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The link to "Shape Stencils from Stencil Ease" http://www.stencilease.com/ is a link to a commercial website. I think this link should be removed, as it is purely commercial, and does not in any way enhance the information on the subject. If such a link is allowed, why not a link for Mary's Hair Shaping website, and Don's AutoBody Custom Shape Designs, and Sam's Shaped Bakery Items? Where do you draw the line?
I am no expert at editing Wikipedia, although I do contribute small insignificant tweaks when I see a clear problem. In this case however, I think a veteran contributor familiar with the ins and outs of sandboxing and TOS for Wikipedia should make the call, so I am not attempting to remove the link myself, and am instead bringing it up here in the Talk for consideration. Thank you.
Hi Oleg,
I adjusted the definition on the shapes page.
I changed the definition, because I am interested in comparing shapes. If two shapes are exactly the same, then there is
"And I will have to agree with him that the way you have put it was too much of a duplication, and that the article is about a mathematical concept, not a computer science one. So whether there is an algorithm that filters out those properties is irrelevant to this article - in math, you can do things without algorithms (isn't math great?)" Nobody mentioned computer science. The Procrustes algorithm dates to Gower, 1975. It has only recently been used as a mathematical tool in computer science.
Just in case you think algorithms are confined to computer science, I got this from wikipedia: "Al-Khwarizmi, the 9th century Persian astronomer of the Caliph of Baghdad, wrote several important books, on the Hindu-Arabid numerals and on methods for solving equations. The word algorithm is derived from his name, and the word algebra from the title of one of his works, Al-Jabr wa-al-Muqabilah."
With respect to the word 'duplication', is this not an encyclopaedia? There are two definitions in the mathematical literature. Is it not more comprehensive to include both? That my original alteration lacked sufficient clarity is unfortunate, but not necessarily a reason to discount it entirely.
I used a cube because it is easy to visualise. I should have made that more clear. As in Oleg's original definition, two objects have the same shape if one can be transformed to exactly match the other, using only Euclidean transformations. These Euclidean transformations are also called rigid motions, or Euclidean motions, in geometry. The question of equivalence of reflections comes up quite a lot. The definition of shape is sometimes extended to include all orthogonal transformations, plus scaling, i.e., transformations that preserve relative distances and angles (google mathworld, orthogonal transformations for a good definition). Orthogonal transformations include reflection. This implies that the shape of an object is equivalent to the shape of its reflection.
"But are these two really considered different shapes?" This question is not clear to me, I am afraid. I would appreciate it if you would expand a little. Are you asking if the object and its reflection have the same shape? Or, are you asking if the object and its reflection are the same objects? Euclidean transformations involve scaling, rotating and translating. The reflection question is a good question, and there is no perfect answer to it.
Finally, Oleg, if you knew what you were talking about, you would know that shape is clearly defined in $n$-dimensional space by the likes of Kendall and Le, and Goodall. And reflection is discussed.
I admire your enthusiasm in extending Wikipedia. My intention was merely to do the same, by adding the extra knowledge I had about the definition of shape. Your reaction was not appreciated.
"According to one common definition, the shape of an object is all the geometrical information that remains after location, scale and rotational effects are filtered out. This definition implicitly assumes that it is possible to filter these effects out. Another definition is that the shape of an object is all of the geometrical information that is invariant to location, scale and rotation."
The definition used in the first sentence originates, according to Dryden & Mardia, 1998, in a 1977 paper by Kendall, "The Diffusion of Shape". Kendall's 1984 paper started off the whole Procrustes analysis methodology, linked to at the bottom of the shapes page.
I agree that I may be incorrect in concluding that the first definition "implicitly assumes" a filtration method is possible. It would be better, in my updated opinion, if I had said "suggests". I feel that this definition unnecessarily motivates Procrustes analysis, a filtration method, to mathematically analyse differences between shapes.
So, yes, the definitions are mathematically equivalent. They are not, however, equivalent. Both definitions are in common use in modern mathematics. As such, it seems reasonable to me that both definitions should be included in an article in an Encyclopaedia, and the reason that there are two definitions should also be included. This is why I had three sentences; two definitions and a reason.
My alterations may have needed improvement. I do not, however, think it is good practice to just try to wipe them out, and call the words I used clumsy without justification. My last comment may have been somewhat antagonistic, but I am not yet ready to retract it. --anon
By the way, how about logging in? You will get a true name and signature. Also a watchlist.
About shapes. This is not my opening paragraph, and I did not write this article. I don't have references either. All started with me removing some rather complicated/almost duplicated definition.
You are the expert, please work on this article if you wish. All I care about is to keep at least the first part of this article accessible to the general public. As far as anything else is concerened, please feel free to do any work you feel like it, actually I would ask you to do so, you may add some useful things. Hope that helps. :) Oleg Alexandrov ( talk) 16:50, 24 January 2006 (UTC)
Sorry for getting into the discussion late. For what its worth I was one of Mardia's postdocs. Some of this might want to be discussed under Talk:Procrustes analysis rather than here. Also it would be good if anon could register.
A few points.
Generally considered to be different shapes. Especially important when considering things like chemical compounds when left handed and right handed compounds can have different properties.
Another extension is to consider shape and scale or shape and size when the size of an object is important.
Dialation not commonly used in the statistics field, normally talk about scaling instead. (Is dilation a more common American term?)
The common usage of the term is much less precise than a mathematical definition. Consider What shape is it? its a rectangle! (even though rectangles have infinitly many different shapes acording to the above definiton). There is a case for including wider definitions of shape with a more topological feel to them.
As to the definition I'd be happier with just the newer definition
I don't think anyone in the field would object to that definition or indeed say that it was a different definition, just a better way of expressing the same concept in English. You would probably find a slight different wording in each paper on the subject.
The pedants among us might object to the concept of the shape of an object instead talk about whether two objects have the same shape. Indeed Procrustes is technically closer to the latter.
To be really pedantic the definition of shape should be expressed in mathematics and not English. The Shape of on object is an equivalence class of objects which can be transformed onto each other by rotation, translation and scaling.
Finally its important to distinguish Statistical shape analysis (Procrustes, Kendal, Goodall, Mardia, Lele etc) from the general concept of shape which has been around since Euclid. Procrustes is one method of discussing shape which has particular statistical underpinning. -- Salix alba ( talk) 19:29, 25 January 2006 (UTC)
I've been pondering a a bit about quite what an appropriate definition of shape would be.
First we need to consider the history of the word. Its been around for a long time and it is only reciently that a particular definition of shape has been used in statistics.
In Wiktionary shape is defined as
There are lots of occurences of the word in mathematical work with a less strict definition. From a text book aimed at 16 year olds. We have
This leads to both a strict and loose definition of shape. -- Salix alba ( talk) 19:54, 26 January 2006 (UTC)
Using dilation reather than scaling is confusing. The only property required for a dilation is that its distance preserving, hence both reflection and translation are dilations. Dilations also include reflection so are not strictly shape preserving. Hence dilation has to go. -- Salix alba ( talk) 19:54, 26 January 2006 (UTC)
"In other words, the shape of a set is all the geometrical information that is invariant to location, scale and rotation." You have got to be kidding. First of all, this isn't much of a definition, in that it tells what shape is not, rather than what it is. Second, it's a bit technical in the introduction. Please fix. 71.102.186.234 01:30, 30 November 2006 (UTC)
This article is still very week here's a few thoughts on a new section
A variety of descriptives names have been used to describe shapes, these are often in comparison with well know objects. Frequently there are many different objects which fit each class
It is also common to describe one aspect of a shape as a whole. The sign of the Gaussian curvature can be used to describe an aspect of the local shape
Certain points and curves on an object will be invariant under rotation, scaling and translation
Topological properties are also invariant under a wider class of transformations
-- Salix alba ( talk) 13:53, 1 February 2007 (UTC)
Salix Alba is essentially proposing this merger above; and it was supported at Wikipedia:Articles for deletion/Glossary of shapes with metaphorical names; so was deleting that list. The declared purpose of the list (having some place for V-shaped to redirect to) can as well be served by this article; and it may produce lesss of an indiscriminate collection of information. Septentrionalis PMAnderson 05:32, 9 February 2007 (UTC)
how can this article be both low priority, start quality, and vital: we have to put in the CD or what not, it's barely better than a stub, and it's not very important? how does that work? Saganatsu ( talk) 02:27, 20 December 2007 (UTC)
kudh yl hhiera uireh aurt n —Preceding unsigned comment added by 65.48.165.150 ( talk) 16:09, 5 October 2008 (UTC)
It might be nice to add a group picture of the more common geometric shapes. Or perhaps two images - one for 2D shapes (square, rectangle, triangle, circle, rhombus, etc) and one for 3D shapes (cube, rectangle, cone, sphere, etc). —Preceding unsigned comment added by 81.156.126.242 ( talk) 19:30, 17 August 2009 (UTC) i like lizards
I was under the impression that, in geometry, shapes are 2-dimensional but figures are 3-dimensional. This article refers to just about anything as a "shape." In fact, in the Introduction section the phrase "plane figure" is a hyperlink back to this article--thus, completely useless! Please help. MorbidAnatomy ( talk) 20:15, 20 March 2011 (UTC)
Shape has a technical meaning in geometry: similar figures have the same shape. This principle has been described using complex numbers in the article section Similarity classes. An editor removed this section, it has now been restored, and discussion is open on the merits of keeping the section. Rgdboer ( talk) 02:52, 16 December 2013 (UTC)
I removed the section, but I do believe it has some merit, and I won't remove it again.. However, it refers entirely to the work of one or two individuals. If a mathematical idea is truly important, it will be in standard textbooks or will be in frequent use. But the mathematician's name is all over this section. Why not refer to other uses of complex geometry in shapes such as the cross-ratio of hyperbolic geometry? Brirush ( talk) 02:58, 16 December 2013 (UTC)
The comment(s) below were originally left at Talk:Shape/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
This article is miserable (barely start class), and there are no signs that it will be improved in the near future. I recommend it be removed from the list of vital articles. Geometry guy 13:08, 7 May 2007 (UTC) |
Last edited at 13:08, 7 May 2007 (UTC). Substituted at 05:53, 30 April 2016 (UTC)
3-D shapes are? 69.79.12.153 ( talk) 22:35, 30 December 2022 (UTC)
View the proposal here. Writehydra ( talk) 05:00, 2 February 2024 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
The link to "Shape Stencils from Stencil Ease" http://www.stencilease.com/ is a link to a commercial website. I think this link should be removed, as it is purely commercial, and does not in any way enhance the information on the subject. If such a link is allowed, why not a link for Mary's Hair Shaping website, and Don's AutoBody Custom Shape Designs, and Sam's Shaped Bakery Items? Where do you draw the line?
I am no expert at editing Wikipedia, although I do contribute small insignificant tweaks when I see a clear problem. In this case however, I think a veteran contributor familiar with the ins and outs of sandboxing and TOS for Wikipedia should make the call, so I am not attempting to remove the link myself, and am instead bringing it up here in the Talk for consideration. Thank you.
Hi Oleg,
I adjusted the definition on the shapes page.
I changed the definition, because I am interested in comparing shapes. If two shapes are exactly the same, then there is
"And I will have to agree with him that the way you have put it was too much of a duplication, and that the article is about a mathematical concept, not a computer science one. So whether there is an algorithm that filters out those properties is irrelevant to this article - in math, you can do things without algorithms (isn't math great?)" Nobody mentioned computer science. The Procrustes algorithm dates to Gower, 1975. It has only recently been used as a mathematical tool in computer science.
Just in case you think algorithms are confined to computer science, I got this from wikipedia: "Al-Khwarizmi, the 9th century Persian astronomer of the Caliph of Baghdad, wrote several important books, on the Hindu-Arabid numerals and on methods for solving equations. The word algorithm is derived from his name, and the word algebra from the title of one of his works, Al-Jabr wa-al-Muqabilah."
With respect to the word 'duplication', is this not an encyclopaedia? There are two definitions in the mathematical literature. Is it not more comprehensive to include both? That my original alteration lacked sufficient clarity is unfortunate, but not necessarily a reason to discount it entirely.
I used a cube because it is easy to visualise. I should have made that more clear. As in Oleg's original definition, two objects have the same shape if one can be transformed to exactly match the other, using only Euclidean transformations. These Euclidean transformations are also called rigid motions, or Euclidean motions, in geometry. The question of equivalence of reflections comes up quite a lot. The definition of shape is sometimes extended to include all orthogonal transformations, plus scaling, i.e., transformations that preserve relative distances and angles (google mathworld, orthogonal transformations for a good definition). Orthogonal transformations include reflection. This implies that the shape of an object is equivalent to the shape of its reflection.
"But are these two really considered different shapes?" This question is not clear to me, I am afraid. I would appreciate it if you would expand a little. Are you asking if the object and its reflection have the same shape? Or, are you asking if the object and its reflection are the same objects? Euclidean transformations involve scaling, rotating and translating. The reflection question is a good question, and there is no perfect answer to it.
Finally, Oleg, if you knew what you were talking about, you would know that shape is clearly defined in $n$-dimensional space by the likes of Kendall and Le, and Goodall. And reflection is discussed.
I admire your enthusiasm in extending Wikipedia. My intention was merely to do the same, by adding the extra knowledge I had about the definition of shape. Your reaction was not appreciated.
"According to one common definition, the shape of an object is all the geometrical information that remains after location, scale and rotational effects are filtered out. This definition implicitly assumes that it is possible to filter these effects out. Another definition is that the shape of an object is all of the geometrical information that is invariant to location, scale and rotation."
The definition used in the first sentence originates, according to Dryden & Mardia, 1998, in a 1977 paper by Kendall, "The Diffusion of Shape". Kendall's 1984 paper started off the whole Procrustes analysis methodology, linked to at the bottom of the shapes page.
I agree that I may be incorrect in concluding that the first definition "implicitly assumes" a filtration method is possible. It would be better, in my updated opinion, if I had said "suggests". I feel that this definition unnecessarily motivates Procrustes analysis, a filtration method, to mathematically analyse differences between shapes.
So, yes, the definitions are mathematically equivalent. They are not, however, equivalent. Both definitions are in common use in modern mathematics. As such, it seems reasonable to me that both definitions should be included in an article in an Encyclopaedia, and the reason that there are two definitions should also be included. This is why I had three sentences; two definitions and a reason.
My alterations may have needed improvement. I do not, however, think it is good practice to just try to wipe them out, and call the words I used clumsy without justification. My last comment may have been somewhat antagonistic, but I am not yet ready to retract it. --anon
By the way, how about logging in? You will get a true name and signature. Also a watchlist.
About shapes. This is not my opening paragraph, and I did not write this article. I don't have references either. All started with me removing some rather complicated/almost duplicated definition.
You are the expert, please work on this article if you wish. All I care about is to keep at least the first part of this article accessible to the general public. As far as anything else is concerened, please feel free to do any work you feel like it, actually I would ask you to do so, you may add some useful things. Hope that helps. :) Oleg Alexandrov ( talk) 16:50, 24 January 2006 (UTC)
Sorry for getting into the discussion late. For what its worth I was one of Mardia's postdocs. Some of this might want to be discussed under Talk:Procrustes analysis rather than here. Also it would be good if anon could register.
A few points.
Generally considered to be different shapes. Especially important when considering things like chemical compounds when left handed and right handed compounds can have different properties.
Another extension is to consider shape and scale or shape and size when the size of an object is important.
Dialation not commonly used in the statistics field, normally talk about scaling instead. (Is dilation a more common American term?)
The common usage of the term is much less precise than a mathematical definition. Consider What shape is it? its a rectangle! (even though rectangles have infinitly many different shapes acording to the above definiton). There is a case for including wider definitions of shape with a more topological feel to them.
As to the definition I'd be happier with just the newer definition
I don't think anyone in the field would object to that definition or indeed say that it was a different definition, just a better way of expressing the same concept in English. You would probably find a slight different wording in each paper on the subject.
The pedants among us might object to the concept of the shape of an object instead talk about whether two objects have the same shape. Indeed Procrustes is technically closer to the latter.
To be really pedantic the definition of shape should be expressed in mathematics and not English. The Shape of on object is an equivalence class of objects which can be transformed onto each other by rotation, translation and scaling.
Finally its important to distinguish Statistical shape analysis (Procrustes, Kendal, Goodall, Mardia, Lele etc) from the general concept of shape which has been around since Euclid. Procrustes is one method of discussing shape which has particular statistical underpinning. -- Salix alba ( talk) 19:29, 25 January 2006 (UTC)
I've been pondering a a bit about quite what an appropriate definition of shape would be.
First we need to consider the history of the word. Its been around for a long time and it is only reciently that a particular definition of shape has been used in statistics.
In Wiktionary shape is defined as
There are lots of occurences of the word in mathematical work with a less strict definition. From a text book aimed at 16 year olds. We have
This leads to both a strict and loose definition of shape. -- Salix alba ( talk) 19:54, 26 January 2006 (UTC)
Using dilation reather than scaling is confusing. The only property required for a dilation is that its distance preserving, hence both reflection and translation are dilations. Dilations also include reflection so are not strictly shape preserving. Hence dilation has to go. -- Salix alba ( talk) 19:54, 26 January 2006 (UTC)
"In other words, the shape of a set is all the geometrical information that is invariant to location, scale and rotation." You have got to be kidding. First of all, this isn't much of a definition, in that it tells what shape is not, rather than what it is. Second, it's a bit technical in the introduction. Please fix. 71.102.186.234 01:30, 30 November 2006 (UTC)
This article is still very week here's a few thoughts on a new section
A variety of descriptives names have been used to describe shapes, these are often in comparison with well know objects. Frequently there are many different objects which fit each class
It is also common to describe one aspect of a shape as a whole. The sign of the Gaussian curvature can be used to describe an aspect of the local shape
Certain points and curves on an object will be invariant under rotation, scaling and translation
Topological properties are also invariant under a wider class of transformations
-- Salix alba ( talk) 13:53, 1 February 2007 (UTC)
Salix Alba is essentially proposing this merger above; and it was supported at Wikipedia:Articles for deletion/Glossary of shapes with metaphorical names; so was deleting that list. The declared purpose of the list (having some place for V-shaped to redirect to) can as well be served by this article; and it may produce lesss of an indiscriminate collection of information. Septentrionalis PMAnderson 05:32, 9 February 2007 (UTC)
how can this article be both low priority, start quality, and vital: we have to put in the CD or what not, it's barely better than a stub, and it's not very important? how does that work? Saganatsu ( talk) 02:27, 20 December 2007 (UTC)
kudh yl hhiera uireh aurt n —Preceding unsigned comment added by 65.48.165.150 ( talk) 16:09, 5 October 2008 (UTC)
It might be nice to add a group picture of the more common geometric shapes. Or perhaps two images - one for 2D shapes (square, rectangle, triangle, circle, rhombus, etc) and one for 3D shapes (cube, rectangle, cone, sphere, etc). —Preceding unsigned comment added by 81.156.126.242 ( talk) 19:30, 17 August 2009 (UTC) i like lizards
I was under the impression that, in geometry, shapes are 2-dimensional but figures are 3-dimensional. This article refers to just about anything as a "shape." In fact, in the Introduction section the phrase "plane figure" is a hyperlink back to this article--thus, completely useless! Please help. MorbidAnatomy ( talk) 20:15, 20 March 2011 (UTC)
Shape has a technical meaning in geometry: similar figures have the same shape. This principle has been described using complex numbers in the article section Similarity classes. An editor removed this section, it has now been restored, and discussion is open on the merits of keeping the section. Rgdboer ( talk) 02:52, 16 December 2013 (UTC)
I removed the section, but I do believe it has some merit, and I won't remove it again.. However, it refers entirely to the work of one or two individuals. If a mathematical idea is truly important, it will be in standard textbooks or will be in frequent use. But the mathematician's name is all over this section. Why not refer to other uses of complex geometry in shapes such as the cross-ratio of hyperbolic geometry? Brirush ( talk) 02:58, 16 December 2013 (UTC)
The comment(s) below were originally left at Talk:Shape/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
This article is miserable (barely start class), and there are no signs that it will be improved in the near future. I recommend it be removed from the list of vital articles. Geometry guy 13:08, 7 May 2007 (UTC) |
Last edited at 13:08, 7 May 2007 (UTC). Substituted at 05:53, 30 April 2016 (UTC)
3-D shapes are? 69.79.12.153 ( talk) 22:35, 30 December 2022 (UTC)
View the proposal here. Writehydra ( talk) 05:00, 2 February 2024 (UTC)