Talk:Osculating circle

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merge: see Talk:Contact (mathematics) --W!B: 03:32, 27 March 2006 (UTC)

In that article, "osculating" seems to mean having three points of intersection. That is not what it means in this article. I was under the impression that this usage is standard in differential geometry. Michael Hardy 22:17, 27 March 2006 (UTC)

[edit] Minor wording question

When reading

Osculate literally means to kiss; the term is used because osculation is a more gentle form of contact than simple tangency.

I am not sure the word "gentle" is the best. To be fair, I am having trouble coming up with a good improvement. "accurate", "tight", "precise", "lingering", "following", "parallel", "consistent", "refined", none seem to better capture the concept here. But I don't like "gentle" either.

Maybe someone with a moment of inspiration Roget could be proud of can come through and help out. Baccyak4H 18:10, 7 September 2006 (UTC)

"Gentle" makes sense because if you go from a tangent line to the curve, your acceleration abruptly changes, whwereas if you go from the osculating circle to the curve, it does not. Michael Hardy 18:32, 7 September 2006 (UTC)

I agree it makes sense that way. I only suspect there is a much more precise word, a better one. But as I cannot come up with it, it shall stand. If I come up with any ideas, I'll post here first. I encourage others to do the same. Baccyak4H 03:48, 8 September 2006 (UTC)

[edit] Four-point contact?

In one of the figures, this expression is used, although it is never defined nor described in the article. My best guess is that it means the circle shares one additional order of derivative with the curve than a typical osculating circle. I would think this clarification should be pursued in the article in lieu of the caption being altered to avoid this reference. Thoughts? Baccyak4H (Yak!) 20:31, 10 September 2007 (UTC)