From what part of a circle, or other constant or formula, does the formula 1718.87/radius, derive?

1718.87 divided by the radius of a circle gives you the deflections per minute per foot of arc, for laying out points on a curve with a transit or theodolite. I can't remember how the 1718.87 number is derived, but it has to do with other curve information, such as 5729.577 divided by the diameter of a circle gives you the radius of the circle, etc.

I'm not familiar with your formula but your number 1718.87 is just the number of arc minutes in a circle (360*60) divided by 4π. The deflection 'd' of a curve of radius 'r' over angle 'a' is

The arc length 'L' for a circle of radius 'r' is related to the angle in radians 't' by:

t = L/r

The angle in arc minutes 'a' is related to the angle in radians by:

a = 180*60*t/π = 3437.74 t

So the angle in arc minutes defined by the arc length 'L' is:

a = 3437.74 L/r

This is exactly twice the number you mentioned (1718.87). I'm not sure what you mean by "deflection" I'm not a surveyor so I can't figure where the factor of 2 comes from.

On your second question, there must be some mistake since diameter divided by 2 is radius.

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