Talk:Area (geometry)

message: The text under the picture is senseless: the limits of the integrals must be the same!
Equal polygons have equal area.
Don't you mean "Congruent polygons have equal area."?????
It says "A point, line or plane is thus considered to have no area."  Surely plane should be omitted there, right?
:Do you mean a plane has an area of infinity? I don't think that is usually the case. -- Taku 07:17, Mar 26, 2005 (UTC)
:Well, let's be precise here.  When we say "area," we mean a finite number ascribed to certain regions of R^2.  Therefore, area is not defined on the whole plane (it diverges in some sense).  It is, however, defined on points and lines, and happens to be 0 for those figures
::Not necessarily. In measure theory, the convention is normally to allow measurable sets S with measure(S) = infinity, i.e. the measure function's target set is [0, ∞]. There are lots of different notions of "area", closely related. You can talk about the area function defined just on nice polygons, e.g., or you can talk about Lebesgue measure on R2 defined on Lebesgue measurable sets. There is no single "area" function.
It is unclear to say "in the Euclidean plane or surface" at the beginning.  We should say something like, area describes the size of figures in the Euclidean plane, and more generally, describes the size of surfaces embedded in more than two dimensions.
Somehow, some parallel should be drawn between distance, area, volume, and content in general.  The articles do not form a coherent whole -- the distance and volume articles are largely non-theoretical but have theoretical sections; area has a general section and an area (geometry) section.  Would it perhaps be possible to make some meta-article involving all of these concepts, or providing links to all of them?  Or at least to make the mathematical treatment of these articles more similar?
: It would be nice if you make yourself an account. It will be easier to talk then. Oleg Alexandrov 15:53, 28 Mar 2005 (UTC)
thread_title:  comment 

message: I was glad to see the discussion of definition of area, since (as mentioned in the article) dumbed-down books used for teaching mathematics these days like to avoid the issue altogether. I was somewhat put off by the comment about non-measurable sets, however: is axiom of choice really necessary to show that area cannot be defined for all sets? On a related theme, using Lebesgue integration for "geometric" areas seems like an overkill. Arcfrk 15:14, 19 March 2007 (UTC)
thread_title:  Definition of area 

message: Your section on how to define area is as vague as most of your other articles. Area is easy to define: It is the product of two averages. Volume is not 'analogous' to area - whoever wrote this, needs to look up the word analogous. Volume is defined as the product of three averages. It is also accurate to say that area has no extent - just like a point or line. Area only begins to take on understandable dimensions once a point or line is assigned extent. As an example: If a line is made up of 3 points of zero extent, it's length is zero. If it is made up of 3 points whose centers are half a unit from the circumference of a circle formed around the same, then the line has length of 3 units. More ridiculous articles: Fundamental theorem of Calculus, Proof that 0.999... = 1 and Infinitesimals. 98.195.24.26 (talk) 13:47, 12 December 2007 (UTC)
thread_title:  Another ridiculous article by WikiPedia 

message: The article talks entirely about area in a two-dimensional sense until the formulae, where it adds in formulae for surface area, with no definition of what surface area is. This should be rectified, probably by explaining surface area mathematically in a separate section. Argyriou (talk) 18:36, 26 September 2007 (UTC)
thread_title:  surface area