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:
So I’m watching a video from 2012, featuring a young-looking Graham Hancock
Which, before they got all wooshie about the Mayan 21 December 2012 end of the world thing, had some interesting info. In particular, the observation concerning the difference between two sides of the great pyramid, and its height, which goes like this:
two side of pyramid = 440 x 2 cubits. In metres, that’s 460.7669 m.
height of pyramid = 280 cubits = 146.6077 m
Difference = 460.7669 – 146.6077 = 314.1592 which you may recognise as 100 times pi.
Some updates to the zeptractor, probably done for now until I figure out if this was just a humongous waste of time or not. Well at least I got to learn something about svg drawing.
1. added assorted famous regular polygons: triangle, square, pentagon, hexagon, heptagon, octagon, dodecagon.
2. resized inner circle to divide radius in golden ratio. Also marked where circumference would be divided in golden ration (both directions, measuring from zero).
3. added radian marks (up to 6, only in normal direction).
4. added tau divisors … they’re more logical than the pi divisors. Arial has a sucky tau symbol.
5. put phi symbol on bare radius to avoid confusion.
The zeptractor, the tool for people who really know their way around a circle.
[As per usual I’ll probably revise this over time, changelog is at the bottom.]
This post introduces a new way of dividing the circle. We already have the normal 360° method inherited from the Babylonians, as well as the French misguided attempt to use 400 Gradians, and even binary degrees that divide a circle into 256 parts.
As I delve into the Egyptian way of measuring things, it seems possible that they divided the circle into 336 parts, which I will call Zeps (from Zep Tepi, the first times). I don’t think the classical Egyptians used this, but maybe the people from Zep Tepi who most likely built the Great Pyramid, and came up with the cubit and related measures, did. Reasons why I think so will become clearer during this article.
The British/Imperial inch as we know it today has a long and varied history, stretching back to ancient times, as does the foot. Different countries and empires and ages had different values, which you can read about here,here and here.
The inch is currently “defined” at 2.54 cm “exactly”, but there is no record of them measuring any king’s thumb to get that figure, so I’m guessing other factors convinced them to pick that value.
But as it happens, it is probably a good choice, because there’s a nice relationship between the Royal Cubit and the inch, via the Egyptian digit.
If we take, as I believe was the original case, a cubit as being 1/6 of the circumference of a circle with diameter one metre, then a digit will be one 28th of that.
Then we simply multiply by e/2, where e is the base of the natural logarithm.
That gives us 0.0254 m, or one inch.
From the digit to the inch.
We can simplify that down to the following, noting that both 12 and 28 were important numbers to the Egyptians.