Another die hard legend are "sacred geometries". This theory claims that places on earth both natural, e.g. mountains, and man-made, e.g. churches, were positioned in such a manner they build a geometric pattern. One such theory advocates so called "ley lines" claiming that churches, chapels, holy Celtic places etc. are placed on a line. Another theory of that kind claims that the three pyramids of Gizeh have the same relative position as the three stars of the central axis of the star cluster Sirius. Other theories are based on triangles or, very popular, pentagrams.
The good thing about these theories is that modern map software allows very easily to determine distances and angles between points. This allows to check how much the pattern made of real places differs from the ideal line, or triangle or other geometrical pattern. Usually the allowed accuracy must be set to such a low level that the chance of coincidence rises substantially.
The coincidence chance depends on many more factors. If we allow all sorts of geometrical structures (triangle does not fit? Lets take a pentagram!) the probability of a chance match increases.
It further increases if we allow to expand (zoom in or out) and rotate the pattern.
The same applies if we do not take into consideration all points but only those who fit the picture. In the Sirius example only three stars are considered. It is not required that the other stars have matching pyramids in the Egypt desert. Even then it only works if we take the star position of some 10.000 years ago which causes authors to conclude the pyramids have that age. While it is true that the age of the Gizeh pyramids and the sphinx is not certain this dating approach does not seem promising.
By allowing all these parameters to be varied we get a tremendous amount of geometrical structures. Therefore, it is likely that one of them matches any place pattern on earth just by chance. If we compare the pattern of all McDonalds restaurants on the city map we can probably think of a matching geometric pattern. Nobody will seriously suggest the fast food company had exactly that in mind when erecting their outlets.
Similar to the dowsing rod theory this one loses all credibility when checked against the rules of statistic.