Talk:Generalized trigonometry

Why does "polygonometry" redirect to this article?

Isn't it a bit redundant to have a link in a page (especially a list) redirect to the same page without going to a specific section within it detailing the subject? Also, the description of it in this list does not seem to match up with the description of the list in the top part of the article (I fully admit I'm no expert in this subject, but it seems like it would be fairly obvious to anyone who clicks on it after reading the description). Here is the section it is in. 67.174.75.217 (talk) 00:48, 24 January 2013 (UTC)

EDIT: I think I found a section of another article that might have some potential value in rectifying this, but I'm not sure, primarily because a. it has two links to this, and b. it seems a bit brief to cover it adequately. 67.174.75.217 (talk) 00:54, 24 January 2013 (UTC)

Trigonometry on the space of (compact?) sets in R2

Several years ago at a gathering of undergraduate mathematics researchers, I saw a nice presentation on doing trigonometry in various infinitely-dimensional spaces. Their main example was the space of subsets of the plane. (Maybe it was compact subsets, I'm not sure.) So just to be clear, a "point" in this space is a (compact?) set of points of R^2. They then defined a distance metric on this space. I think they demonstrated all this using a couple different distance metrics, but one would have been the distance between the two most-distant points in the sets. A line segment petween "points" A and B was something like, the set of all "points" X for which the distance from X to A plus the distance from X to B equals the the distance from A to B.

They then proceeded to define perpendicular lines, and thus construct right triangles. Now, I didn't know much of abstraction at the time, so it's possible they weren't getting anything different from what differential geometry would give. But it seemed to me that they were using trigonometry to ask different questions than topology and differential geometry normally ask.

I've never figured out what to google to find their work. But if it's become any sort of established field it surely belongs on this page. 64.186.47.170 (talk) 08:57, 13 June 2016 (UTC)

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