MJ:

I didn't realize you were concerned about decimal inches...I had the impression from previous posts that you never stressed such measures.
One thing I didn't mention regarding AutoCAD...you can decide to what accuracy the measures are taken...up to eight decimal places...but that's a ridiculous accuracy for measuring hand cut stone blocks...don't you think?
I selected the closest inch...as the results indicate.

Well...I gave these measures some thought and since Petrie always adds his +/- decimal inches then I thought why not forget about this precision because it's no more than slicing hairs and that's not the intent since it's impossible to build to that accuracy.
So...I then thought +/- several inches per thousand would not be too bad considering the computations required for construction. That's what Petrie had to face, but he was determined to calculate to the closest decimal of an inch...a stubborn man…yet he succeeded.

As you have confirmed...my measures look satisfactory to me. You don’t get away free on this one…I've added some discrepancies of yours, however, I will not make such a bold statement as this...

"...the measurements that produce your imaginary slope of 4139” are mostly incorrect..."

> Starting at the left side of your drawing:
> 1693 - 1691.6...(Petrie 1693.7-1694.6 after adding wear of step)
> 35 - 35.1...identical
> 1628 - 1627.9...identical
> 681 - 679.7...add to the measure below (681+172) = 853
> 172 - 173 to 173.4...yours added to above (679.7+173.4) = 853.1...identical
> 1390 - 1389.5...identical
> 4534 - 4537.2...east side divided by 2 = 9067.7/2 = 4533.6...mine correct
> 1517 - 1519.8...see the next measure.
> 524 - 525.6 to 527...Petrie 524.1...don't recognize yours. It's probably the reason why yours above is also different. Distance "along" the descending passage should be 1110 inches
> 668 - 668.2...identical.

> Your slope is: vertical = 1693 – 668 = 1025;
> horizontal = 4534 – 524 = 4010; slope therefore
> 4138.9

Correct.

> By Petrie’s measurements: vertical = 1691.6” –
> 668.2 = 1023.4; horizontal = 4537.2” – 525.6 to
> 527 = 4010.2 to 4011.6; slope therefore 4138.7 to
> 4140”.

Incorrect.

> Now, as Jon_B has already rightly pointed out...

You don't need Jon ...I have been stating that fact from the start. Soooo...what's the issue MJ..?

> But if they are for use in a theory about the
> significance of certain measurements, then one
> runs immediately into complications.

No you don't, because the average mathematician works on tolerances otherwise you are fooling yourself.
I've worked on the finest of equipment with their base frames cut to +/- 1/2" yet other aspects of the machine are critical and measured to the closest 1/2 tho.
Practicality is the word...not precision. There is no way any builder of monuments of this magnitude can dictate the accuracy you are calling for. That is also true of the KC...there are too many variations in measure to dictate which one is correct.

> The length of the Descending Passage floor is
> 4148”.

Nope...I told you before...Produce all of the man's calculations, similar to what you have asked from me, then we will determine why the 8" discrepancy...if it exists.
If you cannot produce that information then it is a pointless situation that you are creating...it's a rubber duck...it's all yours and you can play with it as long as you wish...!

> just consider...undoubtedly have recorded the correct measurement of 4148”..."

No he wouldn't because Petrie allowed for the rubble and stated a +/- 3" to compensate...but you are stating it is 8" longer +/- nothing...!

> Now, is there any significance in these two
> measurements being, within 8”, the same length?

MJ:
They are both approximately 4140" and there is a reason for this value, but...I told you that first things first. I show you the simple correlations then we work toward the part that requires some thinking.

> Well, with the entrance to the top of the face of
> the Great Step measurement we have a 90deg
> triangle: height 1023.4”, base 4010.9” ± 0.7”,
> hypotenuse 4139.4” ± 0.6”.

> If the intent was for a slope measuring 4139.4”,
> then what was the other determining factor?

MJ:
Make it simple for all to read...it's 4139 and 4140...no decimals.

> Was it the height @ 1023.4”, or was it the
> horizontal length @ 4010.9”?

Neither.


> And in both cases, how were the vertical and
> horizontal dimensions of the upper Descending
> Passage, Ascending Passage, Grand Gallery and
> Great Step each fitted in?

They lead you to finer details within the design. You have witnessed the "imaginary" line as you call it...you needed intelligence and imagination to discover it...there are lots more hidden within these passages. Think...why are two of the three chambers offset from the center of the pyramid? Why is one formed from bedrock, one comprised of limestone and one of granite?
You may recall and I'll say it again...if you lack understanding the total pyramid site then you will never understand their interior.


> Or could it be that the determining factor was the
> gradient (seked) of the slope?

Believe me...the designers of this structure cared less about rudimentary sekeds.

> But, then, even this does not explain how the
> Descending Passage, etc., were fitted into the
> triangle.

Big puzzle isn't it? Big story goes with it.

> Another possibility is that the vertical and
> horizontal locations of the entrance and the Great
> Step were the determining factors – but how did
> they get to be where they are?

About six months ago I posted one reason why the entrance is at this height...there is one more, but you would never believe it...Don Barone would...but you and most others wouldn't.

> The point is, one cannot say that there is
> significance in the Descending Passage floor
> length (regardless of the 8” difference) being
> almost the same as the imaginary
> entrance-to-Great-Step sloping line without
> explaining the vertical and horizontal
> measurements of and associated with the upper
> passages and the Great Step.

Actually...the passages and chambers relate to astronomy...the "imaginary triangle" relate to higher math and also astronomy.
But do not rule out the sub passages...they also have an important contribution to the design.
Perhaps you can now realize why one drawing with all information included would be mind-boggling to analyze. Every aspect of this structure is an intentional design feature...they didn't miss a single trick...and never overlook what others have. I erred by assuming Petrie's assumed measures of the Grotto to be close enough...bad...bad...egg on my face...it’s embarrassing…!

Best.
Clive