I have a computer graphics plotting application where we often plot regular convex polygon shapes as symbols for different data points. I'd like to scale the radius (aka circumradius, distance from center to vertex) of the polygons so that polygons with different numbers of sides all have equal area (so presumably similar perceptual impact). i.e. if a circle with radius=1 has area Pi*radius^2, how much do I need to scale the radius to get a square or a triangle with the same area? What would the formula be to compute this for regular polygons with arbitrary numbers of sides?
Seems like this should be a simple geometry/algebra problem, but that was a long time ago... :-)
