Trigonometry and Pyramids

Ravnatelj raises an interesting question about my measurements of the equilateral triangle. I’ve measured the tops as though they’re on a plane rather than in 3D space. Does that make a difference? It might. It’s a planar problem because there are only three points but the plane is inclined to the horizontal and that could make a difference.

There’s probably an elegant way to find out, but I’ve used plain number crunching. Using the map supplied from the official site, I can see that the Pyramid of the Dragon and the Pyramid of the Moon are both, to within a few metres 660 metres above sea level. So by measuring that distance that gives me the length of the side of the triangle, which is about 2,250 metres.

Now when I measure the distance between the Pyramid of the Moon and the Pyramid of the Sun I only get a distance of about 2,060 metres. Ravnatelj points out that the Pyramid of the Sun is higher, so you’d expect this distance to be shorter. Below is a diagram which shows that the discrepancy is due to the height. We can therefore work out the height of the Pyramid of the Sun using Pythagoras’ Theorem.

(distance)² = (base)² + (height)²

so (distance)² – (base2) = (height)²

(2,250)² – (2,060)² = (height)²

5062500 – 4243600 = (height)²

818900 = (height)²

therefore height = 904 metres.

That would not be 904 metres above sea level, that’s 904 metres above the Pyramids of the Moon and the Dragon that we used for the baseline. This puts the top of the Pyramid of the Sun at 1564m above sea level. The height on the map is 767 metres above sea level which is only 100 metres higher than the Pyramid of the Moon.

This will have taken an hour’s work to write up and check and check again because I didn’t expect the result to be that bad. This is why I think I could be wrong about how I’ve done my calculations. I don’t mind the time spent, no-one’s forced me to do it. I thought it was an interesting question because the difference was only 10% so I thought that perhaps Ravnatelj could be on to something. But as it turns out the official line is so badly wrong then why, when the next claim comes out, should I be interested in checking?

Further if the figure had created an equilateral triangle would that have been significant? There’s something missing from this triangle. What about the Pyramid of the Earth? It seems to have been dropped because it doesn’t fit the desired result. I can’t find any reason why a dragon is more geometrically important than the Earth. Sometimes not every does fit into a unified grid, but if you’re going to make those sort of claims you have to explain why that doesn’t matter if you want to be convincing.

Archaeology Magazine now has a page on the topic.

Previous entries on this are:
Bosnian Pyramid
The Price of a Pyramid
and the inaccurately named Final Thoughts on Bosnian Pyramid.
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