Talk:Area (geometry)

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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)

Area of a Rhombus: 1/2 the product of its diagonals (don't know anything really about editing, so someone can add this.)