Talk:Geodesic

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Change the sentence order in the lead paragraph

Obviously a lot of technically skilled people have edited this article. But that seems to have blinded them to the obvious. For the majority of readers coming to this article all they are interested is great the circle idea of a geodesic. They just need a simple sentence to inform or confirm their notion of what a geodesic is.

The don't need or want a topic sentence like this : "...In the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it. If this connection is the Levi-Civita connection induced by a Riemannian metric, then the geodesics are (locally) the shortest path between points in the space....". This sentence contains a raft of references to concepts and words that a general reader will be unfamiliar with. A general reader is likely to either skip the article or start on a trip through the internet trying to figure out what the heck this sentence means.

What the general reader is probably interested in is contained nicely in this paragraph: "The term "geodesic" comes from geodesy, the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, a segment of a great circle. The term has been generalized to include measurements in much more general mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph."

It seems to this reader that the problems of the lead section could be fixed easily by just reversing the order of the two paragraphs. The technical reader can easily skip past the opening section that he probably is well aware of and begin to try to understand the more technical uses of the word in mathematics and physics with the second paragraph of the lead section serving as a summary of the technical information to follow. — Preceding unsigned comment added by Davefoc (talk • contribs) 05:47, 15 April 2016‎ (UTC)[reply]

JRSpriggs made the edit suggested above. Thank you. Davefoc (talk) 05:01, 20 September 2016 (UTC)[reply]

Use of t as an affine parameter

Across, much of the article "t" is used as the affine parameter along a geodesic curve. This is a rather unfortunate choice as to many readers it will suggest a relation with time, where no such connection need to exist (or even make sense in the case or Riemannian geometry). I would suggest changing it to something more "neutral" such as λ.T R 11:26, 29 September 2016 (UTC)[reply]

Need more accurate short description

The current short description is misleading in several regards. First, in a lorentzian manifold a geodesic maximizes the interval rather than minimizing it. Second, in a manifold with a connection but no metric, geodesics are defined but path length is not. Can anybody come up with wording that is more accurate but still concise? Shmuel (Seymour J.) Metz Username:Chatul (talk) 23:01, 4 September 2020 (UTC)[reply]

Short description

The article has the short title Shortest path on a curved surface or a Riemannian manifold. That is correct for a manifold with a positive definite metric, but it is incorrect for a manifold with a Lorentzian metric. I've considered changing it to "Extremal path", but that's not quite right either. Your thoughts? Shmuel (Seymour J.) Metz Username:Chatul (talk) 01:10, 28 January 2021 (UTC)[reply]

It is clear that the article as it stands is solely concerned with the notion in Riemannian geometry so the original version seems fine (up to some points of detail that should be relegated to the body of the article). I think the notion in Lorentzian geometry (or in more general settings) is very much secondary compared to the metric notion so might without harm be discussed in the articles about these notions (with perhaps a link in the "see also" section at the bottom). jraimbau (talk) 12:58, 28 January 2021 (UTC)[reply]

That is not clear; the article has references to, e.g., General Relativity as a special case. If the article is solely concerned with the notion in Riemannian geometry then the {{about}}, lede and Introduction should be modified accordingly, e.g., {{about|geodesics in general|geodesics in general relativity|Geodesic (general relativity)|Geodesey|Geodesy|other uses}}, remove "and pseudo-Riemannian manifolds". Shmuel (Seymour J.) Metz Username:Chatul (talk) 21:33, 28 January 2021 (UTC)[reply]

Yes. jraimbau (talk) 06:17, 29 January 2021 (UTC)[reply]

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