Figuring out how many 300 yard radiuses will fit within into different sized polygons.

[JasonFink]

I have been tasked to find out exactly how many 300 square yard radiuses will fit completely into several different sized polygons.  I can figure it the math out on paper, but I need to show it with a map.  There has to be an easier way than just creating radius buffers over and over and over again one at a time until the polygon is filled.  Can some one with coding experience help me out?  It may be some simple tool that I'm just overlooking.

[DarrenWiens2]

You should share how you figured out the math on paper, and perhaps someone will be able to turn it into code.

[DanPatterson_Retired]

inscribed circle is the keyword search

[DarrenWiens2]

I'm not seeing any actual solutions by searching for inscribed circles, except possibly through ET GeoWizards, which I can't get to until tomorrow. At this point I'm interested in a Python implementation. Ideas?

[DanPatterson_Retired]

not too hard for general shapes (ie squares, triangles, hexagons etc)

a messy situation at best for convex polygons

really really messy for concave polygons

to get your started

then you are on your own 

[DarrenWiens2]

Thanks. I could work out the simpler geometries, just curious if there was some magical algorithm for figuring out more complicated shapes.

[DanPatterson_Retired]

I like the analogy of growing bubbles to reduce internal pressure... but it falls apart since the sweet spot has to be know ahead of time... at least you can think about it whilst drinking beer rapidly