Advanced mathematics encrypted in Stone-Age and ancient 'artwork'

[Jiri]

.
you blame the shoddy builders for not building the pyramids to your imagined floor plan

it seems that the builders did an absolutely incredible job sticking to the plan, and Petrie did a superlative job measuring it all

You call that blaming the pyramid builders? Speaking of twisting, you put pretzel makers to shame.

[Foster Zygote]

Zombie Thread want brainnnnnns!

[Paul]

Originally Posted by Jiri

The meat of the matter is that because you know that I am not a native English speaker

Even given that English is not your first language, you must know that they are not synonymous with sour grapes; mousing over them gives the definitions, which demonstrate that care is needed with taking the internet at face value.

[JonnyFive]

Originally Posted by Jiri

Follow links from the dictionary.com, and you get tons of meanings like the below examples. The meat of the matter is that because you know that I am not a native English speaker, you try to get out of hot soup by spooon-feeding us skeletal ideas of English for chokecherries.

36 Moby Thesaurus words for "sour grapes":
acid, acidulant, belittling, bread-and-butter pickle, chokecherry,
comedown, contempt, crab apple, decrial, depreciation, derogation,
detraction, dill pickle, disapproval, discrediting, disgrace,
disparagement, faint praise, green apple, indignity, knocking,
lemon, lime, lukewarm support, minimizing, pickle, putting down,
slighting, sour, sour balls, sour cream, sour pickle, sourdough,
verjuice, vinegar, yogur

As English is not your first language, I would like to point out that a thesaurus often gives words or phrases that may have quite different meanings from the word referenced, even if the intent is slightly similar.

Anyway, let's not belittle a stupid point. You said your layout doesn't match the actual layout, but that it's somehow more accurate? How did you determine that your layout is correct? Did you pick a layout that produced better "golden ratios?" If so, why?

In any case, if you used a constructed layout, surely you could've done better than to approximate phi to one decimal place. That's quite poor performance for a manufactured approximation.

[Jiri]

I said sour grapes, and Wollery knew what I meant. The term has a loose enough meaning to be interpreted in tune with the context. In this case there is apparent avoidance of the subject at hand, i.e., reconstruction of the Giza layout, and steering the discussion into nitpicking over something else.
The reconstruction has its merits, and tangible scientific value, although it is not exactly up there with transmutation of spring water into high-octane gas. What is so hard about acknowledging the evident? How can that be unattainable?

[Hokulele]

Until you understand the difference between accuracy and precision, there is no scientific value, tangible or otherwise, at all. None.

[Jiri]

You said your layout doesn't match the actual layout, but that it's somehow more accurate? How did you determine that your layout is correct?

How so? I specified exactly how my layout matches Petrie's plan, where it can be considered exact, and where it's lacking. If you can point me to a better reconstruction from a clean slate than mine, please do so.
I think that you should agree that the reconstruction of the third pyramid in the layout is indeed exact. So is one diagonal of the second pyramid. The Great Pyramid in the same reconstruction will be precisely positioned by its N.E. corner, but its sides will be over six inches shorter. Its center will fall three inches from Petrie's plan. The second pyramid's center will be five inches off. All these results are sufficiently close to the plan considering the scale of Giza to be considered right on.
The reconstruction is a simple procedure, and gives the best results, so far. That is despite the fact that the reconstruction is not yet complete, because it doesn't give the size of the second pyramid. There is one Golden Section idea, which takes this size to within 22 inches overlap by the original, not close enough for me, although I see reconstructions out there being out by whole cubits and still suggesting that they reflect the original plan by the ancient Egyptians. In comparison, my reconstruction is so close to reality, an idea suggests itself that the original Egyptian plan was the same, as my reconstruction.

In any case, if you used a constructed layout, surely you could've done better than to approximate phi to one decimal place. That's quite poor performance for a manufactured approximation.

Really? Where do you get this nonsense. The reconstruction uses exact means, CAD, a start from an exact Golden rectangle, etc, etc.

[Jiri]

Until you understand the difference between accuracy and precision, there is no scientific value, tangible or otherwise, at all. None.

Perhaps, you don't understand, otherwise you would not oversimplify. The reconstruction deals with exact ideas above all. The architects planned Giza according to exact ideas, and the builders built Giza with great precision in adhering to those ideas, and specifications, so that the result accurately reflects the underlying exact ideas. Do you understand that?

[Hokulele]

Originally Posted by Jiri

As things stand today, I can get some absolutely right, and some not with varying degree of accuracy. Scaled to real size of Giza (the maximum NS distance between the pyramid edges), the Menkaure's base and position are faultless. The reconstructed base is an inch shorter than in the plan given by Petrie. So this base than has 0 fault on the south, 1 inch in the north, 1.2 inches in the west, and 2.25 inches in the east. The same plan will fit in the NE corner of the Great Pyramid (in Petrie's plan) exactly, but the sides will be more than six inches shorter. However, one great plus of my algorithm is that it also gets you one diagonal of the Second Pyramid exactly right, because the difference to Petrie's plan is 0.58 inch.

Reread this section. Which numbers are more accurate? Which are more precise? Do you realize the very first sentence in this quote pretty much throws your whole idea out the window?

As others have said, this is a very impressive exercise in confirmation bias.

[Gravy]

Jiri, I understand your frustration at the hostile reception to your ideas. It's well-established that some members here are shills for Big Maths and Big Sanity.

[Jiri]

Take a turn rereading the section. Since the reconstruction deals with exact ideas, getting those ideas right would mean that the numbers given all concern cumulative errors by builders and Petrie himself and that those numbers are so small as to be negligible. The original exact ideas still shine right through.

[Jiri]

A shill is a shill is a shill.

[wollery]

I have a simple question. You say that you get one diagonal of the second pyramid right. I assume that this means that the others are wrong. My question is, you assume that this is because the builders got it wrong, but what if that one diagonal was the bit they got wrong? Would that not mean that the pyramid was not built to the specifications you say it was built to?

[Jiri]

I have a simple question. You say that you get one diagonal of the second pyramid right. I assume that this means that the others are wrong.

I have an even simpler question. How many diagonals does a square have? I always thought two, but you seem to imply at least three.
The second diagonal for the second pyramid escapes me so far. Count with me: One. That's one out of six total for the three pyramids. I admit that. There seems to be an alternative construction for its center however, which comes to within five inches of the original vertical axis. This in conjunction with the diagonal, which is right on (0.58 inch is right on the mark, no?) takes the center of the reconstructed pyramid to five inches below the center as given by Petrie. This would be entirely in permissible error range by most standards.

[Hokulele]

In the previous post of yours I had quoted, you managed to get one line correct out of six. One. Using a CAD system and scans, it would be impossible to get zero correct (using basic match tools), so I will state that your entire system is bunk.

By the way, did you process the scan to remove any camera lens distortion, scanning errors, or biasing?

[Jiri]

No, you misunderstood. I got five out of six lines right on, with the biggest discrepancy being three inches.
There was no camera scanning, are you in a dream, or something? Petrie gives numbers, which you can use to reconstruct his plan exactly as he gave it. So, I will state that your entire critique is pathetically unrelated to my work.

[Macoy]

It's from Æsop's fable 'The Fox And The Grapes', whereby the fox cannot reach the topmost grapes, and turning away disgruntled after many fruitless attempts, remarks that that they were probably sour anyway.

So wollery wins.

[wollery]

Originally Posted by Jiri

No, you misunderstood. I got five out of six lines right on, with the biggest discrepancy being three inches.
There was no camera scanning, are you in a dream, or something? Petrie gives numbers, which you can use to reconstruct his plan exactly as he gave it. So, I will state that your entire critique is pathetically unrelated to my work.

So your construction is based on Petrie's measurements, which were made in 1880-1882 and can't be repeated today with better equipment because of erosion due to modern pollution.

And on the basis that your construction seems to fit reasonably well with Petrie's measurements you state that Petrie's measurements were accurate and the Giza site was built to the plan you've worked out, despite the discrepancies.

There's some circular reasoning in there somewhere!

[Hokulele]

Let's take a look at the numbers.

Originally Posted by Jiri

As things stand today, I can get some absolutely right, and some not with varying degree of accuracy. Scaled to real size of Giza (the maximum NS distance between the pyramid edges), the Menkaure's base and position are faultless. The reconstructed base is an inch shorter than in the plan given by Petrie.

Reconstruction is off. Strike one.

Quote:

So this base than has 0 fault on the south, 1 inch in the north, 1.2 inches in the west, and 2.25 inches in the east.

One number right, 3 wrong. Strike two.

Quote:

The same plan will fit in the NE corner of the Great Pyramid (in Petrie's plan) exactly, but the sides will be more than six inches shorter.

Another one wrong. Strike three.

Quote:

However, one great plus of my algorithm is that it also gets you one diagonal of the Second Pyramid exactly right, because the difference to Petrie's plan is 0.58 inch.

One right, one wrong. Strike four. (We must be playing cricket now.)

Quote:

That's a whole lot of things right for a simple geometrical procedure with emphasis on the Golden Section.

Two right, five wrong. Since you said yourself you are scaling something up in the CAD system, once again, it would impossible to get all of teh numbers wrong. Not impressed.

Originally Posted by Jiri

How so? I specified exactly how my layout matches Petrie's plan, where it can be considered exact, and where it's lacking. If you can point me to a better reconstruction from a clean slate than mine, please do so.

And here you are admitting it doesn't match up.

Quote:

I think that you should agree that the reconstruction of the third pyramid in the layout is indeed exact. So is one diagonal of the second pyramid. The Great Pyramid in the same reconstruction will be precisely positioned by its N.E. corner, but its sides will be over six inches shorter. Its center will fall three inches from Petrie's plan. The second pyramid's center will be five inches off. All these results are sufficiently close to the plan considering the scale of Giza to be considered right on.

One diagonal correct, both center and all sides wrong. Still not impressed.

Quote:

The reconstruction is a simple procedure, and gives the best results, so far. That is despite the fact that the reconstruction is not yet complete, because it doesn't give the size of the second pyramid. There is one Golden Section idea, which takes this size to within 22 inches overlap by the original, not close enough for me, although I see reconstructions out there being out by whole cubits and still suggesting that they reflect the original plan by the ancient Egyptians. In comparison, my reconstruction is so close to reality, an idea suggests itself that the original Egyptian plan was the same, as my reconstruction.

Way off. Now I am even less impressed.

[Jiri]

So wollery wins

Roos arise, court dismissed.

[wollery]

Originally Posted by Hokulele

One right, one wrong. Strike four. (We must be playing cricket now.)

There are no strikes in cricket, those would be dot balls, or wickets, or wides, or no balls, depending on which side you were referring to.

And always remember, there's no point to cricket, but there is a silly point.

[Jiri]

Wollery, you have an amusing way of counting. A discrepancy of an inch out of 4,153.6 inches is negligible indeed. It is a plus for me, hombre, not for you. It is not nice trying to rustle points.
A difference of over six inches for the big pyramid is also within the tolerance limit, other than yours&comp. Between the initial exact concept, and eventual reconstruction intervenes construction, and Petrie's measurements. Plus time, of course. Yet, Petrie's plan, and my reconstruction are virtually identical. Highly indicative of ancient pre-existence of my reconstruction.
Then there is also the fact that you would expect the Egyptians to treat Giza as sacred grounds. Therefore, the architecture reflects the fact. The golden section is suitable for sacred architecture. That's why Golden Section dominates my reconstruction. Nothing else works.

[Hokulele]

Originally Posted by Jiri

A discrepancy of an inch out of 4,153.6 inches is negligible indeed.

This one sentence proves perfectly that you have no idea at all what are the roles of precision and accuracy in design/construction.

[wollery]

Oh, don't misunderstand me, I'm not saying that your basic thesis is wrong. The Ancient Egyptians may well have planned all of Giza to a golden ratio plan, I have no idea. What I'm saying is that your method of exploring this thesis sucks. It doesn't stand scrutiny. At best it's pure speculation.

[JonnyFive]

Originally Posted by wollery

Oh, don't misunderstand me, I'm not saying that your basic thesis is wrong. The Ancient Egyptians may well have planned all of Giza to a golden ratio plan, I have no idea. What I'm saying is that your method of exploring this thesis sucks. It doesn't stand scrutiny. At best it's pure speculation.

This.

There are a lot of issues with your constructions, many of which stem from the sources you've been using. The same problem was present in your analysis of various carvings using low-res scans of worn, eroded figures. By the way, since a lot of people mention precision vs. accuracy, let me explain simply.

In mathematical analysis, the accuracy is the amount of correctness to an approximation. Basically, the closer your approximation is to the actual answer, the more accurate it is.

Precision, on the other hand, refers to the level of correctness that can be expected to be expressed by an approximation. The distinction is kind of nuanced (and if English is not your first language or you lack a mathematical background, it may sound like the two concepts are the same), but you can think of precision as being a sort of boundary of how accurate a given approximation can be.

So, if you have a method that approximates a value to within +/- 0.5, and one that does it to within +/- 0.005, then the second method is more precise. You can be more sure that your approximation is accurate with the second method. However, with either method you can't be sure of the level of accuracy beyond the level of precision.

When it comes to graphical analysis, this is important because your choice of source may limit your precision - limit your ability to make accurate estimates to within a certain amount. For example, if you have a source image with very fuzzy lines, or where the scale is very big but the image resolution is low, you can't say that you have a high level of precision, because you can't be sure that your approximations are, in fact, accurate.

If you want to be fair in your analysis, you need to account for the potential error due to lack of precision. From what I've read of your graphical plots, you don't do this. You use some really low-res source images, and you don't ever say "well, it could be within this range." Rather, you choose to assume it is a certain value.

Do you see the problem here?

Also, please learn to use the quote feature on this message board. It is not difficult and would make your posts much easier to read.

[Jiri]

Originally Posted by Jiri

The reconstruction deals with exact ideas above all. The architects planned Giza according to exact ideas, and the builders built Giza with great precision in adhering to those ideas, and specifications, so that the result accurately reflects the underlying exact ideas.

Quoting myself from an earlier post, because the quote shows a basic understanding of what you expound on. Not that your words are wasted, mind you.
Right now, I am a little busy, plus, I found another simplification, which makes things even better, and more interesting. Funny thing again, ideas of others seem to integrate with my concept and the Giza plan more accurately than into their own.

[wollery]

Jiri, the bottom line is that your idea is unprovable.

You could reconstruct Giza with extreme accuracy and precision, and show that it fits into a golden ratio scheme, and you will still have proven nothing. Except that it's possible to fit it into a golden ratio scheme. It doesn't prove that that was how the Egyptians planned it, let alone that they even knew about the golden ratio.

And this is your biggest problem. What you are doing is, ultimately, a waste of time. The only way to prove that the Egyptians knew about the golden ratio, or that they used it in the planning of Giza, is to find a contemporary account that says that that's what they did. An architect's plan with a notation that says, "Here's where we use the golden ratio". An historian or scribe noting that they measured out distances from one pyramid to the next, carefully noting diagonals as they did it would be a start, but not proof.

There is no proof that you idea is correct. None. And no amount of reproducing floor plans on your part will change that, even if your floor plans were 100% accurate, which they aren't, it would still be mere speculation.

[jimbob]

Originally Posted by Gravy

Jiri, I understand your frustration at the hostile reception to your ideas. It's well-established that some members here are shills for Big Maths and Big Sanity.

Johnny Five, Wollery and Hokulele are shills for "Big Sanity"....

Those three are especially prominent on this page...
Nominated

[jsfisher]

Originally Posted by wollery

...An architect's plan with a notation that says, "Here's where we use the golden ratio"...

The total lack of such evidence is compelling. The only (I repeat, only) credible conclusion is that it must have been the result of aliens. Yep, aliens. Aliens with a chief spokesman who looked incredibly like Edward G. Robinson. They encrypted the advanced Mathematics into the ancient artwork. Sort of an inside joke, I guess, but it just goes to show yet again, the Jews did it.

Fortunately, Charleton somebody or other led them away from Egypt before they could cause too much more mischief.

[Jiri]

Can't delete duplicate message.. So, I use this space to put some perspective on how big the biggest miss in my reconstruction is. Make a map of Giza according to Petrie, so it is nine meters tall. The biggest fault presently in the reconstruction is 3.94 inches. That is about one nine-thousandth of the total 35,713 inches for the S.N. distance between the outside pyramid edges. So, on our map on the wall, which is nine meters tall, this fault would become one millimeter. I'll let you decide if this is close, or not.

[Jiri]

Nice uncompromising statement Wollery! So, you declare circumstantial evidence worthless. But, is circumstantial evidence worthless? Certainly not, because even if it cannot be considered perfect proof, it carries enough weight to cast doubt on, and invalidate any conclusions to the contrary. Whether proof or not, the fact is that the Golden Section clock-work is inherent in the Giza arrangement. It is true. In combination with other data on design characteristics we have of Egyptian architecture, circumstantial evidence may become so overbearing that the only rational conclusion will be that Egyptians had knowledge of the Golden Section, and used it in sacred architecture.

[jsfisher]

Originally Posted by Jiri

Nice uncompromising statement Wollery! So, you declare circumstantial evidence worthless. But, is circumstantial evidence worthless?

Perhaps a better question, Jiri, is how would you protect against confirmation bias?

[wollery]

Originally Posted by Jiri

Nice uncompromising statement Wollery! So, you declare circumstantial evidence worthless. But, is circumstantial evidence worthless? Certainly not, because even if it cannot be considered perfect proof, it carries enough weight to cast doubt on, and invalidate any conclusions to the contrary. Whether proof or not, the fact is that the Golden Section clock-work is inherent in the Giza arrangement. It is true. In combination with other data on design characteristics we have of Egyptian architecture, circumstantial evidence may become so overbearing that the only rational conclusion will be that Egyptians had knowledge of the Golden Section, and used it in sacred architecture.

Reread what I said, but try to remove the paranoia and confirmation bias before you do.

[Jiri]

Originally Posted by JSFISHER

Perhaps a better question, Jiri, is how would you protect against confirmation bias?

Thanks for asking, but no need to protect against my powerful confirmation bias, because it has been amply satisfied by all this confirmation I've been getting.
I've had so much confirmation lately that I decided to spare you of some, knowing it is an irritant to you.

[jsfisher]

Originally Posted by Jiri

Thanks for asking, but no need to protect against my powerful confirmation bias, because it has been amply satisfied by all this confirmation I've been getting.
I've had so much confirmation lately that I decided to spare you of some, knowing it is an irritant to you.

Yes, excellent approach. Flippancy will protect any pursuit for knowledge from confirmation bias.

[JonnyFive]

Originally Posted by Jiri

Thanks for asking, but no need to protect against my powerful confirmation bias, because it has been amply satisfied by all this confirmation I've been getting.
I've had so much confirmation lately that I decided to spare you of some, knowing it is an irritant to you.

Do you know what confirmation bias is? If you're serious about any of the stuff your doing rather than, pardon the expression, simply blowing smoke up our asses, then you really need to do more to outline how you're ensuring that your methods are objective. For one thing, you should really consider improving the quality of your source data. There are a bunch of other things you could do as well, but that would be a start.

Anyhow, you don't need to be so flippant towards the people responding to you. Jsfisher has been polite to you and has accomodated you to a great degree - I don't see why you have say things like that to him (unless you genuinely misunderstand what confirmation bias is, in which case I apologize).

And, as wollery said, ultimately you aren't really proving your hypothesis, even with the best data and the most meticulous methodology. At best all you could prove was that, if the Egyptians wanted to plan their pyramids according to a golden ratio scheme of some kind, that they succeeded.

If you want to prove their intent, you'll need to do some research into the records available from the time. Learning to read hieroglyphics would be a good start, rather than diddling around with geometry.

[Jiri]

Originally Posted by JonnyFive

..you really need to do more to outline how you're ensuring that your methods are objective. For one thing, you should really consider improving the quality of your source data.

Holey Schmoe, Jonny, please, don't tell me that you don't know that I have simply fed Petrie's measurements into a CAD drawing. You can't do better than that unless you get a project under way, whereby Giza gets remeasured to the best of today's capabilities. Petrie's measurements have been repeatedly confirmed as solid. The point is that even best effort at remeasurement will introduce rather insignificant changes. But why am I telling you this? You knew it anyway. Still you said the above, which then strikes me as highly disingenuous.

Originally Posted by JonnyFive

Anyhow, you don't need to be so flippant towards the people responding to you. Jsfisher has been polite to you and has accomodated you to a great degree - I don't see why you have say things like that to him (unless you genuinely misunderstand what confirmation bias is, in which case I apologize).

JSF is a polite man, and so am I. He hasn't said anything more concrete than 'Aliens did it' this far. I didn't get offended, did I? I could have become Alienated, and retort that JSF and some other participants in this discussion know a certain mathematical tidbit, specifically, how to construct a regular pentagram using only thirteen geometrical steps, which it is quite impossible to learn from existing sources. It is a fact that the only source on the Internet today for this method is a prehistoric monkey - the Nazca monkey. It has taught me, and I taught it to you, while refining my method by also learning from JSF's technique. The moral is that learning any mathematics from a monkey is as noteworthy as learning it from an Alien.
JSF has since said that there are other methods of how to do the same in as many steps. Where are they? No one here was able to produce any. Anyway, no offense, JSF.
,
No, I don't misunderstand the confirmation bias concept. Perhaps, you don't understand that what I am doing is unavoidable. I have to look for confirmation. Without confirmation, there would be no point in carrying on. The issue is something else, it is in the quality of confirmation. Here is why I meant no offense, when I mentioned that there is indeed a lot of stuff, which serves to confirm my concept.
What is my concept? It is exploration within the framework of the Pyramid Square. It is this concept, which enables one to make observations of regularities, which encourage the hypothesis of a Grand Plan of Giza derived by an exact method starting from a clean slate.
There is only one thing, which may defend the concept - success! In this case, success is evident from the exactitude, with which even ideas of others integrate into the concept. Those ideas had until then existed as mere inexactitudes. Success is also evident from the accuracy of the final result, whereby your scaled up plan of Giza is superimposed over the existing plan of Giza. Do the two correspond significantly? Check the report, I say they do.
If your CAD drawing produces spectacular exactitudes, are you supposed to not notice those as a positive? There is one such exactitude, which serves as strong confirmation for the concept, but is missing in my report, because I only discovered it today:
As soon as you complete the first stage of reconstruction by inserting the two initial golden rectangles into the Pyramid Square, you can learn that Petrie's overall width between the pyramids at 45 degrees (counterclockwise) equals the distance from the top side of your rectangles to the horizontal axis of the Second Pyramid. How close is this?
0.94383844.. of an inch. Petrie would say that it is where it's supposed to be, considering his own fault tolerance limit. So, what about it? Is finding and citing a fact like this just excercising one's confirmation bias, or is it something more? Well, whatever it is, it is spectacularly precise.

Quote:

..ultimately you aren't really proving your hypothesis, even with the best data and the most meticulous methodology. At best all you could prove was that, if the Egyptians wanted to plan their pyramids according to a golden ratio scheme of some kind, that they succeeded.

That is good enough for me. Anyway, here is a diagram for the stuff I mentioned above. It shows also one other interesting instance of exactitude. If you do Vesica Pisces with a circle expressing the 45 degree width of the pyramids starting from the Third Pyramid's diagonal then the third and fourth circles intersect just 0.31 inch from the diagonal 'd' of the Second pyramid.
Note both the above described phenomena involve the width between the pyramids, a show of consistency. Or is it confirmation bias? By the way, the main idea of the diagram is that the central axis of the 45 degree width between the pyramids is also one of the second Pyramid's diagonals. This is a well known idea among explorers. How well does it work in my reconstruction? It works to a a half of an inch..

[wollery]

Originally Posted by Jiri

Anyway, here is a diagram for the stuff I mentioned above. It shows also one other interesting instance of exactitude. If you do Vesica Pisces with a circle expressing the 45 degree width of the pyramids starting from the Third Pyramid's diagonal then the third and fourth circles intersect just 0.31 inch from the diagonal 'd' of the Second pyramid.
Note both the above described phenomena involve the width between the pyramids, a show of consistency. Or is it confirmation bias? By the way, the main idea of the diagram is that the central axis of the 45 degree width between the pyramids is also one of the second Pyramid's diagonals. This is a well known idea among explorers. How well does it work in my reconstruction? It works to a a half of an inch..

http://forums.randi.org/imagehosting...8f49ab8a17.gif

Okay, I seem to remember doing something similar with one of your previous drawings, but here we go again.

The 1st and 3rd circles are not at the same spacing as the 2nd and 4th circles, which renders the "accuracy" of the diagonal agreement between the pyramid and the intersection of the 3rd and 4th circles rather moot.

None of the rectangles have the golden ratio, although two are close to 1 decimal place.

[Jiri]

You are relying on low-res bitmap images. In the CAD drawing everything works exactly as I said it does. You have a perfectly good opportunity to make the same CAD drawing from Petrie's specs, and then see for yourself. If I say that some distance is 0.36408664.. then in your reproduction this reading should be exactly the same, if you follow my instructions. That's all I can do for you.

[Hokulele]

45 degrees is not a width measurement.


ETA: Unless you are claiming the Egyptians were using transits.