More Bosnian Trigonometry
You can read an overiew of some of the other flaws in the Bosnian Pyramid saga at Revise and Dissent in the posting Bosnian Pyramids: Absence of Evidence is not Evidence of Atlantis
Thanks, if that’s the right word, go to Doug Weller for passing along a better map of the equilateral triangle connecting the peaks of the Bosnian pyramids. It turns out that Bosnianpyramids.com is not an official site, so my measurements based on that don’t necessarily disprove the claim that the peaks of the pyramids mark the vertices of a triangle with “not one minute difference”. So I’ve looked at this map.
What I’m interested in is whether or not there are three equal angles. The easiest way for me to check is to measure the lengths of the sides and calculate from there. What I’ve done is put the map into Google Earth, placed it over the ocean, to ensure I’m measuring it flat and measured the three sides. The lengths of the sides will not be accurate, but their relative lengths will because their lengths will all be out by the same factor.
Measuring the three sides I get:
Sun — Moon : 2563
Moon — Dragon : 2638
Dragon — Sun : 2598
If you click on the photos you’ll see those measurements are metres, but in reality that’s misleading because the overlay is almost certainly not scaled correctly. It’s just the relative lengths that matter because the vertical and horizontal scaling will be out by the same factor.
You can work out the angles in degrees for the triangle through the Cosine Rule which will work because it’s independent of units. Alternatively you could use the Triangle Calculator which does the same thing with much less effort. Using this I get angles (converted from decimal degrees to degrees and minutes):
Sun: 61º 29′
Moon: 59º 55′
Dragon: 58º 37′
Is that an equilateral triangle?
If you want to stick with Osmanagić’s claim that there is not a minute difference then the claim doesn’t hold up. However it is quite close. It’s hard to say exactly whether this is evidence on an equilateral triangle or not. My measurements won’t have been precisely over the same points on the map and the map won’t be an exact representation of the measurements, so perhaps this could work if the points of the triangle on the map roughly match the peaks of the pyramids. Do the vertices match the peaks of the pyramids?
What I’ve set up is a file with the triangle map overlay, points marking the Official measurements and suggestions of my own showing where I think the peaks of the hills are more likely to be. You’ll need Google Earth, but with that you should be able to follow my own points and decide for yourself if they’re any good or not (lost in the move to this site). I’ve put the placemarks 100m over the ground, with lines connecting them to the ground so you can see if they’re over the map correctly or not.
I’ve started by looking at the top of the Pyramid of the Dragon, because that’s a difficult one. It’s quite a flat topped hill. I decided on my place for the peak based on the angle of the corners of the two best defined edges, which mark the east side of the hill.
If this is a pyramid then the point where the corners meet should mark the centre of the pyramid. In this instance they cross at a point about 30 metres east of the official peak. You can also see that I’ve ignored the north-west corner. This is because it doesn’t meet where the other two lines do. That suggests the hill isn’t a pyramid to me, but you may disagree and feel the Bosnian Geodetic Institute put the vertex over the right point. There is a bigger disagreement over where the peak of the Pyramid of the Sun is.
I’ve drawn lines on the northwestern and northeastern corners and they’ve cross closer to the peak of the hill than the position given by the Bosnian Geodetic Institute. If this hill is a pyramid then the peak according to this map is somewhere near the top of the north face. You might want to argue this point if you check this in Google Earth, because if you look at it, Google does seem to show that the official vertex is higher than my peak. This is a substanstial disagreement, the two points are fifty metres apart.
So what’s going on? The vertical resolution of Google Earth isn’t very good. For instance in the same file you can find a point I’ve labelled ‘the place where the river runs uphill’.
I don’t know which way downstream is, but either way — if Google Earth is accurate — the river has to flow uphill. In reality what has happened is the Google Earth has a series of sampled points of heights and these get averaged over the landscape. Occasionally it leads to strange effects. If you look at the Google Earth renditions of the Giza Pyramids, you’ll see that the peaks of the pyramids aren’t the highest points, according to Google. So the fact that the official vertex looks higher doesn’t bother me. Certainly the official vertex over the Pyramid of the Moon makes no sense.
My peak is marked by the intersection of the red lines, and this does hit on the measured peak of the hill. The peak advocated by Osmanagić is seventy-five metres away, off the top of the hill. I don’t know what that vertex marks, but it’s not top of the Pyramid of the Moon. Do these difference make a big change to the marked triangle?
Using the alternative peaks I get distances of:
Sun — Moon : 2078
Moon — Dragon : 2204
Dragon — Sun : 2168
which gives angles of
Sun: 62º 30′
Moon: 60º 45′
Dragon: 56º 45′
If you’re wondering what a degree looks like, then hold your little finger out at arm’s length. The fingernail is about half a degree. The Sun and Moon are also about half a degree across. So is an error of 2 degrees, or four fingernails important? Yes, if you want to argue for exact accuracy. However I think the question is back to front.
Why would you look for such a triangle of the peaks anyway? There are no sites I can think of that have this kind of planning. You don’t find it in Egypt or Mexico, so why is it so important for Bosnian claims. It seems to be post-hoc reasoning. For instance I used to own a car with registration OTX 969 L. What are the chances of that happening? Well over a million to one. But that doesn’t make it automatically meaningful. If you highlight hits and ignore anything that contradicts you then you’re bound to find amazing features.
Similarly one combination of three peaks out of five claimed pyramids is close to an equilateral triangle. That leaves ten combinations which aren’t geometrically exciting — because we’re ignoring five other combinations which aren’t triangles, four combinations which aren’t squares and one combination which fails to be a pentagon. This is justified because if the Pyramids of Sun, Moon and Earth had formed an equilateral triangle instead wouldn’t that have been equally amazing? Or if the Pyramids of the Moon, Earth and Love (that’s a new one he’s found) had formed an equilateral triangle then that would have been amazing too. Why pick just one combination you like? There is no a priori reason to assume that any pyramid must only feature Osmanagić’s three chosen pyramids. With only one very approximate hit and ten failures you have to ask if Osmanagić already knew the answer before he asked the question.
It helps to approach research with an open mind.
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I’ve read an interesting article on http://www.bosnian-pyramid.net
about the corners of the pyramid. It would be an easy way to proof
quickly the existence, but they dig near the corners but not the
corners. Then they’ve dug something on the top of it, but not the
top!? I’ve seen some pictures on that really let me think again about
this whole thing. Every day I believe less in this mystery.