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:

1. We start with the metre. Don’t ask how they knew this length, researchers don’t know how, but accept that they knew it. So 1 metre = 100 cm.

2. Now we add the royal cubit, which is derived from a circle with diameter of 1 metre. That gives a circumference of 3.14159265 metres, which gets divided by 6, giving the Royal Cubit length of 0.523599 metres. We add this to the metre, giving a total length of 152.3599 cm.

3. Now we scale this in the ratio of 6/5. A hexagram has six sides, a pentagram five sides, and we can also draw the so-called Seal of Solomon (5-pointed star) in the pentagram, and the so-called Seal of David (6-pointed star aka Star of David) in the hexagon. These shapes appear to have had special meaning. So we scale 152.3599  by 6/5, which gives 182.8319 cm (which is basically 6 foot imperial)

4. Now the difference between this number, and the metre-plus-cubit, is 182.8319  – 152.3599 = 30.472 cm.

5. 30.472 cm converted to inches (30.472/2.54) = 11.9969 inches == 12 inches == 1 foot.

6. Another way of looking at it is that 1 foot = 1/5 of meter+cubit.

Metre, cubit and foot


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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The Irrational Mathematicians of Giza, Part 1

Changelog is at end of part 3.

The Giza plateau is one of the most studied places on Earth, while curiously some parts remain off-limits and unexplored. Various people have studied both the pyramids themselves, and the layout of the site, in great detail, which led to various different ideas about the site plan, which are summarised/detailed here:

1. The Orion alignment:
2. The Cygnus alignment:
3. A possible method of how it was planned:
4. Another way of drawing the site:
5. Another analysis:
6. Online book with analysis:
7. Edward Nightingale’s analysis:
8. Golden ratios on the site plan:
9. [placeholder for another site with lots of maths, can’t find at the moment.]

I’ve done some analysis of my own, kicked off by looking for phi circles/arcs, which I learned about when I watched a documentary about the Nebra disc…

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The curious alignments of ancient monuments, part 1

While playing around and researching things, I came across a curious alignment of two sites. The first is the pyramids at Giza, the second is Göbekli Tepe in Turkey. Currently Göbekli Tepe is the oldest megalithic site discovered, and its discovery forced historians  to rewrite the history books and rethink their timeline for civilization. The site dates back to around 9000 BCE, which is long before the copper, bronze or iron ages, which would have provided some tools needed for building the monuments.

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