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I don't see how your example proves your point. It is not plausible to think about curvature when discussing triangles (you may discuss curvature of constructed circles, but that's tautological to the size of the circles...) so searching for "Steiner Curvature Point" should help find what you need faster.


But at the time I didn't know the phrase "Steiner curvature centroid", I just knew "Steiner point". The definition I knew was not in terms of the curvature, or in the terms I gave above, but as a certain integral of the support function.

As an aside, the Steiner curvature centroid has a perfectly reasonable interpretation in terms of the "curvature" of a triangle. For a convex set in the plane with smooth boundary, the Steiner curvature centroid is equal to the barycenter of the probability measure on the boundary weighted proportionally to the curvature. Given a triangle, take a sequence of smooth convex sets converging in Hausdorff metric to the triangle, and the limit of the Steiner points of these will converge to the following thing: the average of the vertices of the triangle weighted proportionally to pi - the angle. This is the analogue of the barycenter of the curvature-weighted perimeter for triangles.


The thrust of the original article's point is that more descriptive names for theorems and definitions is better. "Steiner curvature centroid" is more descriptive than "Steiner Point", and by the metric of being able to Google for relevant information, it is indeed better.

I see now, rereading, that you were in fact making two points. First, that understanding the definition dwarfs learning the name. (I'd argue that a better name won't make you instantly understand a definition, but it can help but the very example of Steiner point vs Steiner curvature centroid.) Second, that sometimes multiple defintions and theorems are named for the same person, which causes confusion. So you were making a for-and-against argument.




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