Mecca and golden ratio 1.618. Miracle or coincidence ?

The Earth and its Golden Ratio point based on Phi

by Contributors, golden number.net
May 22nd 2012
 


Is there a Golden Ratio point of the Earth?

It has been claimed that the Golden Ratio of the Earth is in Mecca.  (See video or website.)  Is this true?

Latitude

Let’s first look at latitudes.  Phi to 15 places is 1.6180339887499.  There are 180 degrees between the North Pole and the South Pole, so 180 divided by Phi is 111.2461179749810.  As latitudes are expressed in degrees and distance from the Equator, we subtract 90 degrees and convert this to a latitude of 21 degrees, 14 minutes and 46.02 seconds, North or South.

The latitude of Mecca, according to Google Earth, is 21 degrees, 25 minutes and 38.56 seconds.  This puts it only 10 minutes and 52.54 seconds north of the exact northern golden ratio latitude of the Earth.  This is a variance of less about 1/10 of a percent, about 12 miles or 20 kilometers north of the exact golden ratio latitude point.

Longitude

Latitudes have a clear reference point of origin that is determined by the poles defined by the Earth’s axis of rotation.  Selecting the origin point of the longitudes is not as clear as there is no single definitive reference point.  Those who claim Mecca as the Golden Ratio of point of the Earth’s longitudes base this on a Mercator projection of the Earth, to which a Golden Section has been overlayed using the PhiMatrix software available from this site:

One could start from any longitude to get to any location, but using a world projection is a reasonable approach.  The challenge though is that there are hundreds of different renditions of world projections that vary considerably.  Here’s an example of others that produce similar results:

 

The top image is the familiar Mercator projection.  The bottom  image is a Peters projection which eliminates the bias of the Mercator to highlight the Northern hemisphere.

Rather than use an image subject to interpretation to determine the golden ratio of the latitude, perhaps it is better to use actual longitude measurements.

If you accept the premise that a world projection map that divides East and West is the right foundation, the most accurate starting longitudinal reference point would then be the midpoint between Alaska and Russia at 168 degrees, 52 minutes and 42 seconds found in the satellite photo below.  Using this as a starting point, the Golden Ratio point falls at 31 degrees, 22 minutes and 16.05 seconds, which is 938 km to the west of Mecca, which according to Google Earth is at 39 degrees, 48 minutes and 53.42 second East.  If we use mankind’s own Meridian at 180 degrees as the origin point, the Golden Ratio point is at 42 degrees, 29 minutes and 32.05 seconds, which is 298 km to the east of Mecca.  

The  image below shows the midpoint between Alaska and Russia.

The image below shows the resulting Golden Ratio points of longitude from the midpoint at left and also from the 180 degree meridian.  Click on either image to enlarge it.

An alternate way to approach this is to start at the longitude of Mecca and move a Golden Ratio of 360 degrees away (222 degrees, 29 minutes and 32.05 seconds) to see where you land.  This point is at 117 degrees, 19 minutes and 21.37 seconds West, which is inside the border of Russia as shown below.  Click on the image to enlarge.

So, is Mecca really at the Golden Ratio point of the Earth?  

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