The original **architectural **base-breadth was 9131.05 inches
…9131,05
- 9130.8
…0.25 inches = 0.635 cm
Um, ok. I still don’t get it. What’s so special about 0.25 inches?
Where in the book does Flinders Petrie say this?
It’s not the length, but the girth…so to speak…
-XT
I don’t want to bother you, sorry!
Peace be with you!
Noooo! Now I’ll never know!
Let’s go through this again. I had to check your measurements, so I checked this thing called “The Internets” and lo and behold, found the actual height and length:
Height (including capstone): 480.69 feet (5768 inches)
Your measurement is off by 45 inches.
Length of Grand Gallery: 156.9 ft (1882.8)
Your measurement is off by an inch
Now:
5768 inches * 1.618033988 = 9,332.820042784
9,332.8200 / 5 = 1,866.5640085568
Riddle me this:
Why take the height of the pyramid and the length of the grand chamber? Why not the width and height of the pyramid? Or, the height of the grand chamber? Or, maybe the hundreds of other possible dimensions of the pyramid?
Most importantly, why the division by 5? If this was truly a mystical number that the Egyptians were after, you’d think they’d make it a bit more obvious. After all, almost all Ancient Greek architecture is in a ratio of phi because the Greeks thought it was an important ratio that denoted true beauty.
Any why measurements in millionths of an inch? Could the Egyptians measure that precisely? If they could, then why aren’t the lengths of the sides off by almost half a foot?
Since your measurements are off, and then in an accuracy that’s almost impossible today, it appears that someone fudged the data to get what they want.
The person who came up with this looked at all the various measurements of the pyramid looking for phi, but the best they could come up with was the height of the pyramid and the length of the great chamber, but only if they first divided the height by five.
That came close, but not quite, so they munged the numbers just a bit. Add a bit of height and make the great chamber just a tad longer, and by almost amazing coincidence, the mystical phi amazingly appears!
That’s sheer proof! And, proof can’t get much more sheer than that!
I guess this probably follows somehow from the continued fraction 1 + 1/(1 + 1/(1 + 1/(1 + … for phi, but I can’t quite see how the argument goes (not that I know exactly what theorem to establish). Can you expand on the argument?
Yeah, well, it makes the baby Julian of Norwich cry, too.
Don’t forget to add the length of the coastline of Britain.
Shall we take the proof that all numbers are interesting as read?
No, I can’t. As a physicist, it’s enough for me to know it works, not necessarily how, and it was a very long time ago indeed that I first encountered it (before college, certainly). But I seem to vaguely recall it being related to the Fibonacci thing, not to the continued fraction (of course, there are probably multiple independent lines of proof for it).
You’ve got me curious now, though, so I’ll do some looking and see if I can turn anything up. IIRC, the context in which I first saw it was that some plants have leaves spaced that way, so as to minimize shading from other leaves.
I like this. It says so much. I think I’ll make a sticky note and attach it to my screen.
OK, I found a good discussion of the use of phi in sampling (this is for the plant leaf context, but it should be generally-applicable). It looks like the first proof of it was by Douady and Couder in 1993 (which was probably after I had first read about it, so apparently it was believed correct before that), and that page does give a non-rigorous argument based on the continued fraction.
Unfortunately, they do tend to mumble a lot. 
This approach is used in certain computerized algorithms for scheduling and hashing.
(I’m not completely sure the following is completely correct, but I’d give myself at least even-money 
)
First note that φ is, in a sense, the “most irrational” of numbers because its continued-fraction approximants converge so slowly.
Unless I am mistaken, the special virtue Chronos speaks of can be considered to have two components: A virtue when the number of points is smallish, and a virtue when the number of points is largish.
The virtuousness of φ for the few-point case obtains in part, I think, because it is the Golden Mean. The virtuousness of φ for the many-point case obtains, I think, because it is so “very irrational.”
You can verify this fact with simple experimentation using, for example,
0.610000 (a rational approximation to the Golden Mean)
and
0.723607 = .5+sqrt(5)/10 (“very irrational” number, not the G.M.)
With ten points, the first number outperforms the second; with a hundred points, this is reversed.
That φ is both the Golden Mean and very irrational and thus optimizes both virtues for the problem Chronos describes does seem somewhat “magical” if not “mystical”!
I’m having a little difficulty following you, septimus. What do you mean by “number of parts”?
ETA: Ok, I think you mean the number of discrete bins you split [0, 1) into when counting collisions. Is that right?
Yes, although I minimize a segment-length statistic, rather than just “counting collisions,” segment-length being the distance between adjacent selected points. (You must have clicked too soon because the “Edited by septimus” was my changing every “parts” to “points”! I usually ignore the “Reason for edit” box – with my luck, filling in a Reason would cause me to miss the 5-minute window.)
What do you think, was my post clear? Better yet, was it correct? :dubious: