In addition to /u/CubicZircon's comment on the math, which is beyond me but sounds correct, it is worth noting that I have never come across any suggestion that this is the basis for the location of Mecca in either academic or Islamic religious sources.

Moreover there doesn't seem to be anything in the pre-Islamic history of Mecca that distinguishes it from other sanctuary sites in the Arabian peninsula. It was, in fact, quite a humble sanctuary:

The temple (ka‘ba) was built in pre-Islamic times with loose stones, without clay. Its height was such that young goats could leap into it. It had no roof and its drapes were merely laid upon it, hanging down.

This is without getting into the interesting if slightly dubious revisionist questions, going back to Crone's essay Meccan Trade and the Rise of Islam, about whether the present location of Mecca is the same as its ancient location.

In other words, it sounds like all of the other specious pseudo-scientific claims made about Islam, and for that matter every other religion, that takes coincidences as scientific evidence for divine inspiration of sacred texts.

That means that the ratio of the distance from the south pole to mecca to the distance between north pole to mecca equals to the ratio between the distance between poles to the distance between south pole to mecca, which equals 1.618.

For the curious, I did the math: this “golden ratio latitude” would be at 90°-180°/((3+√5)/2) ≈ 21.24611 degrees of latitude, or 21°14'46". Mecca is at about 21°25'. This is an error of about 10 minutes of arc: roughly 19km. The cities of Honolulu, Cancún, Surat, Nagpur, Hanoi, and León (Mexico) are closer to the “golden ratio latitude” than Mecca.

If this was intentional, then this error must be explained away. There are two possible sources for such an error: mathematical and measurement.

Mathematical error: the best rational approximations to the “golden ratio” are the ratios between consecutive Fibonacci numbers (and even without explicit knowledge of the Fibonacci sequence, a naive iterative process for “extreme and mean ratio” gives this same approximation). These approximations are very good: they improve exponentially and 55/34 already offers a better precision than the Mecca latitude. There is also a geometric construction given in Euclid (II.11), so we can basically say that the mathematical error is negligible when compared to 10'.

Astronomical error: Ptolemy gives latitudes with about 5' of error. Again, this is not enough.

-> busted.

edit to add: if you want a more precise (and just as interesting) geographical coincidence, the antipode of the Bering strait meridian passes right through the Ponte Vecchio in Florence.

Hi, Thanks for the relevant comments, an error of about 0.09% is tolerable. My question is that if its not a coincidence and not a miracle, then is it possible for the people of the 8th century (or before) to have noticed something about that place and hence built the kaaba there ? We know that they used the stars to navigate in the desert and on sea, so they did have some knowledge of astronomy, could that have revealed anything peculiar for them to have built the kaaba there ? Something related to the moon ? Thanks.

Hi CubicZircon, Thanks for reply, 10 minutes of 180 degrees is 0.09%, perhaps you are taking 90 degrees to arrive at an error of 0.2% Lets not obfuscate the question, I am not asking if its a coincidence or not, nor if the error is tolerable or not. My question is could the scientist (geophysicists/astrologers) of the eighth century have noticed anything peculiar to build a shrine at that place, if yes then what could it have been. If the answer is no, still that does not make it a miracle so we do not need to explain it as a coincidence, yes coincidences happen, but I am not interested in that explanation. If a better explanation is found, that would be a nice coincidence :) Thanks.