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.

Continue reading

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.

Continue reading

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.

Continue reading

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:

Continue reading

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:

Continue reading

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…

Continue reading

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.

Continue reading