If you draw a circle, then draw another one of the same diameter with its center on the first circle, then another, using an intersection of the two circles for its center, and continue around the original circle, centering on the intersection of the original and the last one drawn, you get six overlapping circles going around the original one, and can draw a regular hexagon using the intersections. I played around with that on a CAD program a few years ago, and was trying to come up with different combinations of whole numbers (one being the radius of the base circle, and the other the radius of the circles going around it) for each regular polygon. Some weren't exact but very close. I lost all that. I was trying it again today, and did some web searches to see if there's a formula or anything to find the combination that would make a regular polygon of however many sides I want. I don't see anything like it. The closest thing I found was "kissing numbers", but that's dealing with circles around the outside of the original. Does anyone know if there's a name for what I'm talking about so I can look it up? Or do you have any information yourself that would help me figure out what combinations to use? Thanks for your time. Here's a screenshot of what I'm talking about, using six circles.
