No body parts were harmed producing this post

[Note: the formulas below have been superseded by Cubit parts and more, updated ]

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.

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Egyptians being annoying again

Was playing around with the calculator, still exploring exactly what that kink in the alignment of the three pyramids is.

The great pyramid has a designed height of 280 cubits.

The second pyramid has a designed height of 274 cubits.

That’s a difference of 6 cubits. Which is not very interesting until we turn that difference into metres (and you may guess where this is going …)

6 cubits = 6 x π/6 metres = π metres = 3.1415926+ metres ….

Am still pondering difference in height to the third pyramid …. nothing jumping out like π at the moment….

Stonehenge and the Golden Ratio

So as I’m watching the video referenced in Metre, cubit, foot, megalithic yard, (https://www.youtube.com/watch?v=33dKFtCXEFA), and this image pops up on the screen:

Stonehenge 1

Which is a view of how the first version of Stonehenge looked. And I say, “Hang on a mo, that looks familiar …. ” and indeed it is … that’s the same arc from the Nebra Sky disc:

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Metre, cubit, foot, megalithic yard …..

So I’m watching a video on megalithic building, and they introduce the concept of a megalithic yard:

The length was apparently found via careful measurement of existing structures, as well as finding cross-referenced methods using astronomical means.

They claim it to be 2.72 feet or 0.83m, although the Wikipedia editors generally are sceptical of the whole idea.

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.

Another way of getting the cubit

[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 minutes 56 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.

Now we do this sum.

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The Irrational Mathematicians of Giza, Part 4

(continues from Part 1, Part 2 and Part 3)

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.

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The Irrational Mathematicians of Giza, Part 3

Continues from Part 1 and Part 2.

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.

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The origin of the foot

The Nebra disc video (see The Irrational Mathematicians of Giza) points out that not only does the disc encode the metre, but also the inch. Which is of course rather disturbing, as the disc is thousands of years old and predates the Romans, from where the Brits got the inch.

So I’ve stumbled across the origin of the foot, and it dates all the way back to Ancient Egypt. This also might explain the whole concept of “pyramid inches” which some researchers came up when measuring things in the Great Pyramid.

The maths works like this:

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The Irrational Mathematicians of Giza, Part 2

In Part 1 we dealt with numbers and ratios that were not unknown in the ancient world, even if we still think it was the Greeks that invented π and φ and the whole Pythagoras theorem etc.

Now we introduce ℯ (2.71828…), the base of the natural logarithm, which is defined as the limit of (1 + 1/n)n  as n approaches infinity. There is no evidence that the Egyptians knew of this number, but here it is:

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