Random math patterns time. If you take a quarter, or any other coin, you can fit 6 other coins around it so they are all touching the center coin and their neighbors on either side. Why 6? I dunno. But what size does the middle one have to be for 5 outside circles? or 4?

Start

So lets assume the radius of the circles on the outside (our quarters) is 1. A quarter is 2 quarter-radius' in diameter...go figure.

If you draw a line between the centers of our circles you will get a bunch of angles. In the case of our 6 quarters, we get a hexagon.
The sum of the outer angles for a polygon is ∑a = 180*(n-2), so for a hexagon we get 720 degrees, or 120 degrees for each angle.
Now if you draw a 2 lines from the center of 2 next door circles into the center you get a triangle. Each of the 2 outer angles will be half the original outer angle (120/2 = 60) and the center will be 180 minus the sum of the 2 angles (180-60-60=60).
So, how can we compare the number of outer circles to the inner angles?

inner angle = 180 - (2 * ( ∑a / 2 ) / x)
or simplified:   inner angle = 180 - ( ∑a / x )

So then we can calculate out for each shape:

Inner Circle Diameter

Now, how do we relate the inner angle to the radius of the middle circle?
Something like this:

inner radius = outer radius / ( SIN( inner angle / 2 ) - outer radius
with numbers:   inner radius = 1 / ( SIN( inner angle / 2 ) - 1

So:

And This Affects Me How?

Hopefully not at all really. But according to wikipedia and some quicky ratio-ization lets have some fun:

Well that was really an excersize in letdown...oh well, my questions were answered, and your time wasted, so 2 points to me!