Wow... you

*REALLY* just don't get it, do you? Why are you still debating this with me?

Radius is a geometry term. Period. If they don't mean that, (WHICH I AGREE WITH YOU THAT THEY DON'T, OK?????? Got that?), they should

*use a different term* and then we wouldn't be discussing it. Would we?

"Zone", for example, would be a better term. A "zone" is an area, and can be "around" something or someone.

You are using radius wrong.

More specifically, you are taking one geometrical use of radius that you happen to be aware of, and declaring that any other use is wrong.

That isn't evidence you are right. That is evidence you only know of some uses of the word radius.

Any wedge of a circle can be said to have a radius, not just circles. So can any curve -- this is known as the radius of curvature.

If you want a formal geometrical definition, radius around a non-point object can be mathematically described by creating a derived metric where the distance between any two points in the object is defined to be zero, and that "short cut" can be used to measure distances between other points. Then do the usual equivalence classes of neighborhoods.

This reduces the object to a single point in a metric space, and we can now define a sphere of radius 15' around that single point. All points in this modified metric space correspond to points in the space we derived it from, so we can map this back to the original space.

If the original object was (say) a 5' cube, the 15' radius sphere centered on that 5' cube is a 20' radius cube with rounded corners. Those rounded corners have a radius of curvature 15'.

Is that mathematical enough?

I suspect not; I suspect you aren't actually interested in radius as a mathematical concept other than insofar as it supports your position. But, if you are only using radius as a mathematical concept insofar as it supports your position, then radius as a mathematical concept

**doesn't support your position**.