34 Ways to calculate the Royal Cubit

Updated versions of the different ways of approximating the cubit. Also includes separate table for Grand Metre (1 plus royal cubit) == 1.5236…. == 1.524.

These are done with pi, phi, e, roots and powers (usually of basic primes), as well as ln, log, sin, cos and tan.

See square roots, cube roots and ln(4) for formulas not shown below.

Changelog at the bottom.See also The Magical Mystical Royal Cubit for the Pretty Picture version.

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The Spooky Stuff

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.

Changelog:
2018-11-29: added Spooky Stuff 7 and 8
2018-12-03: added Spooky Stuff 9
2018-12-04: added Spooky Stuff 10
2019-04-24: added Spooky Stuff 11

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:

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The royal cubit and the stars

There are still some things that bother me about the Royal Cubit, in particular, why did they choose π/6, and why did they use it in preference to the metre.

Something interesting related to the first question has surfaced. Which may just be another random co-incidence like all the others, or maybe not.

First up, a reminder that the Royal Cubit is ⅙ of the circumference of a circle with diameter 1 metre, in other words the arc on a 360/6 = 60° segment, as follows:

Circle, 60 degrees, royal cubit

As you may know, the ancient Egyptians were very fond of their ankh, which looks like this:

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Playing with numbers

Playing around with the great pyramid.

Length of base + height = 440 + 280 = 720 royal cubits.

720/360 = 2 (save this for later)

If we convert to digits by multiplying by 28 (because 28 digits in royal cubit), we get

720 x 28 = 20160

If we divide by 360, we get

20160/360 = 56, which is the number of digits in 2 cubits (see saved value of 2)

As you may know, I’m developing a theory that whoever came up with the cubit system also divided the circle into 336 Zeps. So if we divide by 336 instead….

20160 / 336 = 60

Which is um, all sorts of things, and maybe a hat-tip (or the finger) to the Sumerians and their sexagesimal system.

But what the 60 also equates to, is if you had a wheel of radius 1 metre, then 60 rolls of the wheel would equal the sum of the side and the height.

If your wheel had a diameter of 1 metre (like a chariot), then it would be 120 turns of the wheel. Exactly.

Another large link to the metre

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.

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Poly wants a cracker

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.

Changes:
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.

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Introducing the Zep

[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.

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Inching along

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.

pi and e inch formula