Rain in the real world and GURPS MAGIC

[whswhs]

Originally Posted by maximara

Bill Stoddard seems to be saying the circle is inside the hexagon ie A= 2 * √(3) * R^2

I don't see how you reach that conclusion. A formula for the area of any circle must include π. The formula I gave does not include π. It implicitly includes the square root of 3, which would not be in a formula for circles, but which emerges naturally from the analysis of a regular hexagon as partitioned into twelve 30° right triangles.

The "radius" of a hexagon in this analysis is one-half the distance from the hexagon's central point to the central point of an adjacent hexagon. That seems the most natural extension of the concept.