What is the mark at 19" 3/16th on a tape measure, and why does it repeat itself ?
The so-called diamond mark is actually positioned at exactly 8/5 of a foot (that's exactly 1.6' or 19.2 inches, which is indeed pretty close to 19" 3/16 ).
The diamond marks are also called "black truss" markings, because they correspond to the truss layout which is used with 8-foot sheets of plywood (or other material), namely 5 trusses per sheet.
This is to be contrasted with "red stud" markings which appear every 16 inches by showing the corresponding inch number in red instead of black. The black markings and the red markings coincide at 8-foot intervals (96 inches).
That is to say: 5 black intervals or 6 red ones in an 8-foot width.
5/8 = 0.625 is a standard slope for a roof, which may thus be built by measuring horizontally as many diamonds as there are vertical feet.
The ratio 8/5 = 1.6 is very close to the so-called Golden Ratio, which has been used extensively in architecture since antiquity...
The golden ratio is the aspect ratio of a rectangle whose larger side is to the smaller side what the sum of the two sides is to the larger side. It is also equal to the diagonal of a regular pentagon of unit side. Its precise value is (1+sqrt(5))/2, which is about 1.618034
