# Talk:Carathéodory's theorem (convex hull)

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Field: Geometry (historical)

Any opinion on whether ${\displaystyle {\mathbb {R}}}$ is a good idea instead of R? Does ${\displaystyle {\mathbb {R}}}$ help comprehension and look good; or does ${\displaystyle {\mathbb {R}}}$ look kind of awkward/ugly? WpZurp 07:40, 11 Aug 2004 (UTC)

As I mentioned in my edit comment, we do not usually use TeX inline. The agreed convention is to use R. Dysprosia 07:44, 11 Aug 2004 (UTC)

Did Constantin Carathéodory actually discover/prove this theory? If so, then merely saying the theorem "is named after" him would seem to be slighting his work.

Probably, I'm sure he was involved somehow in it, so it's safe to say it was named after him, since his name is given with the theorem.

By the way Dysprosia, I like your good, clear example example of the theorem. Now I actually understand it! I even understand the point about the curve being a convex hull. (Mostly, I just wanted some practice on working in math on Wikipedia. Had no real clue what I was doing.)

Thanks Dysprosia 10:20, 11 Aug 2004 (UTC)

WpZurp 08:07, 11 Aug 2004 (UTC)

Isn't this his theorem not in measure theory, though? The measure theory one being about outer measures?

Charles Matthews 15:57, 11 Aug 2004 (UTC)

There are links to (what I had believed were) other formulations of the theory. In particular, see the theory external links especally outer measure formulation (in pdf). I believe that saying d+1 is a less convoluted (or more rigourous?) way of saying things like countably additive set. Perhaps a Wikipedia mathematician should make a ruling.

Well, if there is a connection, I don't see it in the PDF file, and it is something unfamiliar. Your comment about 'countably additive set' doesn't mean much to me. Charles Matthews 21:12, 11 Aug 2004 (UTC)

As I now understand this theory, you can construct convex hulls and make statements about what they include. Convex hulls enclose volumes and being able to compare volumes is relevant to measure theory. I suspect this theory is useful in building up other theories than with more direct relevant to various measurements. (Caveat: I don't actually know what I'm talking about but this is my gut-feel. We need a real practitioneer to settle this issue.) WpZurp 22:24, 11 Aug 2004 (UTC)
Well, frankly, you are just guessing here ... Charles Matthews 09:43, 12 Aug 2004 (UTC)

It doesn't sound like much of a measure theory thing to me, either, but here's an illustration anyway ;) Dysprosia 21:49, 11 Aug 2004 (UTC)

I've created Carathéodory's theorem (disambiguation). The external links on this page are a mixture. Charles Matthews 10:04, 12 Aug 2004 (UTC)

## Low priority

Just wondering why this is considered to be a low priority article. I always thought Caratheodory's theorem was a "famous" result. 202.36.179.66 (talk) 22:17, 26 September 2009 (UTC)

It is a famous and important result, which is considered a prototype for geometric transversality theory, 52A35 in the mathematics subjects classification system. I upgraded it to "mid" priority. Kiefer.Wolfowitz (talk) 01:12, 14 November 2010 (UTC)

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