Convex curve has been listed as one of the
Mathematics good articles under the
good article criteria. If you can improve it further,
please do so. If it no longer meets these criteria, you can
reassess it. Review: January 12, 2023. ( Reviewed version). |
A fact from Convex curve appeared on Wikipedia's
Main Page in the
Did you know column on 20 January 2023 (
check views). The text of the entry was as follows:
|
This article is rated GA-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
Book "Treatise of Avalysis" Vol. IV DIEUDONNE has nothing common with book of Girkin "Spectral Theory of Random Matrices"/ It look like error link of Google. Jumpow ( talk) 15:04, 23 February 2015 (UTC)Jumpow
Different passages in the article either require or don't require a convex curve to be closed.
From the lead:
From "Definition by supporting lines":
From "Definition by convex sets":
From "Properties":
The first two quotes imply that a parabola is a convex curve, while the last two imply that it is not. If standard terminology requires it to be a closed curve (or subset thereof), the first two quotes should be modified to reflect that. On the other hand, if the term is used both ways, with and without a restriction that the curve be closed, then this should be explicitly mentioned. Thanks. Loraof ( talk) 16:14, 28 May 2015 (UTC)
I would suggest that the following two related issues be discussed in this article:
1. Given the equation of an algebraic plane curve (or perhaps more specifically a closed one), how does one determine whether it is convex?
2. Given the vertex coordinates of a polygon, what is the most efficient way to determine if it is convex?
Loraof ( talk) 20:43, 14 October 2015 (UTC)
I think that I found an error in the proof of the "Parallel tangents". It is said that q1 is the farthest point from p. I guess that q1 has to be the farthest point from L.
Actually taking an axe system in which p=(0,0) and , it is clear that the farthest point from L is a point on which the derivative of $C_y$ vanishes. This is also the meaning of the Hint on page 6 here here.
If no reaction, I'll do the change. — Preceding unsigned comment added by Laurent.Claessens ( talk • contribs) 08:55, 13 April 2016 (UTC)
Once again in the proof of the "Parallel tangents". I guess that the hypothesis "closed" curve is missing. If not, the graph of the function with is a counter-example (even being compact). The point is that a closed curve can be seen as a map , so that every value of the parameter lies in the interior of the domain and the principle "maximum iif vanishing derivative" holds.
This being said, we should also ask for . Laurent.Claessens ( talk) 05:12, 15 April 2016 (UTC)
The Koch snowflake curve would seem to qualify as a convex curve according to the definition. (It has no tangent where the curve lies on both sides.) Is this intended?
Also it probably needs to be made clear that "one side of a line" is here intended to include the line itself. Martin Rattigan ( talk) 16:22, 9 February 2017 (UTC)
Thanks to @ David Eppstein, he did the revert of my commit. Because of his mathematical background I am certainly accepting I was wrong, consequently, I am having a really hard time to understand the difference between a convex curve and a convex function, even after reading the article multiple times. I admit the article states in its first line that it should not be confused with each other, however, if someone could explain the difference in the article a bit better I would be really thankful. Varagk ( talk) 16:12, 28 October 2022 (UTC)
GA toolbox |
---|
Reviewing |
Reviewer: Kusma ( talk · contribs) 10:52, 8 January 2023 (UTC)
Will take this one. Review to follow within a few days. —
Kusma (
talk)
10:52, 8 January 2023 (UTC)
Good Article review progress box
|
Overall well sourced and referenced and nicely illustrated with free images. Appears stable and neutral. Detailed comments to follow below. — Kusma ( talk) 11:08, 10 January 2023 (UTC)
Will do lead section last.
regular, meaning that the moving point never slows to a halt or reverses direction? You later have
regular and has a derivative everywhere, but regular curve is only talking about differentiable curves.
cannot be improved: the source just says the bound is a "nearly best possible result" without making precise what that means. Is the exponent 1/3 the best possible? Is there an optimal constant? Or is this just about the leading term? Also, mention that this is the large-L asymptotics?
Every curve has at most two supporting lines in each direction.can you clarify that we are looking at supporting lines of fixed direction, but at different points here? (The statement is "for every direction, there are at most two points such that there is a supporting line at that point in that direction", not "at every point there are at most two supporting lines")
For strictly convex curves, although the curvature does not change sign, it may reach zero.perhaps add that simple closed curves with strictly positive / negative curvature are strictly convex?
Lead:
Combinations of these properties have also been considered.could perhaps be dropped.
A nice article about a basic topic, not much to complain about. More "advanced properties" like the A-A theorem or some "applications" would be nice, but not necessary for GA. Ping @ David Eppstein: — Kusma ( talk) 14:12, 10 January 2023 (UTC)
The result was: promoted by
Bruxton (
talk)
20:24, 13 January 2023 (UTC)
Improved to Good Article status by David Eppstein ( talk). Self-nominated at 02:45, 13 January 2023 (UTC).
The section Curvature contains this sentence:
"The total absolute curvature of a smooth convex curve, is at most . "
My understanding of the word "smooth" is that it means infinitely differentiable (C∞).
But I have seen it used to mean merely continuously differentiable and other things as well.
The article would be improved if it stated exactly what it means by the word "smooth".
I hope someone knowledgeable about this subject can fix this ambiguity in the article. — Preceding unsigned comment added by 2601:200:c082:2ea0:8563:761:1843:919f ( talk • contribs) 23:40, 16 March 2024 (UTC)
Convex curve has been listed as one of the
Mathematics good articles under the
good article criteria. If you can improve it further,
please do so. If it no longer meets these criteria, you can
reassess it. Review: January 12, 2023. ( Reviewed version). |
A fact from Convex curve appeared on Wikipedia's
Main Page in the
Did you know column on 20 January 2023 (
check views). The text of the entry was as follows:
|
This article is rated GA-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
Book "Treatise of Avalysis" Vol. IV DIEUDONNE has nothing common with book of Girkin "Spectral Theory of Random Matrices"/ It look like error link of Google. Jumpow ( talk) 15:04, 23 February 2015 (UTC)Jumpow
Different passages in the article either require or don't require a convex curve to be closed.
From the lead:
From "Definition by supporting lines":
From "Definition by convex sets":
From "Properties":
The first two quotes imply that a parabola is a convex curve, while the last two imply that it is not. If standard terminology requires it to be a closed curve (or subset thereof), the first two quotes should be modified to reflect that. On the other hand, if the term is used both ways, with and without a restriction that the curve be closed, then this should be explicitly mentioned. Thanks. Loraof ( talk) 16:14, 28 May 2015 (UTC)
I would suggest that the following two related issues be discussed in this article:
1. Given the equation of an algebraic plane curve (or perhaps more specifically a closed one), how does one determine whether it is convex?
2. Given the vertex coordinates of a polygon, what is the most efficient way to determine if it is convex?
Loraof ( talk) 20:43, 14 October 2015 (UTC)
I think that I found an error in the proof of the "Parallel tangents". It is said that q1 is the farthest point from p. I guess that q1 has to be the farthest point from L.
Actually taking an axe system in which p=(0,0) and , it is clear that the farthest point from L is a point on which the derivative of $C_y$ vanishes. This is also the meaning of the Hint on page 6 here here.
If no reaction, I'll do the change. — Preceding unsigned comment added by Laurent.Claessens ( talk • contribs) 08:55, 13 April 2016 (UTC)
Once again in the proof of the "Parallel tangents". I guess that the hypothesis "closed" curve is missing. If not, the graph of the function with is a counter-example (even being compact). The point is that a closed curve can be seen as a map , so that every value of the parameter lies in the interior of the domain and the principle "maximum iif vanishing derivative" holds.
This being said, we should also ask for . Laurent.Claessens ( talk) 05:12, 15 April 2016 (UTC)
The Koch snowflake curve would seem to qualify as a convex curve according to the definition. (It has no tangent where the curve lies on both sides.) Is this intended?
Also it probably needs to be made clear that "one side of a line" is here intended to include the line itself. Martin Rattigan ( talk) 16:22, 9 February 2017 (UTC)
Thanks to @ David Eppstein, he did the revert of my commit. Because of his mathematical background I am certainly accepting I was wrong, consequently, I am having a really hard time to understand the difference between a convex curve and a convex function, even after reading the article multiple times. I admit the article states in its first line that it should not be confused with each other, however, if someone could explain the difference in the article a bit better I would be really thankful. Varagk ( talk) 16:12, 28 October 2022 (UTC)
GA toolbox |
---|
Reviewing |
Reviewer: Kusma ( talk · contribs) 10:52, 8 January 2023 (UTC)
Will take this one. Review to follow within a few days. —
Kusma (
talk)
10:52, 8 January 2023 (UTC)
Good Article review progress box
|
Overall well sourced and referenced and nicely illustrated with free images. Appears stable and neutral. Detailed comments to follow below. — Kusma ( talk) 11:08, 10 January 2023 (UTC)
Will do lead section last.
regular, meaning that the moving point never slows to a halt or reverses direction? You later have
regular and has a derivative everywhere, but regular curve is only talking about differentiable curves.
cannot be improved: the source just says the bound is a "nearly best possible result" without making precise what that means. Is the exponent 1/3 the best possible? Is there an optimal constant? Or is this just about the leading term? Also, mention that this is the large-L asymptotics?
Every curve has at most two supporting lines in each direction.can you clarify that we are looking at supporting lines of fixed direction, but at different points here? (The statement is "for every direction, there are at most two points such that there is a supporting line at that point in that direction", not "at every point there are at most two supporting lines")
For strictly convex curves, although the curvature does not change sign, it may reach zero.perhaps add that simple closed curves with strictly positive / negative curvature are strictly convex?
Lead:
Combinations of these properties have also been considered.could perhaps be dropped.
A nice article about a basic topic, not much to complain about. More "advanced properties" like the A-A theorem or some "applications" would be nice, but not necessary for GA. Ping @ David Eppstein: — Kusma ( talk) 14:12, 10 January 2023 (UTC)
The result was: promoted by
Bruxton (
talk)
20:24, 13 January 2023 (UTC)
Improved to Good Article status by David Eppstein ( talk). Self-nominated at 02:45, 13 January 2023 (UTC).
The section Curvature contains this sentence:
"The total absolute curvature of a smooth convex curve, is at most . "
My understanding of the word "smooth" is that it means infinitely differentiable (C∞).
But I have seen it used to mean merely continuously differentiable and other things as well.
The article would be improved if it stated exactly what it means by the word "smooth".
I hope someone knowledgeable about this subject can fix this ambiguity in the article. — Preceding unsigned comment added by 2601:200:c082:2ea0:8563:761:1843:919f ( talk • contribs) 23:40, 16 March 2024 (UTC)