudinal circumference of earth is 21600 nautical miles at equator.

In 1 nautical mile there is 1852 metres which using the (0.52375 metres) converter gives 3536.03818 royal cubits

3536.03818 divided by 1732 by = (3536.03818 / 1732) = 2.04159

The 2.04159 represents the Giza Plateau north south latitudinal direction length 1732 divided into a single nautical mile, the result is theoretically 2.0 Bear with me and i will explain the significance of the rounding error later on. i.e. 2.04159 to 2.0.

The 2.0 x 21600 means there are 43200 lots of the giza 1732 length that will fill the lattitudinal circumference. Think of a scale on a rule that is circle shape and has 43200 graduations.

The round off causes the following error (2.04159 x 21600) - (2.0 x 21600 )=
44098.344 - 43200= 898.344 round up to 898.4

The 898.4 to the ancients represented up to 898.4 lots of 1732 distance of error variation in the earths theoretical circumferential lattidude.

Since 1 nautical mile is comprised of 2.0 theoretical lots of 1732 royale cubits

Then the theoretical variation 898.4 is made can vary as much up to the limit of 898.4/ 2.0 = 449.2 nautical miles

Therefore the 449.2 nautical mile is the distance tolerance variation I believe the builders of the Giza pyramids are using to male a theoretical calculation of earths circumference).

Now 449.2 nautical mile divided by longitudinal circumference of earth is 21600 nautical miles
= 449.2/21600 = 0.020796 a dimensionless fraction value

In a 24 hour time scale ( 1 full circumferential rotation of earth), there are 86400 seconds.
86400 seconds x 0.020796 = 1796.7744.

1796.8 seconds / 60 seconds = 29.9466 minutes

Therefore in 29.9466 minutes there are 449.2 nautical miles are progressed
In one minute 449.2/ 29.9466 = 15 nautical miles (exact value no round off required) progressed per each minute passed on the 24 hr scale (1440/86400).

Working backwards now to verify result 15 nautical miles of x 1440 minute ( on the 24 hour scale) = 21600 nautical miles the longitudinal circumference of earth.

Therefore i have repeated the calculation using 1732, instead of the 1417.5 that I performed in a previous post for the longitudinal east west direction.. In this calculation for the lattitdinal North south direction i use the same calculation methodoloy but im now applying the calculation to the lattitdinal North south direction using 1732, and incredibly the same result occurs 15 nautical miles.

Therefore the calcutions reveal evidence of a grid pattern. That is in the Lattitudinal North south direction (1732) is made up of lines displaced at 15 nautical miles, and in the longitudinal West east direction (1417.5) is made up of lines displaced also at 15 nautical miles. What these lines represent are a debate in themselve, but they do surprising to me line up with Bruce cathies calculation of the world energy grid. Bruce deduced by a completely different method of calculation there is a energy matrix encompassing the earth in a grid lattice of 15 nautical mile displacement.

posted on Dec, 25 2014 @ 07:28 AM

originally posted by: AthlonSavage

There are 360 degrees in the circumference of circle (earth). In a single degree there are 60 nautical miles.

Therefore the longitudinal circumference of earth is 21600 nautical miles at equator.

In 1 nautical mile there is 1852 metres which using the (0.52375 metres) converter gives 3536.03818 royal cubits

3536.03818 divided by 1732 by = (3536.03818 / 1732) = 2.04159

The 2.04159 represents the Giza Plateau north south latitudinal direction length 1732 divided into a single nautical mile, the result is theoretically 2.0 Bear with me and i will explain the significance of the rounding error later on. i.e. 2.04159 to 2.0.

The 2.0 x 21600 means there are 43200 lots of the giza 1732 length that will fill the lattitudinal circumference. Think of a scale on a rule that is circle shape and has 43200 graduations.

I'm still not getting this. Why are you dividing these two numbers together? You're relying on a value (metres in a nautical mile) that was only standardised in the last 100 years.

If you're suggesting that the giza site represented what they thought was a minute of angle in latitude/longitude (not sure how old that theory is, I thought it originated with Eratosthenes a few thousand years later but maybe the Egyptians used it as well?), then it is quite interesting to note that an actual minute (3536 cubits, 1852 metres) is pretty darn close to the the site dimension (3306 cubits, 1732 meters) - only a divergence of 230 cubits / 120 metres. 93% accuracy isn't to be sniffed at, if that was their intention. Which I don't believe it was.

I understand that you're trying to identify how many times the length goes into the circumference, but (i) it's a really strange way of doing it and (ii) it appears to lead to quite a major inaccuracy. The "distance of error variation" sounds, quite frankly, like a fluff term to assign a significance to something that is not actually significant.

I'll put this in "excel spreadsheet format" to clarify the method I've used to checked your numbers. It might well be that I've made a mistake somewhere, and this provides and opportunity for someone to point out any errors on my part.

Your calc: =round(3536.03818 / 1732 , 0) * 21600
Result = 43200 "graduations" (number of times that the site fits into the circumference)

But, more logically, why not just convert all the units to cubits:

Convert site length from metres to cubits:
Calc: =1732 / 0.52375
Result: 3306.921 (cubits)

Convert circumference from (nautical miles to metres) to cubits:
Calc: =(21600*1852) / 0.52375
Result: 20951676 (cubits)

Divide the circumference by the length of the site:
Calc: = 20951676 / 3306.921
Result: 23096.54 (number of times that the site fits into the circumference)

You could simplify the whole thing even more just by using the same unit that is used in the original survey, only needing to convert nautical miles to metres:
Calc: =(21600*1852) / 1732
Result: 23096.54 (number of times that the site fits into the circumference)

So, we have two very simple methods, both of which agree with each other, and both of which are radically different to the number you have reached: 23096.54 divisions (my calcs) or 43200 divisions (your calcs). If the theory fails at this early stage, it pretty much removes any meaning from the calculations that follow.

I've completely ignored any issues of latitude/longitude/nautical mile usage etc, and just used the numbers you have provided. The Earth is not a perfect sphere so the dimensions differ along the equator and across the poles, but I accept that the ancients may not have anticipated this so I'll accept the use of the same dimensions in this example.

Perhaps it can be explained in a way that makes more sense (Harte, stop s'n-word'ing) but I'm just not seeing it. I'm certainly open to listening if you can shed some light on it.

Edit to add: Wow, the word filter here is harsh! "Chortling" just doesn't have the same ring to it.
edit on 25-12-2014 by EvillerBob because: (no reason given)

posted on Dec, 25 2014 @ 09:35 AM
In my view use of 15 nautical miles was of practical use to the Giza builders in a measurement scale. Ill explain below.
1852 metres in a nautical mile

using the converter factor between Eyptians Royale cubits 0.52375 metres and metres gives
3536.03818 eyptians Royale cubits in a single nautical mile

The 1417.5 the length in Eyptians Royale cubits of Giza in the east west longitudinal direction
Therefore 1417.5 / 3536.03818 = 0.400872 the fraction in 1 nautical mile.

Established 15 nautical miles per minute in a 24 hour time scale

15 nautical/ 60 seconds = 0.25 nautical miles per second (second measured on the 24 hour clock scale)

Summing increments the 0.400872 by 0.25 nautical miles and multiplying by 60 arc seconds
(There are 60 arc seconds in single nautical mile and not to be confused with the 60 seconds minute of the 24Hr clock)

The increments of 0.25 nautical miles we see 15 arc seconds displacement between them.

(0.400872 ) x 60 arc seconds = 24.05232 (arc seconds)

(0.400872 + 0.25) x 60 arc seconds = 39.05232 (arc seconds)
39.05232 -24.05232 = 15 arc seconds

(0.400872 + 2 x 0.25) x 60 = 54.05232 (arc seconds)
54.05232 - 39.05232 = 15 arc seconds

(0.400872 + 3 x 0.25) x 60 = 69.05232
69.05232 - 54.05232 = 15 arc seconds

(0.400872 + 4 x 0.25) x 60 = 84.05232
84.05232 - 69.05232 = 15 arc seconds

(0.400872 + 5 x 0.25) x 60 = 99.05232
99.05232 - 84.05232 = 15 arc seconds

(0.400872 + 6 x 0.25) x 60 = 114.05232
114.05232 - 99.05232 = 15 arc seconds

The 15 +15 +15 + 15 + 15 + 15 = 90 arc seconds represents 0.400872 + 6 x 0.25 = 1.900872 nautical miles

It will take 360 / 90 = 4 increments to complete a 360 degrees arc second cycle.

Therefore 4 x 1.900872 = nautical miles = 7.60348 for 360 degrees arc second cycle.

The ancients I believed measured 7.60 nautical miles in a 360 degrees arc second cycle.

Gonna xmas break and think this one out a bit more.

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