To borrow a phrase from Robert Bauval, this falls under the Spooky Stuff category.
It is a very strange connection between the Grand Metre (1 + royal cubit), the base of the natural logarithm ⅇ, and the royal cubit as measured in inches.
Royal cubit, e and inch
I have no explanation for this. It just highlights again the ancient origins of the metre, inch and royal cubit, and how they mysteriously link together with π and ⅇ. But what about φ you ask?…. here you go:
It is the mainstream academic consensus that ancient people based their measurements on body parts. As discussed in Some thoughts on the cubit (and foot) , I don’t think that’s necessarily so, despite at least two (the Persian and Roman feet) at one point being based on the length of the foot of their leader (or his over-sized statue).
I still think the names that these measurements became known as (cubit, foot, palm, etc) were backnyms to create a easy-to-use-and-remember name for a length.
Even something simple like measuring the width of a hand is not exact because fingers move, flesh compresses, etc., and fingers are not all the same width.
So… here’s a little exercise to show that we can get the same list of parts of the cubit just with maths. In some cases two different methods produce values on either side of the target.
The nautical mile has a chequered history. The basic idea was to have it set to one degree of arc of the circumference, but that depends on what latitude you are at. You can read Wiki’s take for some background.
Anyway, yes, that royal cubit can be related to a good approximation of the nautical mile, given that the exact definition has varied over time. It’s currently “defined” at 1852 metres.
Be that as it may… I just found the correlation between this 0.83 metre (or 0.8296 if you want to be more precise), and the sum of the cubit + foot of 0.8319m (they’re both 0.83 if you work to two decimals) as discussed on the Origin of the Foot page, to be rather curious.
The close similarity is hard to ignore, and cubit+foot may make a more compelling origin argument than arguing for a circle divided into 366 degrees instead of 360.
[Note: I’m not entirely convinced that my “average year” calculations are correct. I was looking for a way to get 364.75 and since it is tantalizingly close to 365.25 I was looking for a way to get there from that. It may be better to just use 365.25 – 0.5 … now need a Reason Why.]
I was playing around with the calculator and stumbled across this curious sum.
Let’s start with how long a year is. As you should know, it’s 365.25 days for a solar year. If however, we measure against the background stars, it’s about 364.25 days.
From Wikipedia: “Both the stellar day and the sidereal day are shorter than the mean solar day by about 3 minutes56 seconds. ”
If we take those 3 minutes 56 seconds == 236 seconds, and work out the difference over a year (x 365), we get 86140 seconds, which is 23.927777 hours, effectively one day.
So if we take the average of a solar year and stellar year, we get (365.25 + 364.25)/2 which is 364.75 days, or more precisely, 364.7436921 days.
When I started this exercise I was hoping to find “interesting” alignments between the centres of the three pyramids, in part to explain the curious “kink”. So in that regard I failed spectacularly (so far).
What I did find was a whole host of other interesting alignments. The table below summarizes the best ones, those that are within 0.5° of the correct angle.
The first two parts dealt with more important mathematical constants, and or otherwise interesting alignments. This part has “the rest”, which are either not so important mathematically (well, in terms of what we expect the pyramid builders to know) or less-accurate alignments, but are posted here “for the record’. There is minimal exposition.