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Rename

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I think this article should be moved to "Length space" or "Length metric". Also, there should be a definition of "Geodesic length space". I'll make these changes in a few weeks if no-one comments further. WLior -- 2006-3-25

Midpoints

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The metric d is intrinsic if it has approximate midpoints

The statement is false, as is shown by the rationals. It's possibly true if the space is path-connected, but I'm a little wary: what if none of the paths connecting x and y is rectifiable? AxelBoldt 06:20, 10 April 2006 (UTC)[reply]

  1. Sometimes it also taken as a def of intrinsic metric and what is defined here called length metric space, I can not tell waht is the most standard def right now.
  2. The statement above is correct if the space is complete. Tosha 19:40, 10 April 2006 (UTC)[reply]

d_l vs. d_I

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In section Properties, I changed to throughout. It's hard to see the difference with a sans serif font, and d_l ("ell") makes no sense to me, so I think the ell must have been an error. -- UKoch (talk) 19:41, 9 September 2014 (UTC)[reply]

I don't think it's an error; I think it stands for "length". Sniffnoy (talk) 19:29, 10 September 2014 (UTC)[reply]
doesn't occur anywhere before "Properties". does, and it's the subject of the article. How would you motivate the introduction of in section Properties? -- UKoch (talk) 18:23, 13 September 2014 (UTC)[reply]
Oh, my mistake. I didn't actually take a good look at the old article. I had mistakenly assumed that was used throughout. Sniffnoy (talk) 18:44, 13 September 2014 (UTC)[reply]
Then it's settled. Something else just occurred to me: It should be rather than , since the I ("eye") is not a placeholder for anything. I'll make the changes. -- UKoch (talk) 18:25, 14 September 2014 (UTC)[reply]

Surely we can do better than this

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The section Definitions contains this passage:

"Here, a path from to is a continuous map

with and . The length of such a path is defined as explained for rectifiable curves."

Oh, come on. Instead of referring the reader to the entire article on rectifiable curves — which contains many definitions of length of a path that are not appropriate for continuous curves — this article should just give the appropriate definition for continuous curves.216.161.117.162 (talk) 20:18, 25 August 2020 (UTC)[reply]