Am I asking this question in the wrong place?
I am assuming that the radius in the app refers to the radius of the circumcircle, not the incircle.
I threw the question out to some students who developed a procedure to try to "calibrate" the polygon tool. We will run a test carve series in MDF, creating a series of n side polygons where n is divisible by 2, and labeling each with selected values for R. (Not a mathematician, but I believe R refers to the Radius of the circumcircle while r is the radius of the incircle).
This should give the students a table of values from which they can derive formulae to calculate incircle and circumcircle radii for a given input for polygons with even numbers of sides.
With some basic data, they should then be able to derive a formula that can calculate incircle and circumcircle radii for any n sided polygon, and then we can carve a display "tile" that explains the radii of polygons.
And to think this all stated because I was making a dust extractor...
Ain't technology just the coolest?