The Square Root of Two proportion is incredibly common amongst Masonic art and architecture, yet in many ways it goes unnoticed.
Here its value is reaffirmed, and many examples are included from a broad Masonic spectrum.
The Square Root of two is best known for being the diagonal of a square, when the sides of the square are 1.
Experienced Freemasons will recognize this symbol from Masonic art. Here is a classic example from a George Washington:
This is not to be confused with the 345 right triangle.
Although both of these have right angles in similar forms, the Square Root of Two on the right is identifiable via its symmetry.
This formation specifically is a representation of the Square Root of two.
In the Grand Lodge of Pennsylvania this ratio is engraved on a sculpted book, underneath the Latin 'Precepta Veritatis', precepts of truth.
In fact, the Square Root of Two is so important, that it relates directly to any depiction of a Masonic Square.
Between the ends of any Masonic Square is effectively a Square Root of Two.
Here are some more examples directly from the Freemasons.
The square symbol is very common on old masonic tracing boards. You can see it here on the bottom left.
Paul Revere, the well known American Revolutionist, featured this square in his impressive Masonic work.
It is interesting that many of these depictions begin to show the square root of two proportion in three-dimensions, as a cube or cuboid, most notably suggesting associations with structures such as the Perfect Ashlar of Freemasonry.
There are many points of interest that can be derived from this Square Root of Two formation.
First, some more Masonic Geometry needs to be introduced.