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


Sans Forgetica

The clever people at RMIT University have come up with a font that is specifically designed to help you study … by making your brain work harder when reading.

They achieve this by slanting the text slightly left, and leaving our parts of the letters, forcing the brain to fill in the gaps.

The alphabet looks like this:

Sans Forgetica font

Only the regular weight is available for now, and you can download Sans Forgetica font here

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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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Natural faces

Nature sometimes plays interesting tricks. Perhaps you have heard of the face on Mars, or at least The Man in the Moon.

Back down on earth, there is a curious feature in Canada known as the Badlands Guardian, which, seen from far out in space, looks like an indigenous face:

Badlands Guardian

Well, not to be outdone, we down here in Sunny South Africa have our own version, also an indigenous face, seen from space:

Southern Africa indigenous face

If you’re having trouble spotting it, here’s a cut-out:

Face cut-out.

I guess we can dub this The Guardian of the Cape.

And yes, a little to the right of the neck in the bigger picture, is the mask from Scream ….

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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Rethinking English, part 1

It is well known that English is a mess, mostly because of it’s diversified history, and the diverse people who have overrun England, coupled with the diverse peoples that the English have overrun.

The mess creates problems for kids growing up English and trying to learn the language, as well as people coming from other language and writing backgrounds. There is just so much that is inconsistent and does not make sense.

Some random examples:

1. 1 cow, 2 cows, 1 bull, 2 bulls, 1 ox, 2 oxen
2. 1 ram, 2 rams, 1 ewe, 2 ewes, 1 sheep, 2 sheep.
3. 1 shark, 2 sharks, 1 fish, 2 fish.
4. 1 rat, 2 rats, 1 mouse, 2 mice, 1 house, 2 houses.
5. 1 elephant, 2 elephants, 1 hippopotamus, 2 hippopotami.
6. same word, two meanings, e.g. stick, box, cleave.
7. same word, different tense depending on pronunciation: read.
8. same word, different meanings depending on pronunciation: minute.
9. concatenation vs. possession: it’s Jack’s.
10. same letters, different pronunciations: I thought it was tough, though.
11. silent letters: gnome, knife, herb. (but not as bad as French.)
12. stationary / stationery (etc…)

I could go on but you get the point. But before we even get to vocabulary and grammar, we need to deal with the alphabet.

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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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